diff --git a/docs/pyerrors.html b/docs/pyerrors.html
index 0283701e..1fcaf5e8 100644
--- a/docs/pyerrors.html
+++ b/docs/pyerrors.html
@@ -3,14 +3,14 @@
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diff --git a/docs/pyerrors/correlators.html b/docs/pyerrors/correlators.html
index 543600bd..58f559ef 100644
--- a/docs/pyerrors/correlators.html
+++ b/docs/pyerrors/correlators.html
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diff --git a/docs/pyerrors/covobs.html b/docs/pyerrors/covobs.html
index 80a4ef5f..23c67442 100644
--- a/docs/pyerrors/covobs.html
+++ b/docs/pyerrors/covobs.html
@@ -3,14 +3,14 @@
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diff --git a/docs/pyerrors/dirac.html b/docs/pyerrors/dirac.html
index 450c573a..329567eb 100644
--- a/docs/pyerrors/dirac.html
+++ b/docs/pyerrors/dirac.html
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diff --git a/docs/pyerrors/fits.html b/docs/pyerrors/fits.html
index 802779dc..c93d60ca 100644
--- a/docs/pyerrors/fits.html
+++ b/docs/pyerrors/fits.html
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diff --git a/docs/pyerrors/input.html b/docs/pyerrors/input.html
index 3fd783ff..2cba7892 100644
--- a/docs/pyerrors/input.html
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diff --git a/docs/pyerrors/input/bdio.html b/docs/pyerrors/input/bdio.html
index afaebcd8..3d0afda5 100644
--- a/docs/pyerrors/input/bdio.html
+++ b/docs/pyerrors/input/bdio.html
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diff --git a/docs/pyerrors/input/dobs.html b/docs/pyerrors/input/dobs.html
index b148d5c3..f8d1d6a8 100644
--- a/docs/pyerrors/input/dobs.html
+++ b/docs/pyerrors/input/dobs.html
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diff --git a/docs/pyerrors/input/hadrons.html b/docs/pyerrors/input/hadrons.html
index fcd3dec1..b01320be 100644
--- a/docs/pyerrors/input/hadrons.html
+++ b/docs/pyerrors/input/hadrons.html
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diff --git a/docs/pyerrors/input/json.html b/docs/pyerrors/input/json.html
index b7217b7f..0c8a0ebe 100644
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+++ b/docs/pyerrors/input/json.html
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@@ -664,206 +664,201 @@
 </span><span id="L-571"><a href="#L-571"><span class="linenos">571</span></a>    <span class="n">counter</span> <span class="o">=</span> <span class="mi">0</span>
 </span><span id="L-572"><a href="#L-572"><span class="linenos">572</span></a>
 </span><span id="L-573"><a href="#L-573"><span class="linenos">573</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">dict_replace_obs</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
-</span><span id="L-574"><a href="#L-574"><span class="linenos">574</span></a>        <span class="k">nonlocal</span> <span class="n">ol</span>
-</span><span id="L-575"><a href="#L-575"><span class="linenos">575</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
-</span><span id="L-576"><a href="#L-576"><span class="linenos">576</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">{}</span>
-</span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-</span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">([</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">v</span><span class="p">]):</span>
-</span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">obslist_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
-</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">list_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">obstypes</span><span class="p">):</span>
-</span><span id="L-585"><a href="#L-585"><span class="linenos">585</span></a>                <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
-</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
-</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
-</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a>                <span class="k">if</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">v</span><span class="p">)):</span>
-</span><span id="L-590"><a href="#L-590"><span class="linenos">590</span></a>                    <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Dict contains string </span><span class="si">%s</span><span class="s1"> that matches the placeholder! </span><span class="si">%s</span><span class="s1"> Cannot be safely exported.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">reps</span><span class="p">))</span>
-</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a>            <span class="n">x</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-</span><span id="L-592"><a href="#L-592"><span class="linenos">592</span></a>        <span class="k">return</span> <span class="n">x</span>
-</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a>
-</span><span id="L-594"><a href="#L-594"><span class="linenos">594</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">list_replace_obs</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
-</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a>        <span class="k">nonlocal</span> <span class="n">ol</span>
-</span><span id="L-596"><a href="#L-596"><span class="linenos">596</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
-</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
-</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
-</span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
-</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">list_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">([</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">e</span><span class="p">]):</span>
-</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">obslist_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-605"><a href="#L-605"><span class="linenos">605</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">obstypes</span><span class="p">):</span>
-</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a>                <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
-</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
-</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
-</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a>                <span class="k">if</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">e</span><span class="p">)):</span>
-</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a>                    <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Dict contains string </span><span class="si">%s</span><span class="s1"> that matches the placeholder! </span><span class="si">%s</span><span class="s1"> Cannot be safely exported.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">reps</span><span class="p">))</span>
-</span><span id="L-612"><a href="#L-612"><span class="linenos">612</span></a>            <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a>        <span class="k">return</span> <span class="n">x</span>
-</span><span id="L-614"><a href="#L-614"><span class="linenos">614</span></a>
-</span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">obslist_replace_obs</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
-</span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a>        <span class="k">nonlocal</span> <span class="n">ol</span>
-</span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
-</span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a>        <span class="n">il</span> <span class="o">=</span> <span class="p">[]</span>
-</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
-</span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a>            <span class="n">il</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a>
-</span><span id="L-622"><a href="#L-622"><span class="linenos">622</span></a>        <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">il</span><span class="p">)</span>
-</span><span id="L-623"><a href="#L-623"><span class="linenos">623</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
-</span><span id="L-624"><a href="#L-624"><span class="linenos">624</span></a>        <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
-</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a>        <span class="k">return</span> <span class="n">x</span>
-</span><span id="L-626"><a href="#L-626"><span class="linenos">626</span></a>
-</span><span id="L-627"><a href="#L-627"><span class="linenos">627</span></a>    <span class="n">nd</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">ind</span><span class="p">)</span>
+</span><span id="L-574"><a href="#L-574"><span class="linenos">574</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
+</span><span id="L-575"><a href="#L-575"><span class="linenos">575</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">{}</span>
+</span><span id="L-576"><a href="#L-576"><span class="linenos">576</span></a>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+</span><span id="L-577"><a href="#L-577"><span class="linenos">577</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="L-578"><a href="#L-578"><span class="linenos">578</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-579"><a href="#L-579"><span class="linenos">579</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">([</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">v</span><span class="p">]):</span>
+</span><span id="L-580"><a href="#L-580"><span class="linenos">580</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">obslist_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-581"><a href="#L-581"><span class="linenos">581</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+</span><span id="L-582"><a href="#L-582"><span class="linenos">582</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">list_replace_obs</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-583"><a href="#L-583"><span class="linenos">583</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">obstypes</span><span class="p">):</span>
+</span><span id="L-584"><a href="#L-584"><span class="linenos">584</span></a>                <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-585"><a href="#L-585"><span class="linenos">585</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
+</span><span id="L-586"><a href="#L-586"><span class="linenos">586</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
+</span><span id="L-587"><a href="#L-587"><span class="linenos">587</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+</span><span id="L-588"><a href="#L-588"><span class="linenos">588</span></a>                <span class="k">if</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">v</span><span class="p">)):</span>
+</span><span id="L-589"><a href="#L-589"><span class="linenos">589</span></a>                    <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Dict contains string </span><span class="si">%s</span><span class="s1"> that matches the placeholder! </span><span class="si">%s</span><span class="s1"> Cannot be safely exported.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="n">reps</span><span class="p">))</span>
+</span><span id="L-590"><a href="#L-590"><span class="linenos">590</span></a>            <span class="n">x</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
+</span><span id="L-591"><a href="#L-591"><span class="linenos">591</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-592"><a href="#L-592"><span class="linenos">592</span></a>
+</span><span id="L-593"><a href="#L-593"><span class="linenos">593</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">list_replace_obs</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
+</span><span id="L-594"><a href="#L-594"><span class="linenos">594</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
+</span><span id="L-595"><a href="#L-595"><span class="linenos">595</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
+</span><span id="L-596"><a href="#L-596"><span class="linenos">596</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
+</span><span id="L-597"><a href="#L-597"><span class="linenos">597</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+</span><span id="L-598"><a href="#L-598"><span class="linenos">598</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">list_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-599"><a href="#L-599"><span class="linenos">599</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">all</span><span class="p">([</span><span class="nb">isinstance</span><span class="p">(</span><span class="n">o</span><span class="p">,</span> <span class="n">Obs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">e</span><span class="p">]):</span>
+</span><span id="L-600"><a href="#L-600"><span class="linenos">600</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">obslist_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-601"><a href="#L-601"><span class="linenos">601</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="L-602"><a href="#L-602"><span class="linenos">602</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-603"><a href="#L-603"><span class="linenos">603</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">obstypes</span><span class="p">):</span>
+</span><span id="L-604"><a href="#L-604"><span class="linenos">604</span></a>                <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-605"><a href="#L-605"><span class="linenos">605</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
+</span><span id="L-606"><a href="#L-606"><span class="linenos">606</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
+</span><span id="L-607"><a href="#L-607"><span class="linenos">607</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">str</span><span class="p">):</span>
+</span><span id="L-608"><a href="#L-608"><span class="linenos">608</span></a>                <span class="k">if</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">e</span><span class="p">)):</span>
+</span><span id="L-609"><a href="#L-609"><span class="linenos">609</span></a>                    <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Dict contains string </span><span class="si">%s</span><span class="s1"> that matches the placeholder! </span><span class="si">%s</span><span class="s1"> Cannot be safely exported.&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="n">reps</span><span class="p">))</span>
+</span><span id="L-610"><a href="#L-610"><span class="linenos">610</span></a>            <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-611"><a href="#L-611"><span class="linenos">611</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-612"><a href="#L-612"><span class="linenos">612</span></a>
+</span><span id="L-613"><a href="#L-613"><span class="linenos">613</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">obslist_replace_obs</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
+</span><span id="L-614"><a href="#L-614"><span class="linenos">614</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
+</span><span id="L-615"><a href="#L-615"><span class="linenos">615</span></a>        <span class="n">il</span> <span class="o">=</span> <span class="p">[]</span>
+</span><span id="L-616"><a href="#L-616"><span class="linenos">616</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
+</span><span id="L-617"><a href="#L-617"><span class="linenos">617</span></a>            <span class="n">il</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-618"><a href="#L-618"><span class="linenos">618</span></a>
+</span><span id="L-619"><a href="#L-619"><span class="linenos">619</span></a>        <span class="n">ol</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">il</span><span class="p">)</span>
+</span><span id="L-620"><a href="#L-620"><span class="linenos">620</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;</span><span class="si">%d</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">counter</span><span class="p">)</span>
+</span><span id="L-621"><a href="#L-621"><span class="linenos">621</span></a>        <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
+</span><span id="L-622"><a href="#L-622"><span class="linenos">622</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-623"><a href="#L-623"><span class="linenos">623</span></a>
+</span><span id="L-624"><a href="#L-624"><span class="linenos">624</span></a>    <span class="n">nd</span> <span class="o">=</span> <span class="n">dict_replace_obs</span><span class="p">(</span><span class="n">ind</span><span class="p">)</span>
+</span><span id="L-625"><a href="#L-625"><span class="linenos">625</span></a>
+</span><span id="L-626"><a href="#L-626"><span class="linenos">626</span></a>    <span class="k">return</span> <span class="n">ol</span><span class="p">,</span> <span class="n">nd</span>
+</span><span id="L-627"><a href="#L-627"><span class="linenos">627</span></a>
 </span><span id="L-628"><a href="#L-628"><span class="linenos">628</span></a>
-</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a>    <span class="k">return</span> <span class="n">ol</span><span class="p">,</span> <span class="n">nd</span>
-</span><span id="L-630"><a href="#L-630"><span class="linenos">630</span></a>
+</span><span id="L-629"><a href="#L-629"><span class="linenos">629</span></a><span class="k">def</span><span class="w"> </span><span class="nf">dump_dict_to_json</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+</span><span id="L-630"><a href="#L-630"><span class="linenos">630</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Export a dict of Obs or structures containing Obs to a .json(.gz) file</span>
 </span><span id="L-631"><a href="#L-631"><span class="linenos">631</span></a>
-</span><span id="L-632"><a href="#L-632"><span class="linenos">632</span></a><span class="k">def</span><span class="w"> </span><span class="nf">dump_dict_to_json</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-</span><span id="L-633"><a href="#L-633"><span class="linenos">633</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Export a dict of Obs or structures containing Obs to a .json(.gz) file</span>
-</span><span id="L-634"><a href="#L-634"><span class="linenos">634</span></a>
-</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a><span class="sd">    Parameters</span>
-</span><span id="L-636"><a href="#L-636"><span class="linenos">636</span></a><span class="sd">    ----------</span>
-</span><span id="L-637"><a href="#L-637"><span class="linenos">637</span></a><span class="sd">    od : dict</span>
-</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a><span class="sd">        Dict of JSON valid structures and objects that will be exported.</span>
-</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
-</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
-</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a><span class="sd">    fname : str</span>
-</span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a><span class="sd">        Filename of the output file.</span>
-</span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a><span class="sd">    description : str</span>
-</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a><span class="sd">        Optional string that describes the contents of the json file.</span>
-</span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a><span class="sd">    indent : int</span>
-</span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a><span class="sd">        Specify the indentation level of the json file. None or 0 is permissible and</span>
-</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a><span class="sd">        saves disk space.</span>
-</span><span id="L-648"><a href="#L-648"><span class="linenos">648</span></a><span class="sd">    reps : str</span>
-</span><span id="L-649"><a href="#L-649"><span class="linenos">649</span></a><span class="sd">        Specify the structure of the placeholder in exported dict to be reps[0-9]+.</span>
-</span><span id="L-650"><a href="#L-650"><span class="linenos">650</span></a><span class="sd">    gz : bool</span>
-</span><span id="L-651"><a href="#L-651"><span class="linenos">651</span></a><span class="sd">        If True, the output is a gzipped json. If False, the output is a json file.</span>
-</span><span id="L-652"><a href="#L-652"><span class="linenos">652</span></a>
-</span><span id="L-653"><a href="#L-653"><span class="linenos">653</span></a><span class="sd">    Returns</span>
-</span><span id="L-654"><a href="#L-654"><span class="linenos">654</span></a><span class="sd">    -------</span>
-</span><span id="L-655"><a href="#L-655"><span class="linenos">655</span></a><span class="sd">    None</span>
-</span><span id="L-656"><a href="#L-656"><span class="linenos">656</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-632"><a href="#L-632"><span class="linenos">632</span></a><span class="sd">    Parameters</span>
+</span><span id="L-633"><a href="#L-633"><span class="linenos">633</span></a><span class="sd">    ----------</span>
+</span><span id="L-634"><a href="#L-634"><span class="linenos">634</span></a><span class="sd">    od : dict</span>
+</span><span id="L-635"><a href="#L-635"><span class="linenos">635</span></a><span class="sd">        Dict of JSON valid structures and objects that will be exported.</span>
+</span><span id="L-636"><a href="#L-636"><span class="linenos">636</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
+</span><span id="L-637"><a href="#L-637"><span class="linenos">637</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
+</span><span id="L-638"><a href="#L-638"><span class="linenos">638</span></a><span class="sd">    fname : str</span>
+</span><span id="L-639"><a href="#L-639"><span class="linenos">639</span></a><span class="sd">        Filename of the output file.</span>
+</span><span id="L-640"><a href="#L-640"><span class="linenos">640</span></a><span class="sd">    description : str</span>
+</span><span id="L-641"><a href="#L-641"><span class="linenos">641</span></a><span class="sd">        Optional string that describes the contents of the json file.</span>
+</span><span id="L-642"><a href="#L-642"><span class="linenos">642</span></a><span class="sd">    indent : int</span>
+</span><span id="L-643"><a href="#L-643"><span class="linenos">643</span></a><span class="sd">        Specify the indentation level of the json file. None or 0 is permissible and</span>
+</span><span id="L-644"><a href="#L-644"><span class="linenos">644</span></a><span class="sd">        saves disk space.</span>
+</span><span id="L-645"><a href="#L-645"><span class="linenos">645</span></a><span class="sd">    reps : str</span>
+</span><span id="L-646"><a href="#L-646"><span class="linenos">646</span></a><span class="sd">        Specify the structure of the placeholder in exported dict to be reps[0-9]+.</span>
+</span><span id="L-647"><a href="#L-647"><span class="linenos">647</span></a><span class="sd">    gz : bool</span>
+</span><span id="L-648"><a href="#L-648"><span class="linenos">648</span></a><span class="sd">        If True, the output is a gzipped json. If False, the output is a json file.</span>
+</span><span id="L-649"><a href="#L-649"><span class="linenos">649</span></a>
+</span><span id="L-650"><a href="#L-650"><span class="linenos">650</span></a><span class="sd">    Returns</span>
+</span><span id="L-651"><a href="#L-651"><span class="linenos">651</span></a><span class="sd">    -------</span>
+</span><span id="L-652"><a href="#L-652"><span class="linenos">652</span></a><span class="sd">    None</span>
+</span><span id="L-653"><a href="#L-653"><span class="linenos">653</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-654"><a href="#L-654"><span class="linenos">654</span></a>
+</span><span id="L-655"><a href="#L-655"><span class="linenos">655</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="L-656"><a href="#L-656"><span class="linenos">656</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;od has to be a dictionary. Did you want to use dump_to_json?&#39;</span><span class="p">)</span>
 </span><span id="L-657"><a href="#L-657"><span class="linenos">657</span></a>
-</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;od has to be a dictionary. Did you want to use dump_to_json?&#39;</span><span class="p">)</span>
-</span><span id="L-660"><a href="#L-660"><span class="linenos">660</span></a>
-</span><span id="L-661"><a href="#L-661"><span class="linenos">661</span></a>    <span class="n">infostring</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;This JSON file contains a python dictionary that has been parsed to a list of structures. &#39;</span>
-</span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a>                  <span class="s1">&#39;OBSDICT contains the dictionary, where Obs or other structures have been replaced by &#39;</span>
-</span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a>                  <span class="s1">&#39;&#39;</span> <span class="o">+</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;[0-9]+. The field description contains the additional description of this JSON file. &#39;</span>
-</span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>                  <span class="s1">&#39;This file may be parsed to a dict with the pyerrors routine load_json_dict.&#39;</span><span class="p">)</span>
+</span><span id="L-658"><a href="#L-658"><span class="linenos">658</span></a>    <span class="n">infostring</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;This JSON file contains a python dictionary that has been parsed to a list of structures. &#39;</span>
+</span><span id="L-659"><a href="#L-659"><span class="linenos">659</span></a>                  <span class="s1">&#39;OBSDICT contains the dictionary, where Obs or other structures have been replaced by &#39;</span>
+</span><span id="L-660"><a href="#L-660"><span class="linenos">660</span></a>                  <span class="s1">&#39;&#39;</span> <span class="o">+</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;[0-9]+. The field description contains the additional description of this JSON file. &#39;</span>
+</span><span id="L-661"><a href="#L-661"><span class="linenos">661</span></a>                  <span class="s1">&#39;This file may be parsed to a dict with the pyerrors routine load_json_dict.&#39;</span><span class="p">)</span>
+</span><span id="L-662"><a href="#L-662"><span class="linenos">662</span></a>
+</span><span id="L-663"><a href="#L-663"><span class="linenos">663</span></a>    <span class="n">desc_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;INFO&#39;</span><span class="p">:</span> <span class="n">infostring</span><span class="p">,</span> <span class="s1">&#39;OBSDICT&#39;</span><span class="p">:</span> <span class="p">{},</span> <span class="s1">&#39;description&#39;</span><span class="p">:</span> <span class="n">description</span><span class="p">}</span>
+</span><span id="L-664"><a href="#L-664"><span class="linenos">664</span></a>    <span class="n">ol</span><span class="p">,</span> <span class="n">desc_dict</span><span class="p">[</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">_ol_from_dict</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
 </span><span id="L-665"><a href="#L-665"><span class="linenos">665</span></a>
-</span><span id="L-666"><a href="#L-666"><span class="linenos">666</span></a>    <span class="n">desc_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;INFO&#39;</span><span class="p">:</span> <span class="n">infostring</span><span class="p">,</span> <span class="s1">&#39;OBSDICT&#39;</span><span class="p">:</span> <span class="p">{},</span> <span class="s1">&#39;description&#39;</span><span class="p">:</span> <span class="n">description</span><span class="p">}</span>
-</span><span id="L-667"><a href="#L-667"><span class="linenos">667</span></a>    <span class="n">ol</span><span class="p">,</span> <span class="n">desc_dict</span><span class="p">[</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">_ol_from_dict</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
+</span><span id="L-666"><a href="#L-666"><span class="linenos">666</span></a>    <span class="n">dump_to_json</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="n">desc_dict</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="n">indent</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">)</span>
+</span><span id="L-667"><a href="#L-667"><span class="linenos">667</span></a>
 </span><span id="L-668"><a href="#L-668"><span class="linenos">668</span></a>
-</span><span id="L-669"><a href="#L-669"><span class="linenos">669</span></a>    <span class="n">dump_to_json</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="n">desc_dict</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="n">indent</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">)</span>
-</span><span id="L-670"><a href="#L-670"><span class="linenos">670</span></a>
-</span><span id="L-671"><a href="#L-671"><span class="linenos">671</span></a>
-</span><span id="L-672"><a href="#L-672"><span class="linenos">672</span></a><span class="k">def</span><span class="w"> </span><span class="nf">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">ind</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
-</span><span id="L-673"><a href="#L-673"><span class="linenos">673</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Parse a list of Obs or structures containing Obs and an accompanying</span>
-</span><span id="L-674"><a href="#L-674"><span class="linenos">674</span></a><span class="sd">    dict, where the structures have been replaced by placeholders to a</span>
-</span><span id="L-675"><a href="#L-675"><span class="linenos">675</span></a><span class="sd">    dict that contains the structures.</span>
-</span><span id="L-676"><a href="#L-676"><span class="linenos">676</span></a>
-</span><span id="L-677"><a href="#L-677"><span class="linenos">677</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
-</span><span id="L-678"><a href="#L-678"><span class="linenos">678</span></a>
-</span><span id="L-679"><a href="#L-679"><span class="linenos">679</span></a><span class="sd">    Parameters</span>
-</span><span id="L-680"><a href="#L-680"><span class="linenos">680</span></a><span class="sd">    ----------</span>
-</span><span id="L-681"><a href="#L-681"><span class="linenos">681</span></a><span class="sd">    ol : list</span>
-</span><span id="L-682"><a href="#L-682"><span class="linenos">682</span></a><span class="sd">        List of objects -</span>
-</span><span id="L-683"><a href="#L-683"><span class="linenos">683</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
-</span><span id="L-684"><a href="#L-684"><span class="linenos">684</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
-</span><span id="L-685"><a href="#L-685"><span class="linenos">685</span></a><span class="sd">    ind : dict</span>
-</span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a><span class="sd">        Dict that defines the structure of the resulting dict and contains placeholders</span>
-</span><span id="L-687"><a href="#L-687"><span class="linenos">687</span></a><span class="sd">    reps : str</span>
-</span><span id="L-688"><a href="#L-688"><span class="linenos">688</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
-</span><span id="L-689"><a href="#L-689"><span class="linenos">689</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-690"><a href="#L-690"><span class="linenos">690</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="n">reps</span><span class="o">.</span><span class="n">isalnum</span><span class="p">():</span>
-</span><span id="L-691"><a href="#L-691"><span class="linenos">691</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Placeholder string has to be alphanumeric!&#39;</span><span class="p">)</span>
-</span><span id="L-692"><a href="#L-692"><span class="linenos">692</span></a>
-</span><span id="L-693"><a href="#L-693"><span class="linenos">693</span></a>    <span class="n">counter</span> <span class="o">=</span> <span class="mi">0</span>
-</span><span id="L-694"><a href="#L-694"><span class="linenos">694</span></a>
-</span><span id="L-695"><a href="#L-695"><span class="linenos">695</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">dict_replace_string</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
-</span><span id="L-696"><a href="#L-696"><span class="linenos">696</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
-</span><span id="L-697"><a href="#L-697"><span class="linenos">697</span></a>        <span class="k">nonlocal</span> <span class="n">ol</span>
-</span><span id="L-698"><a href="#L-698"><span class="linenos">698</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">{}</span>
-</span><span id="L-699"><a href="#L-699"><span class="linenos">699</span></a>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
-</span><span id="L-700"><a href="#L-700"><span class="linenos">700</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="L-701"><a href="#L-701"><span class="linenos">701</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-702"><a href="#L-702"><span class="linenos">702</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
-</span><span id="L-703"><a href="#L-703"><span class="linenos">703</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">list_replace_string</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
-</span><span id="L-704"><a href="#L-704"><span class="linenos">704</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">v</span><span class="p">)):</span>
-</span><span id="L-705"><a href="#L-705"><span class="linenos">705</span></a>                <span class="n">index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">reps</span><span class="p">):])</span>
-</span><span id="L-706"><a href="#L-706"><span class="linenos">706</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">ol</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-</span><span id="L-707"><a href="#L-707"><span class="linenos">707</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
-</span><span id="L-708"><a href="#L-708"><span class="linenos">708</span></a>            <span class="n">x</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
-</span><span id="L-709"><a href="#L-709"><span class="linenos">709</span></a>        <span class="k">return</span> <span class="n">x</span>
-</span><span id="L-710"><a href="#L-710"><span class="linenos">710</span></a>
-</span><span id="L-711"><a href="#L-711"><span class="linenos">711</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">list_replace_string</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
-</span><span id="L-712"><a href="#L-712"><span class="linenos">712</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
-</span><span id="L-713"><a href="#L-713"><span class="linenos">713</span></a>        <span class="k">nonlocal</span> <span class="n">ol</span>
-</span><span id="L-714"><a href="#L-714"><span class="linenos">714</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
-</span><span id="L-715"><a href="#L-715"><span class="linenos">715</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
-</span><span id="L-716"><a href="#L-716"><span class="linenos">716</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
-</span><span id="L-717"><a href="#L-717"><span class="linenos">717</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">list_replace_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-718"><a href="#L-718"><span class="linenos">718</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="L-719"><a href="#L-719"><span class="linenos">719</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-720"><a href="#L-720"><span class="linenos">720</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">e</span><span class="p">)):</span>
-</span><span id="L-721"><a href="#L-721"><span class="linenos">721</span></a>                <span class="n">index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">reps</span><span class="p">):])</span>
-</span><span id="L-722"><a href="#L-722"><span class="linenos">722</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">ol</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
-</span><span id="L-723"><a href="#L-723"><span class="linenos">723</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
-</span><span id="L-724"><a href="#L-724"><span class="linenos">724</span></a>            <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
-</span><span id="L-725"><a href="#L-725"><span class="linenos">725</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-669"><a href="#L-669"><span class="linenos">669</span></a><span class="k">def</span><span class="w"> </span><span class="nf">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">ind</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
+</span><span id="L-670"><a href="#L-670"><span class="linenos">670</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Parse a list of Obs or structures containing Obs and an accompanying</span>
+</span><span id="L-671"><a href="#L-671"><span class="linenos">671</span></a><span class="sd">    dict, where the structures have been replaced by placeholders to a</span>
+</span><span id="L-672"><a href="#L-672"><span class="linenos">672</span></a><span class="sd">    dict that contains the structures.</span>
+</span><span id="L-673"><a href="#L-673"><span class="linenos">673</span></a>
+</span><span id="L-674"><a href="#L-674"><span class="linenos">674</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
+</span><span id="L-675"><a href="#L-675"><span class="linenos">675</span></a>
+</span><span id="L-676"><a href="#L-676"><span class="linenos">676</span></a><span class="sd">    Parameters</span>
+</span><span id="L-677"><a href="#L-677"><span class="linenos">677</span></a><span class="sd">    ----------</span>
+</span><span id="L-678"><a href="#L-678"><span class="linenos">678</span></a><span class="sd">    ol : list</span>
+</span><span id="L-679"><a href="#L-679"><span class="linenos">679</span></a><span class="sd">        List of objects -</span>
+</span><span id="L-680"><a href="#L-680"><span class="linenos">680</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
+</span><span id="L-681"><a href="#L-681"><span class="linenos">681</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
+</span><span id="L-682"><a href="#L-682"><span class="linenos">682</span></a><span class="sd">    ind : dict</span>
+</span><span id="L-683"><a href="#L-683"><span class="linenos">683</span></a><span class="sd">        Dict that defines the structure of the resulting dict and contains placeholders</span>
+</span><span id="L-684"><a href="#L-684"><span class="linenos">684</span></a><span class="sd">    reps : str</span>
+</span><span id="L-685"><a href="#L-685"><span class="linenos">685</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
+</span><span id="L-686"><a href="#L-686"><span class="linenos">686</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-687"><a href="#L-687"><span class="linenos">687</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="n">reps</span><span class="o">.</span><span class="n">isalnum</span><span class="p">():</span>
+</span><span id="L-688"><a href="#L-688"><span class="linenos">688</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Placeholder string has to be alphanumeric!&#39;</span><span class="p">)</span>
+</span><span id="L-689"><a href="#L-689"><span class="linenos">689</span></a>
+</span><span id="L-690"><a href="#L-690"><span class="linenos">690</span></a>    <span class="n">counter</span> <span class="o">=</span> <span class="mi">0</span>
+</span><span id="L-691"><a href="#L-691"><span class="linenos">691</span></a>
+</span><span id="L-692"><a href="#L-692"><span class="linenos">692</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">dict_replace_string</span><span class="p">(</span><span class="n">d</span><span class="p">):</span>
+</span><span id="L-693"><a href="#L-693"><span class="linenos">693</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
+</span><span id="L-694"><a href="#L-694"><span class="linenos">694</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">{}</span>
+</span><span id="L-695"><a href="#L-695"><span class="linenos">695</span></a>        <span class="k">for</span> <span class="n">k</span><span class="p">,</span> <span class="n">v</span> <span class="ow">in</span> <span class="n">d</span><span class="o">.</span><span class="n">items</span><span class="p">():</span>
+</span><span id="L-696"><a href="#L-696"><span class="linenos">696</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="L-697"><a href="#L-697"><span class="linenos">697</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-698"><a href="#L-698"><span class="linenos">698</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+</span><span id="L-699"><a href="#L-699"><span class="linenos">699</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">list_replace_string</span><span class="p">(</span><span class="n">v</span><span class="p">)</span>
+</span><span id="L-700"><a href="#L-700"><span class="linenos">700</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">v</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">v</span><span class="p">)):</span>
+</span><span id="L-701"><a href="#L-701"><span class="linenos">701</span></a>                <span class="n">index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">v</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">reps</span><span class="p">):])</span>
+</span><span id="L-702"><a href="#L-702"><span class="linenos">702</span></a>                <span class="n">v</span> <span class="o">=</span> <span class="n">ol</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+</span><span id="L-703"><a href="#L-703"><span class="linenos">703</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
+</span><span id="L-704"><a href="#L-704"><span class="linenos">704</span></a>            <span class="n">x</span><span class="p">[</span><span class="n">k</span><span class="p">]</span> <span class="o">=</span> <span class="n">v</span>
+</span><span id="L-705"><a href="#L-705"><span class="linenos">705</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-706"><a href="#L-706"><span class="linenos">706</span></a>
+</span><span id="L-707"><a href="#L-707"><span class="linenos">707</span></a>    <span class="k">def</span><span class="w"> </span><span class="nf">list_replace_string</span><span class="p">(</span><span class="n">li</span><span class="p">):</span>
+</span><span id="L-708"><a href="#L-708"><span class="linenos">708</span></a>        <span class="k">nonlocal</span> <span class="n">counter</span>
+</span><span id="L-709"><a href="#L-709"><span class="linenos">709</span></a>        <span class="n">x</span> <span class="o">=</span> <span class="p">[]</span>
+</span><span id="L-710"><a href="#L-710"><span class="linenos">710</span></a>        <span class="k">for</span> <span class="n">e</span> <span class="ow">in</span> <span class="n">li</span><span class="p">:</span>
+</span><span id="L-711"><a href="#L-711"><span class="linenos">711</span></a>            <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">list</span><span class="p">):</span>
+</span><span id="L-712"><a href="#L-712"><span class="linenos">712</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">list_replace_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-713"><a href="#L-713"><span class="linenos">713</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="L-714"><a href="#L-714"><span class="linenos">714</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-715"><a href="#L-715"><span class="linenos">715</span></a>            <span class="k">elif</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">e</span><span class="p">,</span> <span class="nb">str</span><span class="p">)</span> <span class="ow">and</span> <span class="nb">bool</span><span class="p">(</span><span class="n">re</span><span class="o">.</span><span class="n">match</span><span class="p">(</span><span class="sa">r</span><span class="s1">&#39;</span><span class="si">%s</span><span class="s1">[0-9]+&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">reps</span><span class="p">),</span> <span class="n">e</span><span class="p">)):</span>
+</span><span id="L-716"><a href="#L-716"><span class="linenos">716</span></a>                <span class="n">index</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">e</span><span class="p">[</span><span class="nb">len</span><span class="p">(</span><span class="n">reps</span><span class="p">):])</span>
+</span><span id="L-717"><a href="#L-717"><span class="linenos">717</span></a>                <span class="n">e</span> <span class="o">=</span> <span class="n">ol</span><span class="p">[</span><span class="n">index</span><span class="p">]</span>
+</span><span id="L-718"><a href="#L-718"><span class="linenos">718</span></a>                <span class="n">counter</span> <span class="o">+=</span> <span class="mi">1</span>
+</span><span id="L-719"><a href="#L-719"><span class="linenos">719</span></a>            <span class="n">x</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">e</span><span class="p">)</span>
+</span><span id="L-720"><a href="#L-720"><span class="linenos">720</span></a>        <span class="k">return</span> <span class="n">x</span>
+</span><span id="L-721"><a href="#L-721"><span class="linenos">721</span></a>
+</span><span id="L-722"><a href="#L-722"><span class="linenos">722</span></a>    <span class="n">nd</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">ind</span><span class="p">)</span>
+</span><span id="L-723"><a href="#L-723"><span class="linenos">723</span></a>
+</span><span id="L-724"><a href="#L-724"><span class="linenos">724</span></a>    <span class="k">if</span> <span class="n">counter</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
+</span><span id="L-725"><a href="#L-725"><span class="linenos">725</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;No placeholder has been replaced! Check if reps is set correctly.&#39;</span><span class="p">)</span>
 </span><span id="L-726"><a href="#L-726"><span class="linenos">726</span></a>
-</span><span id="L-727"><a href="#L-727"><span class="linenos">727</span></a>    <span class="n">nd</span> <span class="o">=</span> <span class="n">dict_replace_string</span><span class="p">(</span><span class="n">ind</span><span class="p">)</span>
+</span><span id="L-727"><a href="#L-727"><span class="linenos">727</span></a>    <span class="k">return</span> <span class="n">nd</span>
 </span><span id="L-728"><a href="#L-728"><span class="linenos">728</span></a>
-</span><span id="L-729"><a href="#L-729"><span class="linenos">729</span></a>    <span class="k">if</span> <span class="n">counter</span> <span class="o">==</span> <span class="mi">0</span><span class="p">:</span>
-</span><span id="L-730"><a href="#L-730"><span class="linenos">730</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;No placeholder has been replaced! Check if reps is set correctly.&#39;</span><span class="p">)</span>
-</span><span id="L-731"><a href="#L-731"><span class="linenos">731</span></a>
-</span><span id="L-732"><a href="#L-732"><span class="linenos">732</span></a>    <span class="k">return</span> <span class="n">nd</span>
-</span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a>
+</span><span id="L-729"><a href="#L-729"><span class="linenos">729</span></a>
+</span><span id="L-730"><a href="#L-730"><span class="linenos">730</span></a><span class="k">def</span><span class="w"> </span><span class="nf">load_json_dict</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
+</span><span id="L-731"><a href="#L-731"><span class="linenos">731</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Import a dict of Obs or structures containing Obs from a .json(.gz) file.</span>
+</span><span id="L-732"><a href="#L-732"><span class="linenos">732</span></a>
+</span><span id="L-733"><a href="#L-733"><span class="linenos">733</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
 </span><span id="L-734"><a href="#L-734"><span class="linenos">734</span></a>
-</span><span id="L-735"><a href="#L-735"><span class="linenos">735</span></a><span class="k">def</span><span class="w"> </span><span class="nf">load_json_dict</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
-</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Import a dict of Obs or structures containing Obs from a .json(.gz) file.</span>
-</span><span id="L-737"><a href="#L-737"><span class="linenos">737</span></a>
-</span><span id="L-738"><a href="#L-738"><span class="linenos">738</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
-</span><span id="L-739"><a href="#L-739"><span class="linenos">739</span></a>
-</span><span id="L-740"><a href="#L-740"><span class="linenos">740</span></a><span class="sd">    Parameters</span>
-</span><span id="L-741"><a href="#L-741"><span class="linenos">741</span></a><span class="sd">    ----------</span>
-</span><span id="L-742"><a href="#L-742"><span class="linenos">742</span></a><span class="sd">    fname : str</span>
-</span><span id="L-743"><a href="#L-743"><span class="linenos">743</span></a><span class="sd">        Filename of the input file.</span>
-</span><span id="L-744"><a href="#L-744"><span class="linenos">744</span></a><span class="sd">    verbose : bool</span>
-</span><span id="L-745"><a href="#L-745"><span class="linenos">745</span></a><span class="sd">        Print additional information that was written to the file.</span>
-</span><span id="L-746"><a href="#L-746"><span class="linenos">746</span></a><span class="sd">    gz : bool</span>
-</span><span id="L-747"><a href="#L-747"><span class="linenos">747</span></a><span class="sd">        If True, assumes that data is gzipped. If False, assumes JSON file.</span>
-</span><span id="L-748"><a href="#L-748"><span class="linenos">748</span></a><span class="sd">    full_output : bool</span>
-</span><span id="L-749"><a href="#L-749"><span class="linenos">749</span></a><span class="sd">        If True, a dict containing auxiliary information and the data is returned.</span>
-</span><span id="L-750"><a href="#L-750"><span class="linenos">750</span></a><span class="sd">        If False, only the data is returned.</span>
-</span><span id="L-751"><a href="#L-751"><span class="linenos">751</span></a><span class="sd">    reps : str</span>
-</span><span id="L-752"><a href="#L-752"><span class="linenos">752</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
-</span><span id="L-753"><a href="#L-753"><span class="linenos">753</span></a>
-</span><span id="L-754"><a href="#L-754"><span class="linenos">754</span></a><span class="sd">    Returns</span>
-</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a><span class="sd">    -------</span>
-</span><span id="L-756"><a href="#L-756"><span class="linenos">756</span></a><span class="sd">    data : Obs / list / Corr</span>
-</span><span id="L-757"><a href="#L-757"><span class="linenos">757</span></a><span class="sd">        Read data</span>
-</span><span id="L-758"><a href="#L-758"><span class="linenos">758</span></a><span class="sd">    or</span>
-</span><span id="L-759"><a href="#L-759"><span class="linenos">759</span></a><span class="sd">    data : dict</span>
-</span><span id="L-760"><a href="#L-760"><span class="linenos">760</span></a><span class="sd">        Read data and meta-data</span>
-</span><span id="L-761"><a href="#L-761"><span class="linenos">761</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="L-762"><a href="#L-762"><span class="linenos">762</span></a>    <span class="n">indata</span> <span class="o">=</span> <span class="n">load_json</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="n">verbose</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-</span><span id="L-763"><a href="#L-763"><span class="linenos">763</span></a>    <span class="n">description</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;description&#39;</span><span class="p">]</span>
-</span><span id="L-764"><a href="#L-764"><span class="linenos">764</span></a>    <span class="n">indict</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span>
-</span><span id="L-765"><a href="#L-765"><span class="linenos">765</span></a>    <span class="n">ol</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span>
-</span><span id="L-766"><a href="#L-766"><span class="linenos">766</span></a>    <span class="n">od</span> <span class="o">=</span> <span class="n">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">indict</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
-</span><span id="L-767"><a href="#L-767"><span class="linenos">767</span></a>
-</span><span id="L-768"><a href="#L-768"><span class="linenos">768</span></a>    <span class="k">if</span> <span class="n">full_output</span><span class="p">:</span>
-</span><span id="L-769"><a href="#L-769"><span class="linenos">769</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">description</span>
-</span><span id="L-770"><a href="#L-770"><span class="linenos">770</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">od</span>
-</span><span id="L-771"><a href="#L-771"><span class="linenos">771</span></a>        <span class="k">return</span> <span class="n">indata</span>
-</span><span id="L-772"><a href="#L-772"><span class="linenos">772</span></a>    <span class="k">else</span><span class="p">:</span>
-</span><span id="L-773"><a href="#L-773"><span class="linenos">773</span></a>        <span class="k">return</span> <span class="n">od</span>
+</span><span id="L-735"><a href="#L-735"><span class="linenos">735</span></a><span class="sd">    Parameters</span>
+</span><span id="L-736"><a href="#L-736"><span class="linenos">736</span></a><span class="sd">    ----------</span>
+</span><span id="L-737"><a href="#L-737"><span class="linenos">737</span></a><span class="sd">    fname : str</span>
+</span><span id="L-738"><a href="#L-738"><span class="linenos">738</span></a><span class="sd">        Filename of the input file.</span>
+</span><span id="L-739"><a href="#L-739"><span class="linenos">739</span></a><span class="sd">    verbose : bool</span>
+</span><span id="L-740"><a href="#L-740"><span class="linenos">740</span></a><span class="sd">        Print additional information that was written to the file.</span>
+</span><span id="L-741"><a href="#L-741"><span class="linenos">741</span></a><span class="sd">    gz : bool</span>
+</span><span id="L-742"><a href="#L-742"><span class="linenos">742</span></a><span class="sd">        If True, assumes that data is gzipped. If False, assumes JSON file.</span>
+</span><span id="L-743"><a href="#L-743"><span class="linenos">743</span></a><span class="sd">    full_output : bool</span>
+</span><span id="L-744"><a href="#L-744"><span class="linenos">744</span></a><span class="sd">        If True, a dict containing auxiliary information and the data is returned.</span>
+</span><span id="L-745"><a href="#L-745"><span class="linenos">745</span></a><span class="sd">        If False, only the data is returned.</span>
+</span><span id="L-746"><a href="#L-746"><span class="linenos">746</span></a><span class="sd">    reps : str</span>
+</span><span id="L-747"><a href="#L-747"><span class="linenos">747</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
+</span><span id="L-748"><a href="#L-748"><span class="linenos">748</span></a>
+</span><span id="L-749"><a href="#L-749"><span class="linenos">749</span></a><span class="sd">    Returns</span>
+</span><span id="L-750"><a href="#L-750"><span class="linenos">750</span></a><span class="sd">    -------</span>
+</span><span id="L-751"><a href="#L-751"><span class="linenos">751</span></a><span class="sd">    data : Obs / list / Corr</span>
+</span><span id="L-752"><a href="#L-752"><span class="linenos">752</span></a><span class="sd">        Read data</span>
+</span><span id="L-753"><a href="#L-753"><span class="linenos">753</span></a><span class="sd">    or</span>
+</span><span id="L-754"><a href="#L-754"><span class="linenos">754</span></a><span class="sd">    data : dict</span>
+</span><span id="L-755"><a href="#L-755"><span class="linenos">755</span></a><span class="sd">        Read data and meta-data</span>
+</span><span id="L-756"><a href="#L-756"><span class="linenos">756</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="L-757"><a href="#L-757"><span class="linenos">757</span></a>    <span class="n">indata</span> <span class="o">=</span> <span class="n">load_json</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="n">verbose</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+</span><span id="L-758"><a href="#L-758"><span class="linenos">758</span></a>    <span class="n">description</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;description&#39;</span><span class="p">]</span>
+</span><span id="L-759"><a href="#L-759"><span class="linenos">759</span></a>    <span class="n">indict</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span>
+</span><span id="L-760"><a href="#L-760"><span class="linenos">760</span></a>    <span class="n">ol</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span>
+</span><span id="L-761"><a href="#L-761"><span class="linenos">761</span></a>    <span class="n">od</span> <span class="o">=</span> <span class="n">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">indict</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
+</span><span id="L-762"><a href="#L-762"><span class="linenos">762</span></a>
+</span><span id="L-763"><a href="#L-763"><span class="linenos">763</span></a>    <span class="k">if</span> <span class="n">full_output</span><span class="p">:</span>
+</span><span id="L-764"><a href="#L-764"><span class="linenos">764</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">description</span>
+</span><span id="L-765"><a href="#L-765"><span class="linenos">765</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">od</span>
+</span><span id="L-766"><a href="#L-766"><span class="linenos">766</span></a>        <span class="k">return</span> <span class="n">indata</span>
+</span><span id="L-767"><a href="#L-767"><span class="linenos">767</span></a>    <span class="k">else</span><span class="p">:</span>
+</span><span id="L-768"><a href="#L-768"><span class="linenos">768</span></a>        <span class="k">return</span> <span class="n">od</span>
 </span></pre></div>
 
 
@@ -1372,44 +1367,44 @@ if full_output=True</li>
 
     </div>
     <a class="headerlink" href="#dump_dict_to_json"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="dump_dict_to_json-633"><a href="#dump_dict_to_json-633"><span class="linenos">633</span></a><span class="k">def</span><span class="w"> </span><span class="nf">dump_dict_to_json</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
-</span><span id="dump_dict_to_json-634"><a href="#dump_dict_to_json-634"><span class="linenos">634</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Export a dict of Obs or structures containing Obs to a .json(.gz) file</span>
-</span><span id="dump_dict_to_json-635"><a href="#dump_dict_to_json-635"><span class="linenos">635</span></a>
-</span><span id="dump_dict_to_json-636"><a href="#dump_dict_to_json-636"><span class="linenos">636</span></a><span class="sd">    Parameters</span>
-</span><span id="dump_dict_to_json-637"><a href="#dump_dict_to_json-637"><span class="linenos">637</span></a><span class="sd">    ----------</span>
-</span><span id="dump_dict_to_json-638"><a href="#dump_dict_to_json-638"><span class="linenos">638</span></a><span class="sd">    od : dict</span>
-</span><span id="dump_dict_to_json-639"><a href="#dump_dict_to_json-639"><span class="linenos">639</span></a><span class="sd">        Dict of JSON valid structures and objects that will be exported.</span>
-</span><span id="dump_dict_to_json-640"><a href="#dump_dict_to_json-640"><span class="linenos">640</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
-</span><span id="dump_dict_to_json-641"><a href="#dump_dict_to_json-641"><span class="linenos">641</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
-</span><span id="dump_dict_to_json-642"><a href="#dump_dict_to_json-642"><span class="linenos">642</span></a><span class="sd">    fname : str</span>
-</span><span id="dump_dict_to_json-643"><a href="#dump_dict_to_json-643"><span class="linenos">643</span></a><span class="sd">        Filename of the output file.</span>
-</span><span id="dump_dict_to_json-644"><a href="#dump_dict_to_json-644"><span class="linenos">644</span></a><span class="sd">    description : str</span>
-</span><span id="dump_dict_to_json-645"><a href="#dump_dict_to_json-645"><span class="linenos">645</span></a><span class="sd">        Optional string that describes the contents of the json file.</span>
-</span><span id="dump_dict_to_json-646"><a href="#dump_dict_to_json-646"><span class="linenos">646</span></a><span class="sd">    indent : int</span>
-</span><span id="dump_dict_to_json-647"><a href="#dump_dict_to_json-647"><span class="linenos">647</span></a><span class="sd">        Specify the indentation level of the json file. None or 0 is permissible and</span>
-</span><span id="dump_dict_to_json-648"><a href="#dump_dict_to_json-648"><span class="linenos">648</span></a><span class="sd">        saves disk space.</span>
-</span><span id="dump_dict_to_json-649"><a href="#dump_dict_to_json-649"><span class="linenos">649</span></a><span class="sd">    reps : str</span>
-</span><span id="dump_dict_to_json-650"><a href="#dump_dict_to_json-650"><span class="linenos">650</span></a><span class="sd">        Specify the structure of the placeholder in exported dict to be reps[0-9]+.</span>
-</span><span id="dump_dict_to_json-651"><a href="#dump_dict_to_json-651"><span class="linenos">651</span></a><span class="sd">    gz : bool</span>
-</span><span id="dump_dict_to_json-652"><a href="#dump_dict_to_json-652"><span class="linenos">652</span></a><span class="sd">        If True, the output is a gzipped json. If False, the output is a json file.</span>
-</span><span id="dump_dict_to_json-653"><a href="#dump_dict_to_json-653"><span class="linenos">653</span></a>
-</span><span id="dump_dict_to_json-654"><a href="#dump_dict_to_json-654"><span class="linenos">654</span></a><span class="sd">    Returns</span>
-</span><span id="dump_dict_to_json-655"><a href="#dump_dict_to_json-655"><span class="linenos">655</span></a><span class="sd">    -------</span>
-</span><span id="dump_dict_to_json-656"><a href="#dump_dict_to_json-656"><span class="linenos">656</span></a><span class="sd">    None</span>
-</span><span id="dump_dict_to_json-657"><a href="#dump_dict_to_json-657"><span class="linenos">657</span></a><span class="sd">    &quot;&quot;&quot;</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="dump_dict_to_json-630"><a href="#dump_dict_to_json-630"><span class="linenos">630</span></a><span class="k">def</span><span class="w"> </span><span class="nf">dump_dict_to_json</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="s1">&#39;&#39;</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="mi">1</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">):</span>
+</span><span id="dump_dict_to_json-631"><a href="#dump_dict_to_json-631"><span class="linenos">631</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Export a dict of Obs or structures containing Obs to a .json(.gz) file</span>
+</span><span id="dump_dict_to_json-632"><a href="#dump_dict_to_json-632"><span class="linenos">632</span></a>
+</span><span id="dump_dict_to_json-633"><a href="#dump_dict_to_json-633"><span class="linenos">633</span></a><span class="sd">    Parameters</span>
+</span><span id="dump_dict_to_json-634"><a href="#dump_dict_to_json-634"><span class="linenos">634</span></a><span class="sd">    ----------</span>
+</span><span id="dump_dict_to_json-635"><a href="#dump_dict_to_json-635"><span class="linenos">635</span></a><span class="sd">    od : dict</span>
+</span><span id="dump_dict_to_json-636"><a href="#dump_dict_to_json-636"><span class="linenos">636</span></a><span class="sd">        Dict of JSON valid structures and objects that will be exported.</span>
+</span><span id="dump_dict_to_json-637"><a href="#dump_dict_to_json-637"><span class="linenos">637</span></a><span class="sd">        At the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.</span>
+</span><span id="dump_dict_to_json-638"><a href="#dump_dict_to_json-638"><span class="linenos">638</span></a><span class="sd">        All Obs inside a structure have to be defined on the same set of configurations.</span>
+</span><span id="dump_dict_to_json-639"><a href="#dump_dict_to_json-639"><span class="linenos">639</span></a><span class="sd">    fname : str</span>
+</span><span id="dump_dict_to_json-640"><a href="#dump_dict_to_json-640"><span class="linenos">640</span></a><span class="sd">        Filename of the output file.</span>
+</span><span id="dump_dict_to_json-641"><a href="#dump_dict_to_json-641"><span class="linenos">641</span></a><span class="sd">    description : str</span>
+</span><span id="dump_dict_to_json-642"><a href="#dump_dict_to_json-642"><span class="linenos">642</span></a><span class="sd">        Optional string that describes the contents of the json file.</span>
+</span><span id="dump_dict_to_json-643"><a href="#dump_dict_to_json-643"><span class="linenos">643</span></a><span class="sd">    indent : int</span>
+</span><span id="dump_dict_to_json-644"><a href="#dump_dict_to_json-644"><span class="linenos">644</span></a><span class="sd">        Specify the indentation level of the json file. None or 0 is permissible and</span>
+</span><span id="dump_dict_to_json-645"><a href="#dump_dict_to_json-645"><span class="linenos">645</span></a><span class="sd">        saves disk space.</span>
+</span><span id="dump_dict_to_json-646"><a href="#dump_dict_to_json-646"><span class="linenos">646</span></a><span class="sd">    reps : str</span>
+</span><span id="dump_dict_to_json-647"><a href="#dump_dict_to_json-647"><span class="linenos">647</span></a><span class="sd">        Specify the structure of the placeholder in exported dict to be reps[0-9]+.</span>
+</span><span id="dump_dict_to_json-648"><a href="#dump_dict_to_json-648"><span class="linenos">648</span></a><span class="sd">    gz : bool</span>
+</span><span id="dump_dict_to_json-649"><a href="#dump_dict_to_json-649"><span class="linenos">649</span></a><span class="sd">        If True, the output is a gzipped json. If False, the output is a json file.</span>
+</span><span id="dump_dict_to_json-650"><a href="#dump_dict_to_json-650"><span class="linenos">650</span></a>
+</span><span id="dump_dict_to_json-651"><a href="#dump_dict_to_json-651"><span class="linenos">651</span></a><span class="sd">    Returns</span>
+</span><span id="dump_dict_to_json-652"><a href="#dump_dict_to_json-652"><span class="linenos">652</span></a><span class="sd">    -------</span>
+</span><span id="dump_dict_to_json-653"><a href="#dump_dict_to_json-653"><span class="linenos">653</span></a><span class="sd">    None</span>
+</span><span id="dump_dict_to_json-654"><a href="#dump_dict_to_json-654"><span class="linenos">654</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="dump_dict_to_json-655"><a href="#dump_dict_to_json-655"><span class="linenos">655</span></a>
+</span><span id="dump_dict_to_json-656"><a href="#dump_dict_to_json-656"><span class="linenos">656</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
+</span><span id="dump_dict_to_json-657"><a href="#dump_dict_to_json-657"><span class="linenos">657</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;od has to be a dictionary. Did you want to use dump_to_json?&#39;</span><span class="p">)</span>
 </span><span id="dump_dict_to_json-658"><a href="#dump_dict_to_json-658"><span class="linenos">658</span></a>
-</span><span id="dump_dict_to_json-659"><a href="#dump_dict_to_json-659"><span class="linenos">659</span></a>    <span class="k">if</span> <span class="ow">not</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="nb">dict</span><span class="p">):</span>
-</span><span id="dump_dict_to_json-660"><a href="#dump_dict_to_json-660"><span class="linenos">660</span></a>        <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;od has to be a dictionary. Did you want to use dump_to_json?&#39;</span><span class="p">)</span>
-</span><span id="dump_dict_to_json-661"><a href="#dump_dict_to_json-661"><span class="linenos">661</span></a>
-</span><span id="dump_dict_to_json-662"><a href="#dump_dict_to_json-662"><span class="linenos">662</span></a>    <span class="n">infostring</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;This JSON file contains a python dictionary that has been parsed to a list of structures. &#39;</span>
-</span><span id="dump_dict_to_json-663"><a href="#dump_dict_to_json-663"><span class="linenos">663</span></a>                  <span class="s1">&#39;OBSDICT contains the dictionary, where Obs or other structures have been replaced by &#39;</span>
-</span><span id="dump_dict_to_json-664"><a href="#dump_dict_to_json-664"><span class="linenos">664</span></a>                  <span class="s1">&#39;&#39;</span> <span class="o">+</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;[0-9]+. The field description contains the additional description of this JSON file. &#39;</span>
-</span><span id="dump_dict_to_json-665"><a href="#dump_dict_to_json-665"><span class="linenos">665</span></a>                  <span class="s1">&#39;This file may be parsed to a dict with the pyerrors routine load_json_dict.&#39;</span><span class="p">)</span>
+</span><span id="dump_dict_to_json-659"><a href="#dump_dict_to_json-659"><span class="linenos">659</span></a>    <span class="n">infostring</span> <span class="o">=</span> <span class="p">(</span><span class="s1">&#39;This JSON file contains a python dictionary that has been parsed to a list of structures. &#39;</span>
+</span><span id="dump_dict_to_json-660"><a href="#dump_dict_to_json-660"><span class="linenos">660</span></a>                  <span class="s1">&#39;OBSDICT contains the dictionary, where Obs or other structures have been replaced by &#39;</span>
+</span><span id="dump_dict_to_json-661"><a href="#dump_dict_to_json-661"><span class="linenos">661</span></a>                  <span class="s1">&#39;&#39;</span> <span class="o">+</span> <span class="n">reps</span> <span class="o">+</span> <span class="s1">&#39;[0-9]+. The field description contains the additional description of this JSON file. &#39;</span>
+</span><span id="dump_dict_to_json-662"><a href="#dump_dict_to_json-662"><span class="linenos">662</span></a>                  <span class="s1">&#39;This file may be parsed to a dict with the pyerrors routine load_json_dict.&#39;</span><span class="p">)</span>
+</span><span id="dump_dict_to_json-663"><a href="#dump_dict_to_json-663"><span class="linenos">663</span></a>
+</span><span id="dump_dict_to_json-664"><a href="#dump_dict_to_json-664"><span class="linenos">664</span></a>    <span class="n">desc_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;INFO&#39;</span><span class="p">:</span> <span class="n">infostring</span><span class="p">,</span> <span class="s1">&#39;OBSDICT&#39;</span><span class="p">:</span> <span class="p">{},</span> <span class="s1">&#39;description&#39;</span><span class="p">:</span> <span class="n">description</span><span class="p">}</span>
+</span><span id="dump_dict_to_json-665"><a href="#dump_dict_to_json-665"><span class="linenos">665</span></a>    <span class="n">ol</span><span class="p">,</span> <span class="n">desc_dict</span><span class="p">[</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">_ol_from_dict</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
 </span><span id="dump_dict_to_json-666"><a href="#dump_dict_to_json-666"><span class="linenos">666</span></a>
-</span><span id="dump_dict_to_json-667"><a href="#dump_dict_to_json-667"><span class="linenos">667</span></a>    <span class="n">desc_dict</span> <span class="o">=</span> <span class="p">{</span><span class="s1">&#39;INFO&#39;</span><span class="p">:</span> <span class="n">infostring</span><span class="p">,</span> <span class="s1">&#39;OBSDICT&#39;</span><span class="p">:</span> <span class="p">{},</span> <span class="s1">&#39;description&#39;</span><span class="p">:</span> <span class="n">description</span><span class="p">}</span>
-</span><span id="dump_dict_to_json-668"><a href="#dump_dict_to_json-668"><span class="linenos">668</span></a>    <span class="n">ol</span><span class="p">,</span> <span class="n">desc_dict</span><span class="p">[</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">_ol_from_dict</span><span class="p">(</span><span class="n">od</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
-</span><span id="dump_dict_to_json-669"><a href="#dump_dict_to_json-669"><span class="linenos">669</span></a>
-</span><span id="dump_dict_to_json-670"><a href="#dump_dict_to_json-670"><span class="linenos">670</span></a>    <span class="n">dump_to_json</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="n">desc_dict</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="n">indent</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">)</span>
+</span><span id="dump_dict_to_json-667"><a href="#dump_dict_to_json-667"><span class="linenos">667</span></a>    <span class="n">dump_to_json</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">fname</span><span class="p">,</span> <span class="n">description</span><span class="o">=</span><span class="n">desc_dict</span><span class="p">,</span> <span class="n">indent</span><span class="o">=</span><span class="n">indent</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">)</span>
 </span></pre></div>
 
 
@@ -1455,45 +1450,45 @@ If True, the output is a gzipped json. If False, the output is a json file.</li>
 
     </div>
     <a class="headerlink" href="#load_json_dict"></a>
-            <div class="pdoc-code codehilite"><pre><span></span><span id="load_json_dict-736"><a href="#load_json_dict-736"><span class="linenos">736</span></a><span class="k">def</span><span class="w"> </span><span class="nf">load_json_dict</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
-</span><span id="load_json_dict-737"><a href="#load_json_dict-737"><span class="linenos">737</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Import a dict of Obs or structures containing Obs from a .json(.gz) file.</span>
-</span><span id="load_json_dict-738"><a href="#load_json_dict-738"><span class="linenos">738</span></a>
-</span><span id="load_json_dict-739"><a href="#load_json_dict-739"><span class="linenos">739</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
-</span><span id="load_json_dict-740"><a href="#load_json_dict-740"><span class="linenos">740</span></a>
-</span><span id="load_json_dict-741"><a href="#load_json_dict-741"><span class="linenos">741</span></a><span class="sd">    Parameters</span>
-</span><span id="load_json_dict-742"><a href="#load_json_dict-742"><span class="linenos">742</span></a><span class="sd">    ----------</span>
-</span><span id="load_json_dict-743"><a href="#load_json_dict-743"><span class="linenos">743</span></a><span class="sd">    fname : str</span>
-</span><span id="load_json_dict-744"><a href="#load_json_dict-744"><span class="linenos">744</span></a><span class="sd">        Filename of the input file.</span>
-</span><span id="load_json_dict-745"><a href="#load_json_dict-745"><span class="linenos">745</span></a><span class="sd">    verbose : bool</span>
-</span><span id="load_json_dict-746"><a href="#load_json_dict-746"><span class="linenos">746</span></a><span class="sd">        Print additional information that was written to the file.</span>
-</span><span id="load_json_dict-747"><a href="#load_json_dict-747"><span class="linenos">747</span></a><span class="sd">    gz : bool</span>
-</span><span id="load_json_dict-748"><a href="#load_json_dict-748"><span class="linenos">748</span></a><span class="sd">        If True, assumes that data is gzipped. If False, assumes JSON file.</span>
-</span><span id="load_json_dict-749"><a href="#load_json_dict-749"><span class="linenos">749</span></a><span class="sd">    full_output : bool</span>
-</span><span id="load_json_dict-750"><a href="#load_json_dict-750"><span class="linenos">750</span></a><span class="sd">        If True, a dict containing auxiliary information and the data is returned.</span>
-</span><span id="load_json_dict-751"><a href="#load_json_dict-751"><span class="linenos">751</span></a><span class="sd">        If False, only the data is returned.</span>
-</span><span id="load_json_dict-752"><a href="#load_json_dict-752"><span class="linenos">752</span></a><span class="sd">    reps : str</span>
-</span><span id="load_json_dict-753"><a href="#load_json_dict-753"><span class="linenos">753</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
-</span><span id="load_json_dict-754"><a href="#load_json_dict-754"><span class="linenos">754</span></a>
-</span><span id="load_json_dict-755"><a href="#load_json_dict-755"><span class="linenos">755</span></a><span class="sd">    Returns</span>
-</span><span id="load_json_dict-756"><a href="#load_json_dict-756"><span class="linenos">756</span></a><span class="sd">    -------</span>
-</span><span id="load_json_dict-757"><a href="#load_json_dict-757"><span class="linenos">757</span></a><span class="sd">    data : Obs / list / Corr</span>
-</span><span id="load_json_dict-758"><a href="#load_json_dict-758"><span class="linenos">758</span></a><span class="sd">        Read data</span>
-</span><span id="load_json_dict-759"><a href="#load_json_dict-759"><span class="linenos">759</span></a><span class="sd">    or</span>
-</span><span id="load_json_dict-760"><a href="#load_json_dict-760"><span class="linenos">760</span></a><span class="sd">    data : dict</span>
-</span><span id="load_json_dict-761"><a href="#load_json_dict-761"><span class="linenos">761</span></a><span class="sd">        Read data and meta-data</span>
-</span><span id="load_json_dict-762"><a href="#load_json_dict-762"><span class="linenos">762</span></a><span class="sd">    &quot;&quot;&quot;</span>
-</span><span id="load_json_dict-763"><a href="#load_json_dict-763"><span class="linenos">763</span></a>    <span class="n">indata</span> <span class="o">=</span> <span class="n">load_json</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="n">verbose</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
-</span><span id="load_json_dict-764"><a href="#load_json_dict-764"><span class="linenos">764</span></a>    <span class="n">description</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;description&#39;</span><span class="p">]</span>
-</span><span id="load_json_dict-765"><a href="#load_json_dict-765"><span class="linenos">765</span></a>    <span class="n">indict</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span>
-</span><span id="load_json_dict-766"><a href="#load_json_dict-766"><span class="linenos">766</span></a>    <span class="n">ol</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span>
-</span><span id="load_json_dict-767"><a href="#load_json_dict-767"><span class="linenos">767</span></a>    <span class="n">od</span> <span class="o">=</span> <span class="n">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">indict</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
-</span><span id="load_json_dict-768"><a href="#load_json_dict-768"><span class="linenos">768</span></a>
-</span><span id="load_json_dict-769"><a href="#load_json_dict-769"><span class="linenos">769</span></a>    <span class="k">if</span> <span class="n">full_output</span><span class="p">:</span>
-</span><span id="load_json_dict-770"><a href="#load_json_dict-770"><span class="linenos">770</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">description</span>
-</span><span id="load_json_dict-771"><a href="#load_json_dict-771"><span class="linenos">771</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">od</span>
-</span><span id="load_json_dict-772"><a href="#load_json_dict-772"><span class="linenos">772</span></a>        <span class="k">return</span> <span class="n">indata</span>
-</span><span id="load_json_dict-773"><a href="#load_json_dict-773"><span class="linenos">773</span></a>    <span class="k">else</span><span class="p">:</span>
-</span><span id="load_json_dict-774"><a href="#load_json_dict-774"><span class="linenos">774</span></a>        <span class="k">return</span> <span class="n">od</span>
+            <div class="pdoc-code codehilite"><pre><span></span><span id="load_json_dict-731"><a href="#load_json_dict-731"><span class="linenos">731</span></a><span class="k">def</span><span class="w"> </span><span class="nf">load_json_dict</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="kc">True</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="s1">&#39;DICTOBS&#39;</span><span class="p">):</span>
+</span><span id="load_json_dict-732"><a href="#load_json_dict-732"><span class="linenos">732</span></a><span class="w">    </span><span class="sd">&quot;&quot;&quot;Import a dict of Obs or structures containing Obs from a .json(.gz) file.</span>
+</span><span id="load_json_dict-733"><a href="#load_json_dict-733"><span class="linenos">733</span></a>
+</span><span id="load_json_dict-734"><a href="#load_json_dict-734"><span class="linenos">734</span></a><span class="sd">    The following structures are supported: Obs, list, numpy.ndarray, Corr</span>
+</span><span id="load_json_dict-735"><a href="#load_json_dict-735"><span class="linenos">735</span></a>
+</span><span id="load_json_dict-736"><a href="#load_json_dict-736"><span class="linenos">736</span></a><span class="sd">    Parameters</span>
+</span><span id="load_json_dict-737"><a href="#load_json_dict-737"><span class="linenos">737</span></a><span class="sd">    ----------</span>
+</span><span id="load_json_dict-738"><a href="#load_json_dict-738"><span class="linenos">738</span></a><span class="sd">    fname : str</span>
+</span><span id="load_json_dict-739"><a href="#load_json_dict-739"><span class="linenos">739</span></a><span class="sd">        Filename of the input file.</span>
+</span><span id="load_json_dict-740"><a href="#load_json_dict-740"><span class="linenos">740</span></a><span class="sd">    verbose : bool</span>
+</span><span id="load_json_dict-741"><a href="#load_json_dict-741"><span class="linenos">741</span></a><span class="sd">        Print additional information that was written to the file.</span>
+</span><span id="load_json_dict-742"><a href="#load_json_dict-742"><span class="linenos">742</span></a><span class="sd">    gz : bool</span>
+</span><span id="load_json_dict-743"><a href="#load_json_dict-743"><span class="linenos">743</span></a><span class="sd">        If True, assumes that data is gzipped. If False, assumes JSON file.</span>
+</span><span id="load_json_dict-744"><a href="#load_json_dict-744"><span class="linenos">744</span></a><span class="sd">    full_output : bool</span>
+</span><span id="load_json_dict-745"><a href="#load_json_dict-745"><span class="linenos">745</span></a><span class="sd">        If True, a dict containing auxiliary information and the data is returned.</span>
+</span><span id="load_json_dict-746"><a href="#load_json_dict-746"><span class="linenos">746</span></a><span class="sd">        If False, only the data is returned.</span>
+</span><span id="load_json_dict-747"><a href="#load_json_dict-747"><span class="linenos">747</span></a><span class="sd">    reps : str</span>
+</span><span id="load_json_dict-748"><a href="#load_json_dict-748"><span class="linenos">748</span></a><span class="sd">        Specify the structure of the placeholder in imported dict to be reps[0-9]+.</span>
+</span><span id="load_json_dict-749"><a href="#load_json_dict-749"><span class="linenos">749</span></a>
+</span><span id="load_json_dict-750"><a href="#load_json_dict-750"><span class="linenos">750</span></a><span class="sd">    Returns</span>
+</span><span id="load_json_dict-751"><a href="#load_json_dict-751"><span class="linenos">751</span></a><span class="sd">    -------</span>
+</span><span id="load_json_dict-752"><a href="#load_json_dict-752"><span class="linenos">752</span></a><span class="sd">    data : Obs / list / Corr</span>
+</span><span id="load_json_dict-753"><a href="#load_json_dict-753"><span class="linenos">753</span></a><span class="sd">        Read data</span>
+</span><span id="load_json_dict-754"><a href="#load_json_dict-754"><span class="linenos">754</span></a><span class="sd">    or</span>
+</span><span id="load_json_dict-755"><a href="#load_json_dict-755"><span class="linenos">755</span></a><span class="sd">    data : dict</span>
+</span><span id="load_json_dict-756"><a href="#load_json_dict-756"><span class="linenos">756</span></a><span class="sd">        Read data and meta-data</span>
+</span><span id="load_json_dict-757"><a href="#load_json_dict-757"><span class="linenos">757</span></a><span class="sd">    &quot;&quot;&quot;</span>
+</span><span id="load_json_dict-758"><a href="#load_json_dict-758"><span class="linenos">758</span></a>    <span class="n">indata</span> <span class="o">=</span> <span class="n">load_json</span><span class="p">(</span><span class="n">fname</span><span class="p">,</span> <span class="n">verbose</span><span class="o">=</span><span class="n">verbose</span><span class="p">,</span> <span class="n">gz</span><span class="o">=</span><span class="n">gz</span><span class="p">,</span> <span class="n">full_output</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+</span><span id="load_json_dict-759"><a href="#load_json_dict-759"><span class="linenos">759</span></a>    <span class="n">description</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;description&#39;</span><span class="p">]</span>
+</span><span id="load_json_dict-760"><a href="#load_json_dict-760"><span class="linenos">760</span></a>    <span class="n">indict</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">][</span><span class="s1">&#39;OBSDICT&#39;</span><span class="p">]</span>
+</span><span id="load_json_dict-761"><a href="#load_json_dict-761"><span class="linenos">761</span></a>    <span class="n">ol</span> <span class="o">=</span> <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span>
+</span><span id="load_json_dict-762"><a href="#load_json_dict-762"><span class="linenos">762</span></a>    <span class="n">od</span> <span class="o">=</span> <span class="n">_od_from_list_and_dict</span><span class="p">(</span><span class="n">ol</span><span class="p">,</span> <span class="n">indict</span><span class="p">,</span> <span class="n">reps</span><span class="o">=</span><span class="n">reps</span><span class="p">)</span>
+</span><span id="load_json_dict-763"><a href="#load_json_dict-763"><span class="linenos">763</span></a>
+</span><span id="load_json_dict-764"><a href="#load_json_dict-764"><span class="linenos">764</span></a>    <span class="k">if</span> <span class="n">full_output</span><span class="p">:</span>
+</span><span id="load_json_dict-765"><a href="#load_json_dict-765"><span class="linenos">765</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;description&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">description</span>
+</span><span id="load_json_dict-766"><a href="#load_json_dict-766"><span class="linenos">766</span></a>        <span class="n">indata</span><span class="p">[</span><span class="s1">&#39;obsdata&#39;</span><span class="p">]</span> <span class="o">=</span> <span class="n">od</span>
+</span><span id="load_json_dict-767"><a href="#load_json_dict-767"><span class="linenos">767</span></a>        <span class="k">return</span> <span class="n">indata</span>
+</span><span id="load_json_dict-768"><a href="#load_json_dict-768"><span class="linenos">768</span></a>    <span class="k">else</span><span class="p">:</span>
+</span><span id="load_json_dict-769"><a href="#load_json_dict-769"><span class="linenos">769</span></a>        <span class="k">return</span> <span class="n">od</span>
 </span></pre></div>
 
 
diff --git a/docs/pyerrors/input/misc.html b/docs/pyerrors/input/misc.html
index 125386cf..6949924f 100644
--- a/docs/pyerrors/input/misc.html
+++ b/docs/pyerrors/input/misc.html
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diff --git a/docs/pyerrors/input/openQCD.html b/docs/pyerrors/input/openQCD.html
index bb7a26d4..811493b9 100644
--- a/docs/pyerrors/input/openQCD.html
+++ b/docs/pyerrors/input/openQCD.html
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diff --git a/docs/pyerrors/input/pandas.html b/docs/pyerrors/input/pandas.html
index 8221e9dd..d7fa9de5 100644
--- a/docs/pyerrors/input/pandas.html
+++ b/docs/pyerrors/input/pandas.html
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diff --git a/docs/pyerrors/input/sfcf.html b/docs/pyerrors/input/sfcf.html
index 4219c5cd..5f50c9fa 100644
--- a/docs/pyerrors/input/sfcf.html
+++ b/docs/pyerrors/input/sfcf.html
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index 9ef2d497..91782076 100644
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diff --git a/docs/pyerrors/integrate.html b/docs/pyerrors/integrate.html
index 02cd8ba7..77280b77 100644
--- a/docs/pyerrors/integrate.html
+++ b/docs/pyerrors/integrate.html
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diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html
index d4d856a8..f8eeccf0 100644
--- a/docs/pyerrors/linalg.html
+++ b/docs/pyerrors/linalg.html
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diff --git a/docs/pyerrors/misc.html b/docs/pyerrors/misc.html
index 459032bb..bf111a60 100644
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diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html
index 39569843..136e180a 100644
--- a/docs/pyerrors/obs.html
+++ b/docs/pyerrors/obs.html
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diff --git a/docs/pyerrors/roots.html b/docs/pyerrors/roots.html
index 61335386..acab5089 100644
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diff --git a/docs/pyerrors/special.html b/docs/pyerrors/special.html
index 4641cd83..249553f7 100644
--- a/docs/pyerrors/special.html
+++ b/docs/pyerrors/special.html
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diff --git a/docs/pyerrors/version.html b/docs/pyerrors/version.html
index 7311476e..5a683c1c 100644
--- a/docs/pyerrors/version.html
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diff --git a/docs/search.js b/docs/search.js
index 7a26d026..e4389961 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
 /** elasticlunr - http://weixsong.github.io * Copyright (C) 2017 Oliver Nightingale * Copyright (C) 2017 Wei Song * MIT Licensed */!function(){function e(e){if(null===e||"object"!=typeof e)return e;var t=e.constructor();for(var n in e)e.hasOwnProperty(n)&&(t[n]=e[n]);return t}var t=function(e){var n=new t.Index;return n.pipeline.add(t.trimmer,t.stopWordFilter,t.stemmer),e&&e.call(n,n),n};t.version="0.9.5",lunr=t,t.utils={},t.utils.warn=function(e){return function(t){e.console&&console.warn&&console.warn(t)}}(this),t.utils.toString=function(e){return void 0===e||null===e?"":e.toString()},t.EventEmitter=function(){this.events={}},t.EventEmitter.prototype.addListener=function(){var e=Array.prototype.slice.call(arguments),t=e.pop(),n=e;if("function"!=typeof t)throw new TypeError("last argument must be a function");n.forEach(function(e){this.hasHandler(e)||(this.events[e]=[]),this.events[e].push(t)},this)},t.EventEmitter.prototype.removeListener=function(e,t){if(this.hasHandler(e)){var n=this.events[e].indexOf(t);-1!==n&&(this.events[e].splice(n,1),0==this.events[e].length&&delete this.events[e])}},t.EventEmitter.prototype.emit=function(e){if(this.hasHandler(e)){var t=Array.prototype.slice.call(arguments,1);this.events[e].forEach(function(e){e.apply(void 0,t)},this)}},t.EventEmitter.prototype.hasHandler=function(e){return e in this.events},t.tokenizer=function(e){if(!arguments.length||null===e||void 0===e)return[];if(Array.isArray(e)){var n=e.filter(function(e){return null===e||void 0===e?!1:!0});n=n.map(function(e){return t.utils.toString(e).toLowerCase()});var i=[];return n.forEach(function(e){var n=e.split(t.tokenizer.seperator);i=i.concat(n)},this),i}return e.toString().trim().toLowerCase().split(t.tokenizer.seperator)},t.tokenizer.defaultSeperator=/[\s\-]+/,t.tokenizer.seperator=t.tokenizer.defaultSeperator,t.tokenizer.setSeperator=function(e){null!==e&&void 0!==e&&"object"==typeof e&&(t.tokenizer.seperator=e)},t.tokenizer.resetSeperator=function(){t.tokenizer.seperator=t.tokenizer.defaultSeperator},t.tokenizer.getSeperator=function(){return t.tokenizer.seperator},t.Pipeline=function(){this._queue=[]},t.Pipeline.registeredFunctions={},t.Pipeline.registerFunction=function(e,n){n in t.Pipeline.registeredFunctions&&t.utils.warn("Overwriting existing registered function: "+n),e.label=n,t.Pipeline.registeredFunctions[n]=e},t.Pipeline.getRegisteredFunction=function(e){return e in t.Pipeline.registeredFunctions!=!0?null:t.Pipeline.registeredFunctions[e]},t.Pipeline.warnIfFunctionNotRegistered=function(e){var n=e.label&&e.label in this.registeredFunctions;n||t.utils.warn("Function is not registered with pipeline. This may cause problems when serialising the index.\n",e)},t.Pipeline.load=function(e){var n=new t.Pipeline;return e.forEach(function(e){var i=t.Pipeline.getRegisteredFunction(e);if(!i)throw new Error("Cannot load un-registered function: "+e);n.add(i)}),n},t.Pipeline.prototype.add=function(){var e=Array.prototype.slice.call(arguments);e.forEach(function(e){t.Pipeline.warnIfFunctionNotRegistered(e),this._queue.push(e)},this)},t.Pipeline.prototype.after=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i+1,0,n)},t.Pipeline.prototype.before=function(e,n){t.Pipeline.warnIfFunctionNotRegistered(n);var i=this._queue.indexOf(e);if(-1===i)throw new Error("Cannot find existingFn");this._queue.splice(i,0,n)},t.Pipeline.prototype.remove=function(e){var t=this._queue.indexOf(e);-1!==t&&this._queue.splice(t,1)},t.Pipeline.prototype.run=function(e){for(var t=[],n=e.length,i=this._queue.length,o=0;n>o;o++){for(var r=e[o],s=0;i>s&&(r=this._queue[s](r,o,e),void 0!==r&&null!==r);s++);void 0!==r&&null!==r&&t.push(r)}return t},t.Pipeline.prototype.reset=function(){this._queue=[]},t.Pipeline.prototype.get=function(){return this._queue},t.Pipeline.prototype.toJSON=function(){return this._queue.map(function(e){return t.Pipeline.warnIfFunctionNotRegistered(e),e.label})},t.Index=function(){this._fields=[],this._ref="id",this.pipeline=new t.Pipeline,this.documentStore=new t.DocumentStore,this.index={},this.eventEmitter=new t.EventEmitter,this._idfCache={},this.on("add","remove","update",function(){this._idfCache={}}.bind(this))},t.Index.prototype.on=function(){var e=Array.prototype.slice.call(arguments);return this.eventEmitter.addListener.apply(this.eventEmitter,e)},t.Index.prototype.off=function(e,t){return this.eventEmitter.removeListener(e,t)},t.Index.load=function(e){e.version!==t.version&&t.utils.warn("version mismatch: current "+t.version+" importing "+e.version);var n=new this;n._fields=e.fields,n._ref=e.ref,n.documentStore=t.DocumentStore.load(e.documentStore),n.pipeline=t.Pipeline.load(e.pipeline),n.index={};for(var i in e.index)n.index[i]=t.InvertedIndex.load(e.index[i]);return n},t.Index.prototype.addField=function(e){return this._fields.push(e),this.index[e]=new t.InvertedIndex,this},t.Index.prototype.setRef=function(e){return this._ref=e,this},t.Index.prototype.saveDocument=function(e){return this.documentStore=new t.DocumentStore(e),this},t.Index.prototype.addDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.addDoc(i,e),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));this.documentStore.addFieldLength(i,n,o.length);var r={};o.forEach(function(e){e in r?r[e]+=1:r[e]=1},this);for(var s in r){var u=r[s];u=Math.sqrt(u),this.index[n].addToken(s,{ref:i,tf:u})}},this),n&&this.eventEmitter.emit("add",e,this)}},t.Index.prototype.removeDocByRef=function(e){if(e&&this.documentStore.isDocStored()!==!1&&this.documentStore.hasDoc(e)){var t=this.documentStore.getDoc(e);this.removeDoc(t,!1)}},t.Index.prototype.removeDoc=function(e,n){if(e){var n=void 0===n?!0:n,i=e[this._ref];this.documentStore.hasDoc(i)&&(this.documentStore.removeDoc(i),this._fields.forEach(function(n){var o=this.pipeline.run(t.tokenizer(e[n]));o.forEach(function(e){this.index[n].removeToken(e,i)},this)},this),n&&this.eventEmitter.emit("remove",e,this))}},t.Index.prototype.updateDoc=function(e,t){var t=void 0===t?!0:t;this.removeDocByRef(e[this._ref],!1),this.addDoc(e,!1),t&&this.eventEmitter.emit("update",e,this)},t.Index.prototype.idf=function(e,t){var n="@"+t+"/"+e;if(Object.prototype.hasOwnProperty.call(this._idfCache,n))return this._idfCache[n];var 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n=[e];1==o&&(n=this.index[t].expandToken(e));var r={};n.forEach(function(n){var o=this.index[t].getDocs(n),a=this.idf(n,t);if(s&&"AND"==i){var l={};for(var c in s)c in o&&(l[c]=o[c]);o=l}n==e&&this.fieldSearchStats(u,n,o);for(var c in o){var d=this.index[t].getTermFrequency(n,c),f=this.documentStore.getFieldLength(c,t),h=1;0!=f&&(h=1/Math.sqrt(f));var p=1;n!=e&&(p=.15*(1-(n.length-e.length)/n.length));var v=d*a*h*p;c in r?r[c]+=v:r[c]=v}},this),s=this.mergeScores(s,r,i)},this),s=this.coordNorm(s,u,e.length)):void 0},t.Index.prototype.mergeScores=function(e,t,n){if(!e)return t;if("AND"==n){var i={};for(var o in t)o in e&&(i[o]=e[o]+t[o]);return i}for(var o in t)o in e?e[o]+=t[o]:e[o]=t[o];return e},t.Index.prototype.fieldSearchStats=function(e,t,n){for(var i in n)i in e?e[i].push(t):e[i]=[t]},t.Index.prototype.coordNorm=function(e,t,n){for(var i in e)if(i in t){var o=t[i].length;e[i]=e[i]*o/n}return e},t.Index.prototype.toJSON=function(){var e={};return this._fields.forEach(function(t){e[t]=this.index[t].toJSON()},this),{version:t.version,fields:this._fields,ref:this._ref,documentStore:this.documentStore.toJSON(),index:e,pipeline:this.pipeline.toJSON()}},t.Index.prototype.use=function(e){var t=Array.prototype.slice.call(arguments,1);t.unshift(this),e.apply(this,t)},t.DocumentStore=function(e){this._save=null===e||void 0===e?!0:e,this.docs={},this.docInfo={},this.length=0},t.DocumentStore.load=function(e){var t=new this;return t.length=e.length,t.docs=e.docs,t.docInfo=e.docInfo,t._save=e.save,t},t.DocumentStore.prototype.isDocStored=function(){return this._save},t.DocumentStore.prototype.addDoc=function(t,n){this.hasDoc(t)||this.length++,this.docs[t]=this._save===!0?e(n):null},t.DocumentStore.prototype.getDoc=function(e){return this.hasDoc(e)===!1?null:this.docs[e]},t.DocumentStore.prototype.hasDoc=function(e){return e in this.docs},t.DocumentStore.prototype.removeDoc=function(e){this.hasDoc(e)&&(delete this.docs[e],delete this.docInfo[e],this.length--)},t.DocumentStore.prototype.addFieldLength=function(e,t,n){null!==e&&void 0!==e&&0!=this.hasDoc(e)&&(this.docInfo[e]||(this.docInfo[e]={}),this.docInfo[e][t]=n)},t.DocumentStore.prototype.updateFieldLength=function(e,t,n){null!==e&&void 0!==e&&0!=this.hasDoc(e)&&this.addFieldLength(e,t,n)},t.DocumentStore.prototype.getFieldLength=function(e,t){return null===e||void 0===e?0:e in this.docs&&t in this.docInfo[e]?this.docInfo[e][t]:0},t.DocumentStore.prototype.toJSON=function(){return{docs:this.docs,docInfo:this.docInfo,length:this.length,save:this._save}},t.stemmer=function(){var e={ational:"ate",tional:"tion",enci:"ence",anci:"ance",izer:"ize",bli:"ble",alli:"al",entli:"ent",eli:"e",ousli:"ous",ization:"ize",ation:"ate",ator:"ate",alism:"al",iveness:"ive",fulness:"ful",ousness:"ous",aliti:"al",iviti:"ive",biliti:"ble",logi:"log"},t={icate:"ic",ative:"",alize:"al",iciti:"ic",ical:"ic",ful:"",ness:""},n="[^aeiou]",i="[aeiouy]",o=n+"[^aeiouy]*",r=i+"[aeiou]*",s="^("+o+")?"+r+o,u="^("+o+")?"+r+o+"("+r+")?$",a="^("+o+")?"+r+o+r+o,l="^("+o+")?"+i,c=new RegExp(s),d=new RegExp(a),f=new RegExp(u),h=new RegExp(l),p=/^(.+?)(ss|i)es$/,v=/^(.+?)([^s])s$/,g=/^(.+?)eed$/,m=/^(.+?)(ed|ing)$/,y=/.$/,S=/(at|bl|iz)$/,x=new RegExp("([^aeiouylsz])\\1$"),w=new 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Some of its features are:</p>\n\n<ul>\n<li>automatic differentiation for exact linear error propagation as suggested in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a> (partly based on the <a href=\"https://github.com/HIPS/autograd\">autograd</a> package).</li>\n<li>treatment of slow modes in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>.</li>\n<li>coherent error propagation for data from different Markov chains.</li>\n<li>non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</li>\n<li>real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).</li>\n</ul>\n\n<p>More detailed examples can found in the <a href=\"https://github.com/fjosw/pyerrors/tree/develop/examples\">GitHub repository</a> <a href=\"https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples\"><img src=\"https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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\" alt=\"badge\" /></a>.</p>\n\n<p>If you use <code>pyerrors</code> for research that leads to a publication please consider citing:</p>\n\n<ul>\n<li>Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, <em>pyerrors: a python framework for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 288 (2023) 108750.</li>\n<li>Ulli Wolff, <em>Monte Carlo errors with less errors</em>. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</li>\n<li>Alberto Ramos, <em>Automatic differentiation for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 238 (2019) 19-35.</li>\n</ul>\n\n<p>and</p>\n\n<ul>\n<li>Stefan Schaefer, Rainer Sommer, Francesco Virotta, <em>Critical slowing down and error analysis in lattice QCD simulations</em>. Nucl.Phys.B 845 (2011) 93-119.</li>\n</ul>\n\n<p>where applicable.</p>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a>, <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a> and <a href=\"https://github.com/mbruno46/pyobs\">Python</a>.</p>\n\n<h2 id=\"installation\">Installation</h2>\n\n<p>Install the most recent release using pip and <a href=\"https://pypi.org/project/pyerrors/\">pypi</a>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>python<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>pyerrors<span class=\"w\">     </span><span class=\"c1\"># Fresh install</span>\npython<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>-U<span class=\"w\"> </span>pyerrors<span class=\"w\">  </span><span class=\"c1\"># Update</span>\n</code></pre>\n</div>\n\n<p>Install the most recent release using conda and <a href=\"https://anaconda.org/conda-forge/pyerrors\">conda-forge</a>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>conda<span class=\"w\"> </span>install<span class=\"w\"> </span>-c<span class=\"w\"> </span>conda-forge<span class=\"w\"> </span>pyerrors<span class=\"w\">  </span><span class=\"c1\"># Fresh install</span>\nconda<span class=\"w\"> </span>update<span class=\"w\"> </span>-c<span class=\"w\"> </span>conda-forge<span class=\"w\"> </span>pyerrors<span class=\"w\">   </span><span class=\"c1\"># Update</span>\n</code></pre>\n</div>\n\n<p>Install the current <code>develop</code> version:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>python<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>-U<span class=\"w\"> </span>--no-deps<span class=\"w\"> </span>--force-reinstall<span class=\"w\"> </span>git+https://github.com/fjosw/pyerrors.git@develop\n</code></pre>\n</div>\n\n<p>(Also works for any feature branch).</p>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span> <span class=\"c1\"># Initialize an Obs object</span>\n<span class=\"n\">my_new_obs</span> <span class=\"o\">=</span> <span class=\"mi\">2</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">)</span> <span class=\"o\">/</span> <span class=\"n\">my_obs</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"c1\"># Construct derived Obs object</span>\n<span class=\"n\">my_new_obs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>                     <span class=\"c1\"># Estimate the statistical error</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_new_obs</span><span class=\"p\">)</span>                             <span class=\"c1\"># Print the result to stdout</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.31498</span><span class=\"p\">(</span><span class=\"mi\">72</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h1 id=\"the-obs-class\">The <code>Obs</code> class</h1>\n\n<p><code>pyerrors</code> introduces a new datatype, <code>Obs</code>, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn <code>Obs</code> object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. <strong>It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See <a href=\"#multiple-ensemblesreplica\">Multiple ensembles/replica</a> for details.</strong></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<h2 id=\"error-propagation\">Error propagation</h2>\n\n<p>When performing mathematical operations on <code>Obs</code> objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<p>The <code>Obs</code> class is designed such that mathematical numpy functions can be used on <code>Obs</code> just as for regular floats.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">my_obs1</span> <span class=\"o\">+</span> <span class=\"n\">my_obs2</span>\n\n<span class=\"n\">my_m_eff</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">my_obs1</span> <span class=\"o\">/</span> <span class=\"n\">my_obs2</span><span class=\"p\">)</span>\n\n<span class=\"n\">iamzero</span> <span class=\"o\">=</span> <span class=\"n\">my_m_eff</span> <span class=\"o\">-</span> <span class=\"n\">my_m_eff</span>\n<span class=\"c1\"># Check that value and fluctuations are zero within machine precision</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">iamzero</span> <span class=\"o\">==</span> <span class=\"mf\">0.0</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<h2 id=\"error-estimation\">Error estimation</h2>\n\n<p>The error estimation within <code>pyerrors</code> is based on the gamma method introduced in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nAfter having arrived at the derived quantity of interest the <code>gamma_method</code> can be called as detailed in the following example.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_sum</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">1.70</span><span class=\"p\">(</span><span class=\"mi\">57</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.72046658e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">7.56746598e-02</span> <span class=\"p\">(</span><span class=\"mf\">33.650</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">2.71422900e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.40320983e-01</span> <span class=\"n\">S</span> <span class=\"o\">=</span> <span class=\"mf\">2.00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>The <code>gamma_method</code> is not automatically called after every intermediate step in order to prevent computational overhead.</p>\n\n<p>We use the following definition of the integrated autocorrelation time established in <a href=\"https://link.springer.com/article/10.1007/BF01022990\">Madras &amp; Sokal 1988</a>\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the <code>gamma_method</code> as parameter.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">(</span><span class=\"n\">S</span><span class=\"o\">=</span><span class=\"mf\">3.0</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.30675201e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">1.04585650e-01</span> <span class=\"p\">(</span><span class=\"mf\">37.099</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">3.29909703e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">9.77310102e-01</span> <span class=\"n\">S</span> <span class=\"o\">=</span> <span class=\"mf\">3.00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods <code>pyerrors.obs.Obs.plot_tauint</code> and <code>pyerrors.obs.Obs.plot_rho</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.</p>\n\n<h3 id=\"exponential-tails\">Exponential tails</h3>\n\n<p>Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the <code>gamma_method</code> as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">(</span><span class=\"n\">tau_exp</span><span class=\"o\">=</span><span class=\"mf\">7.2</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.28097762e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.79077524e-02</span> <span class=\"p\">(</span><span class=\"mf\">36.947</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">3.27218667e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">7.99583654e-01</span> <span class=\"n\">tau_exp</span> <span class=\"o\">=</span> <span class=\"mf\">7.20</span><span class=\"p\">,</span>  <span class=\"n\">N_sigma</span> <span class=\"o\">=</span> <span class=\"mi\">1</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For the full API see <code>pyerrors.obs.Obs.gamma_method</code>.</p>\n\n<h2 id=\"multiple-ensemblesreplica\">Multiple ensembles/replica</h2>\n\n<p>Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their <code>name</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble2&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">obs1</span> <span class=\"o\">+</span> <span class=\"n\">obs2</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>   <span class=\"mf\">2.00697958e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">2</span> <span class=\"n\">ensembles</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble2&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Observables from the <strong>same Monte Carlo chain</strong> have to be initialized with the <strong>same name</strong> for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.</p>\n\n<p><code>pyerrors</code> identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar <code>|</code> in the name of the data set.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1|r01&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1|r02&#39;</span><span class=\"p\">])</span>\n\n<span class=\"o\">&gt;</span> <span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">obs1</span> <span class=\"o\">+</span> <span class=\"n\">obs2</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>   <span class=\"mf\">2.00697958e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span>\n<span class=\"o\">&gt;</span>     <span class=\"err\">\u00b7</span> <span class=\"n\">Replicum</span> <span class=\"s1\">&#39;r01&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>     <span class=\"err\">\u00b7</span> <span class=\"n\">Replicum</span> <span class=\"s1\">&#39;r02&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h3 id=\"error-estimation-for-multiple-ensembles\">Error estimation for multiple ensembles</h3>\n\n<p>In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">S_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">2.5</span>\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">tau_exp_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble2&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">8.0</span>\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">tau_exp_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble3&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">2.0</span>\n</code></pre>\n</div>\n\n<p>In case the <code>gamma_method</code> is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the <code>gamma_method</code> still dominates over the dictionaries.</p>\n\n<h2 id=\"irregular-monte-carlo-chains\">Irregular Monte Carlo chains</h2>\n\n<p><code>Obs</code> objects defined on irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"c1\"># Observable defined on configurations 20 to 519</span>\n<span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">20</span><span class=\"p\">,</span> <span class=\"mi\">520</span><span class=\"p\">)])</span>\n<span class=\"n\">obs1</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">9.98319881e-01</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">20</span> <span class=\"n\">to</span> <span class=\"mi\">519</span><span class=\"p\">)</span>\n\n<span class=\"c1\"># Observable defined on every second configuration between 5 and 1003</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span> <span class=\"mi\">1005</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">)])</span>\n<span class=\"n\">obs2</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">9.99100712e-01</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">5</span> <span class=\"n\">to</span> <span class=\"mi\">1003</span> <span class=\"ow\">in</span> <span class=\"n\">steps</span> <span class=\"n\">of</span> <span class=\"mi\">2</span><span class=\"p\">)</span>\n\n<span class=\"c1\"># Observable defined on configurations 2, 9, 28, 29 and 501</span>\n<span class=\"n\">obs3</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples3</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[[</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">9</span><span class=\"p\">,</span> <span class=\"mi\">28</span><span class=\"p\">,</span> <span class=\"mi\">29</span><span class=\"p\">,</span> <span class=\"mi\">501</span><span class=\"p\">]])</span>\n<span class=\"n\">obs3</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.01718064e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">5</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"n\">irregular</span> <span class=\"nb\">range</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><code>Obs</code> objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</p>\n\n<p><strong>Warning:</strong> Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. <code>pyerrors.obs.Obs.plot_rho</code> or <code>pyerrors.obs.Obs.plot_tauint</code>.</p>\n\n<p>For the full API see <code>pyerrors.obs.Obs</code>.</p>\n\n<h1 id=\"correlators\">Correlators</h1>\n\n<p>When one is not interested in single observables but correlation functions, <code>pyerrors</code> offers the <code>Corr</code> class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a <code>Corr</code> objects one needs to arrange the data as a list of <code>Obs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">],</span> <span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">4</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span>\n</code></pre>\n</div>\n\n<p>The individual entries of a correlator can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Error propagation with the <code>Corr</code> class works very similar to <code>Obs</code> objects. Mathematical operations are overloaded and <code>Corr</code> objects can be computed together with other <code>Corr</code> objects, <code>Obs</code> objects or real numbers and integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_new_corr</span> <span class=\"o\">=</span> <span class=\"mf\">0.3</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">+</span> <span class=\"mi\">12</span> <span class=\"o\">/</span> <span class=\"n\">my_corr</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>\n\n<ul>\n<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>\n<li><code>Corr.m_eff</code> to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</li>\n<li><code>Corr.deriv</code> returns the first derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.second_deriv</code> returns the second derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.symmetric</code> symmetrizes parity even correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.anti_symmetric</code> anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.T_symmetry</code> averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</li>\n<li><code>Corr.plateau</code> extracts a plateau value from the correlator in a given range.</li>\n<li><code>Corr.roll</code> periodically shifts the correlator.</li>\n<li><code>Corr.reverse</code> reverses the time ordering of the correlator.</li>\n<li><code>Corr.correlate</code> constructs a disconnected correlation function from the correlator and another <code>Corr</code> or <code>Obs</code> object.</li>\n<li><code>Corr.reweight</code> reweights the correlator.</li>\n</ul>\n\n<p><code>pyerrors</code> can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see <code>pyerrors.correlators.Corr.GEVP</code>).</p>\n\n<p>For the full API see <code>pyerrors.correlators.Corr</code>.</p>\n\n<h1 id=\"complex-valued-observables\">Complex valued observables</h1>\n\n<p><code>pyerrors</code> can handle complex valued observables via the class <code>pyerrors.obs.CObs</code>.\n<code>CObs</code> are initialized with a real and an imaginary part which both can be <code>Obs</code> valued.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_real_part</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">my_imag_part</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_cobs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">CObs</span><span class=\"p\">(</span><span class=\"n\">my_real_part</span><span class=\"p\">,</span> <span class=\"n\">my_imag_part</span><span class=\"p\">)</span>\n<span class=\"n\">my_cobs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_cobs</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">(</span><span class=\"mf\">0.9959</span><span class=\"p\">(</span><span class=\"mi\">91</span><span class=\"p\">)</span><span class=\"o\">+</span><span class=\"mf\">0.659</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span><span class=\"n\">j</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Elementary mathematical operations are overloaded and samples are properly propagated as for the <code>Obs</code> class.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_derived_cobs</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">my_cobs</span> <span class=\"o\">+</span> <span class=\"n\">my_cobs</span><span class=\"o\">.</span><span class=\"n\">conjugate</span><span class=\"p\">())</span> <span class=\"o\">/</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">abs</span><span class=\"p\">(</span><span class=\"n\">my_cobs</span><span class=\"p\">)</span>\n<span class=\"n\">my_derived_cobs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_derived_cobs</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">(</span><span class=\"mf\">1.668</span><span class=\"p\">(</span><span class=\"mi\">23</span><span class=\"p\">)</span><span class=\"o\">+</span><span class=\"mf\">0.0</span><span class=\"n\">j</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h1 id=\"the-covobs-class\">The <code>Covobs</code> class</h1>\n\n<p>In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The <code>Covobs</code> class allows to define such quantities in <code>pyerrors</code>. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</p>\n\n<p>This concept is built into the definition of <code>Covobs</code>. In <code>pyerrors</code>, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). <strong>Note, that the square of the error enters <code>cov_Obs</code></strong>, since the second argument of this function is the covariance matrix of the <code>Covobs</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors.obs</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">mpi</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">(</span><span class=\"mf\">134.9768</span><span class=\"p\">,</span> <span class=\"mf\">0.0005</span><span class=\"o\">**</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s1\">&#39;pi^0 mass&#39;</span><span class=\"p\">)</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.34976800e+02</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.00000000e-04</span> <span class=\"o\">+/-</span> <span class=\"mf\">0.00000000e+00</span> <span class=\"p\">(</span><span class=\"mf\">0.000</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">pi</span><span class=\"o\">^</span><span class=\"mi\">0</span> <span class=\"n\">mass</span>     <span class=\"mf\">5.00000000e-04</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Covobs</span>   <span class=\"s1\">&#39;pi^0 mass&#39;</span>\n</code></pre>\n</div>\n\n<p>The resulting object <code>mpi</code> is an <code>Obs</code> that contains a <code>Covobs</code>. In the following, it may be handled as any other <code>Obs</code>. The contribution of the covariance matrix to the error of an <code>Obs</code> is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the <code>Obs</code> with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.</p>\n\n<p>Correlated auxiliary data is defined similarly to above, e.g., via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">RAP</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">([</span><span class=\"mf\">16.7457</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">19.0475</span><span class=\"p\">],</span> <span class=\"p\">[[</span><span class=\"mf\">3.49591</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">,</span> <span class=\"mf\">10.5834</span><span class=\"p\">]],</span> <span class=\"s1\">&#39;R_AP, 1906.03445, (5.3a)&#39;</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">RAP</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">[</span><span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"mf\">16.7</span><span class=\"p\">(</span><span class=\"mf\">1.9</span><span class=\"p\">)],</span> <span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">19.0</span><span class=\"p\">(</span><span class=\"mf\">3.3</span><span class=\"p\">)]]</span>\n</code></pre>\n</div>\n\n<p>where <code>RAP</code> now is a list of two <code>Obs</code> that contains the two correlated parameters.</p>\n\n<p>Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the <code>Covobs</code> class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an <code>Obs</code> <code>o</code> with respect to a covariance matrix with the identifying string <code>k</code> may be accessed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">covobs</span><span class=\"p\">[</span><span class=\"n\">k</span><span class=\"p\">]</span><span class=\"o\">.</span><span class=\"n\">grad</span>\n</code></pre>\n</div>\n\n<h1 id=\"error-propagation-in-iterative-algorithms\">Error propagation in iterative algorithms</h1>\n\n<p><code>pyerrors</code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<h2 id=\"least-squares-fits\">Least squares fits</h2>\n\n<p>Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with <code>pyerrors.fits.least_squares</code>. As default solver the Levenberg-Marquardt algorithm implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html\">scipy</a> is used.</p>\n\n<p>Fit functions have to be of the following form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><strong>It is important that numerical functions refer to <code>autograd.numpy</code> instead of <code>numpy</code> for the automatic differentiation in iterative algorithms to work properly.</strong></p>\n\n<p>Fits can then be performed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">fits</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">func</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"s2\">&quot;</span><span class=\"se\">\\n</span><span class=\"s2\">&quot;</span><span class=\"p\">,</span> <span class=\"n\">fit_result</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"k\">with</span> <span class=\"mi\">2</span> <span class=\"n\">parameters</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Method</span><span class=\"p\">:</span> <span class=\"n\">Levenberg</span><span class=\"o\">-</span><span class=\"n\">Marquardt</span>\n<span class=\"o\">&gt;</span> <span class=\"err\">`</span><span class=\"n\">ftol</span><span class=\"err\">`</span> <span class=\"n\">termination</span> <span class=\"n\">condition</span> <span class=\"ow\">is</span> <span class=\"n\">satisfied</span><span class=\"o\">.</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">chisquare</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span><span class=\"p\">:</span> <span class=\"mf\">0.9593035785160936</span>\n\n<span class=\"o\">&gt;</span>  <span class=\"n\">Goodness</span> <span class=\"n\">of</span> <span class=\"n\">fit</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">\u03c7</span><span class=\"err\">\u00b2</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span> <span class=\"o\">=</span> <span class=\"mf\">0.959304</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">p</span><span class=\"o\">-</span><span class=\"n\">value</span>   <span class=\"o\">=</span> <span class=\"mf\">0.5673</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"n\">parameters</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.0548</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">1.933</span><span class=\"p\">(</span><span class=\"mi\">64</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is a <code>list</code> or <code>numpy.array</code> of <code>floats</code> and y is a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>Data stored in <code>Corr</code> objects can be fitted directly using the <code>Corr.fit</code> method.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">my_corr</span><span class=\"o\">.</span><span class=\"n\">fit</span><span class=\"p\">(</span><span class=\"n\">func</span><span class=\"p\">,</span> <span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">12</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<p>this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</p>\n\n<p>For fit functions with multiple independent variables the fit function can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.\nDetails about how the required covariance matrix is estimated can be found in <code>pyerrors.obs.covariance</code>.\nDirect visualizations of the performed fits can be triggered via <code>resplot=True</code> or <code>qqplot=True</code>.</p>\n\n<p>For all available options including combined fits to multiple datasets see <code>pyerrors.fits.least_squares</code>.</p>\n\n<h2 id=\"total-least-squares-fits\">Total least squares fits</h2>\n\n<p><code>pyerrors</code> can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/odr.html\">scipy</a>, see <code>pyerrors.fits.least_squares</code>. The syntax is identical to the standard least squares case, the only difference being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors</code> provides wrappers for <code>Obs</code>- and <code>CObs</code>-valued matrix operations based on <code>numpy.linalg</code>. The supported functions include:</p>\n\n<ul>\n<li><code>inv</code> for the matrix inverse.</li>\n<li><code>cholseky</code> for the Cholesky decomposition.</li>\n<li><code>det</code> for the matrix determinant.</li>\n<li><code>eigh</code> for eigenvalues and eigenvectors of hermitean matrices.</li>\n<li><code>eig</code> for eigenvalues of general matrices.</li>\n<li><code>pinv</code> for the Moore-Penrose pseudoinverse.</li>\n<li><code>svd</code> for the singular-value-decomposition.</li>\n</ul>\n\n<p>For the full API see <code>pyerrors.linalg</code>.</p>\n\n<h1 id=\"export-data\">Export data</h1>\n\n<p><a href=\"https://xkcd.com/927/\"><img src=\"https://imgs.xkcd.com/comics/standards_2x.png\" width=\"75%\" height=\"75%\"></a></p>\n\n<p>The preferred exported file format within <code>pyerrors</code> is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</p>\n\n<ul>\n<li>What observables are stored? Possibly: How exactly are they defined.</li>\n<li>How does each single ensemble or external quantity contribute to the error of the observable?</li>\n<li>Who did write the file when and on which machine?</li>\n</ul>\n\n<p>This can be achieved by storing all information in one single file. The export routines of <code>pyerrors</code> are written such that as much information as possible is written automatically as described in the following example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s2\">&quot;test_ensemble&quot;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">tag</span> <span class=\"o\">=</span> <span class=\"s2\">&quot;My observable&quot;</span>\n\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">dump_to_json</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">,</span> <span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n<span class=\"c1\"># For a single observable one can equivalently use the class method dump</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">dump</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n\n<span class=\"n\">check</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">load_json</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">)</span>\n\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_obs</span> <span class=\"o\">==</span> <span class=\"n\">check</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<p>The format also allows to directly write out the content of <code>Corr</code> objects or lists and arrays of <code>Obs</code> objects by passing the desired data to <code>pyerrors.input.json.dump_to_json</code>.</p>\n\n<h2 id=\"jsongz-format-specification\">json.gz format specification</h2>\n\n<p>The first entries of the file provide optional auxiliary information:</p>\n\n<ul>\n<li><code>program</code> is a string that indicates which program was used to write the file.</li>\n<li><code>version</code> is a string that specifies the version of the format.</li>\n<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>\n<li><code>date</code> is a string and contains the creation date of the file.</li>\n<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>\n<li><code>description</code> contains information on the content of the file. This field is not filled automatically in <code>pyerrors</code>. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</li>\n</ul>\n\n<p>The only necessary entry of the file is the field\n-<code>obsdata</code>, an array that contains the actual data.</p>\n\n<p>Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of <code>Obs</code>, <code>list</code>, <code>numpy.ndarray</code>, <code>Corr</code>. All <code>Obs</code> inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array <code>obsdata</code>, are treated independently. Each entry of the array <code>obsdata</code> has the following required entries:</p>\n\n<ul>\n<li><code>type</code> is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</li>\n<li><code>value</code> is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:</li>\n<li><code>layout</code> is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</li>\n<li><code>tag</code> is any JSON type. It contains additional information concerning the structure. The <code>tag</code> of an <code>Obs</code> in <code>pyerrors</code> is written here.</li>\n<li><code>reweighted</code> is a Bool that may be used to specify, whether the <code>Obs</code> in the structure have been reweighted.</li>\n<li><code>data</code> is an array that contains the data from MC chains. We will define it below.</li>\n<li><code>cdata</code> is an array that contains the data from external quantities with an error (<code>Covobs</code> in <code>pyerrors</code>). We will define it below.</li>\n</ul>\n\n<p>The array <code>data</code> contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that contains the name of the ensemble</li>\n<li><code>replica</code>, an array that contains an entry per replica of the ensemble.</li>\n</ul>\n\n<p>Each entry of <code>replica</code> contains\n<code>name</code>, a string that contains the name of the replica\n<code>deltas</code>, an array that contains the actual data.</p>\n\n<p>Each entry in <code>deltas</code> corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each <code>Obs</code> inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</p>\n\n<p>The array <code>cdata</code> contains information about the contribution of auxiliary observables, represented by <code>Covobs</code> in <code>pyerrors</code>, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that identifies the covariance matrix</li>\n<li><code>layout</code>, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").</li>\n<li><code>cov</code>, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.</li>\n<li><code>grad</code>, an array that contains N entries, one for each <code>Obs</code> inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</li>\n</ul>\n\n<p>A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</p>\n\n<p>Julia I/O routines for the json.gz format, compatible with <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">ADerrors.jl</a>, can be found <a href=\"https://github.com/fjosw/ADjson.jl\">here</a>.</p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "<p>The class for a correlator (time dependent sequence of pe.Obs).</p>\n\n<p>Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.</p>\n\n<p>The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the <code>None</code> object.</p>\n\n<h6 id=\"initialization\">Initialization</h6>\n\n<p>A simple correlator can be initialized with a list or a one-dimensional array of <code>Obs</code> or <code>Cobs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">corr11</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs1</span><span class=\"p\">,</span> <span class=\"n\">obs2</span><span class=\"p\">])</span>\n<span class=\"n\">corr11</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"n\">obs1</span><span class=\"p\">,</span> <span class=\"n\">obs2</span><span class=\"p\">]))</span>\n</code></pre>\n</div>\n\n<p>A matrix-valued correlator can either be initialized via a two-dimensional array of <code>Corr</code> objects</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">matrix_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"n\">corr11</span><span class=\"p\">,</span> <span class=\"n\">corr12</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"n\">corr21</span><span class=\"p\">,</span> <span class=\"n\">corr22</span><span class=\"p\">]]))</span>\n</code></pre>\n</div>\n\n<p>or alternatively via a three-dimensional array of <code>Obs</code> or <code>CObs</code> of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "<p>Initialize a Corr object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data_input</strong> (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).</li>\n<li><strong>padding</strong> (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.</li>\n<li><strong>prange</strong> (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">data_input</span>, </span><span class=\"param\"><span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">prange</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "<p>We need to project the Correlator with a Vector to get a single value at each timeslice.</p>\n\n<p>The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">vector_l</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vector_r</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">normalize</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "<p>Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>i</strong> (int):\nFirst index to be picked.</li>\n<li><strong>j</strong> (int):\nSecond index to be picked.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "<p>Outputs the correlator in a plotable format.</p>\n\n<p>Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "<p>Symmetrize the correlator around x0=0.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "<p>Anti-symmetrize the correlator around x0=0.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "<p>Checks whether a correlator matrices is symmetric on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "<p>Calculates the per-timeslice trace of a correlator matrix.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "<p>Symmetrizes the correlator matrices on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "<p>Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.</p>\n\n<p>The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[</span><span class=\"mi\">0</span><span class=\"p\">]</span>  <span class=\"c1\"># Ground state vector(s)</span>\n<span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[:</span><span class=\"mi\">3</span><span class=\"p\">]</span>  <span class=\"c1\"># Vectors for the lowest three states</span>\n</code></pre>\n</div>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t0</strong> (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$</li>\n<li><strong>ts</strong> (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.</li>\n<li><strong>sort</strong> (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n<ul>\n<li>\"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)</li>\n<li>\"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.</li>\n<li>None: The GEVP is solved only at ts, no sorting is necessary</li>\n</ul></li>\n<li><strong>vector_obs</strong> (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).</li>\n</ul>\n\n<h6 id=\"other-parameters\">Other Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.</li>\n<li><strong>method</strong> (str):\nMethod used to solve the GEVP.\n<ul>\n<li>\"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)</li>\n<li>\"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.</li>\n</ul></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"n\">vector_obs</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "<p>Determines the eigenvalue of the GEVP by solving and projecting the correlator</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nThe state one is interested in ordered by energy. The lowest state is zero.</li>\n<li><strong>All other parameters are identical to the ones of Corr.GEVP.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">state</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "<p>Constructs an NxN Hankel matrix</p>\n\n<p>C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>N</strong> (int):\nDimension of the Hankel matrix</li>\n<li><strong>periodic</strong> (bool, optional):\ndetermines whether the matrix is extended periodically</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">N</span>, </span><span class=\"param\"><span class=\"n\">periodic</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "<p>Periodically shift the correlator by dt timeslices</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>dt</strong> (int):\nnumber of timeslices</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">dt</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "<p>Reverse the time ordering of the Corr</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "<p>Thin out a correlator to suppress correlations</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>spacing</strong> (int):\nKeep only every 'spacing'th entry of the correlator</li>\n<li><strong>offset</strong> (int):\nOffset the equal spacing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">spacing</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "<p>Correlate the correlator with another correlator or Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>partner</strong> (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "<p>Reweight the correlator.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "<p>Return the time symmetry average of the correlator and its partner</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>partner</strong> (Corr):\nTime symmetry partner of the Corr</li>\n<li><strong>parity</strong> (int):\nParity quantum number of the correlator, can be +1 or -1</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span>, </span><span class=\"param\"><span class=\"n\">parity</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "<p>Return the first derivative of the correlator with respect to x0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "<p>Return the second derivative of the correlator with respect to x0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "<p>Returns the effective mass of the correlator as correlator object</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2</li>\n<li><strong>guess</strong> (float):\nguess for the root finder, only relevant for the root variant</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;log&#39;</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "<p>Fits function to the data</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>function</strong> (obj):\nfunction to fit to the data. See fits.least_squares for details.</li>\n<li><strong>fitrange</strong> (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\n<code>fitrange=[4, 6]</code> corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.</li>\n<li><strong>silent</strong> (bool):\nDecides whether output is printed to the standard output.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">function</span>, </span><span class=\"param\"><span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "<p>Extract a plateau value from a Corr object</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>plateau_range</strong> (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.</li>\n<li><strong>method</strong> (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.</li>\n<li><strong>auto_gamma</strong> (bool):\napply gamma_method with default parameters to the Corr. Defaults to None</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">plateau_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">method</span><span class=\"o\">=</span><span class=\"s1\">&#39;fit&#39;</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "<p>Sets the attribute prange of the Corr object.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">prange</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "<p>Plots the correlator using the tag of the correlator as label if available.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x_range</strong> (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].</li>\n<li><strong>comp</strong> (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale.</li>\n<li><strong>plateau</strong> (Obs):\nPlateau value to be visualized in the figure.</li>\n<li><strong>fit_res</strong> (Fit_result):\nFit_result object to be visualized.</li>\n<li><strong>fit_key</strong> (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).</li>\n<li><strong>ylabel</strong> (str):\nLabel for the y-axis.</li>\n<li><strong>save</strong> (str):\npath to file in which the figure should be saved.</li>\n<li><strong>auto_gamma</strong> (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.</li>\n<li><strong>hide_sigma</strong> (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.</li>\n<li><strong>references</strong> (list):\nList of floating point values that are displayed as horizontal lines for reference.</li>\n<li><strong>title</strong> (string):\nOptional title of the figure.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"bp\">self</span>,</span><span class=\"param\">\t<span class=\"n\">x_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">comp</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">y_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">plateau</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_res</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_key</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">ylabel</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">hide_sigma</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">references</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">title</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "<p>Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>logscale</strong> (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "<p>Dumps the Corr into a file of chosen type</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">print_range</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "<p>Project large correlation matrix to lowest states</p>\n\n<p>This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>Ntrunc</strong> (int):\nRank of the target matrix.</li>\n<li><strong>tproj</strong> (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.</li>\n<li><strong>t0proj</strong> (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.</li>\n<li><strong>basematrix</strong> (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">Ntrunc</span>, </span><span class=\"param\"><span class=\"n\">tproj</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">t0proj</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">basematrix</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "<p>Initialize Covobs object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>mean</strong> (float):\nMean value of the new Obs</li>\n<li><strong>cov</strong> (list or array):\n2d Covariance matrix or 1d diagonal entries</li>\n<li><strong>name</strong> (str):\nidentifier for the covariance matrix</li>\n<li><strong>pos</strong> (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional</li>\n<li><strong>grad</strong> (list or array):\nGradient of the Covobs wrt. the means belonging to cov.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">mean</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">pos</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "<p>Return the variance (= square of the error) of the Covobs</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "<p>Rank-3 epsilon tensor</p>\n\n<p>Based on <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>elem</strong> (int):\nElement (i,j,k) of the epsilon tensor of rank 3</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "<p>Rank-4 epsilon tensor</p>\n\n<p>Extension of <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>elem</strong> (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span>, </span><span class=\"param\"><span class=\"n\">o</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "<p>Returns gamma matrix in Grid labeling.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">gamma_tag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "<p>Represents fit results.</p>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>fit_parameters</strong> (list):\nresults for the individual fit parameters,\nalso accessible via indices.</li>\n<li><strong>chisquare_by_dof</strong> (float):\nreduced chisquare.</li>\n<li><strong>p_value</strong> (float):\np-value of the fit</li>\n<li><strong>t2_p_value</strong> (float):\nHotelling t-squared p-value for correlated fits.</li>\n</ul>\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "<p>Performs a non-linear fit to y = func(x).\n    ```</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>For an uncombined fit:</strong></li>\n<li><strong>x</strong> (list):\nlist of floats.</li>\n<li><strong>y</strong> (list):\nlist of Obs.</li>\n<li><p><strong>func</strong> (object):\nfit function, has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>OR For a combined fit:</strong></li>\n<li><strong>x</strong> (dict):\ndict of lists.</li>\n<li><strong>y</strong> (dict):\ndict of lists of Obs.</li>\n<li><p><strong>funcs</strong> (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}</p>\n\n<p>def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)</p>\n\n<p>def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)</p>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>priors</strong> (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)</li>\n<li><strong>silent</strong> (bool, optional):\nIf true all output to the console is omitted (default False).</li>\n<li><strong>initial_guess</strong> (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.</li>\n<li><strong>method</strong> (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.</li>\n<li><strong>tol</strong> (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm &lt; edm_max)</li>\n<li><strong>correlated_fit</strong> (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see <code>pyerrors.obs.covariance</code>.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).</li>\n<li><strong>inv_chol_cov_matrix [array,list], optional</strong>: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).</li>\n<li><strong>resplot</strong> (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).</li>\n<li><strong>qqplot</strong> (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).</li>\n<li><strong>num_grad</strong> (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>output</strong> (Fit_result):\nParameters and information on the fitted result.</li>\n</ul>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.stats</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">norm</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.linalg</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">cholesky</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># generating the random data set</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">num_samples</span> <span class=\"o\">=</span> <span class=\"mi\">400</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">N</span> <span class=\"o\">=</span> <span class=\"mi\">3</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x1</span> <span class=\"o\">=</span> <span class=\"n\">norm</span><span class=\"o\">.</span><span class=\"n\">rvs</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">num_samples</span><span class=\"p\">))</span> <span class=\"c1\"># generate random numbers</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x2</span> <span class=\"o\">=</span> <span class=\"n\">norm</span><span class=\"o\">.</span><span class=\"n\">rvs</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">num_samples</span><span class=\"p\">))</span> <span class=\"c1\"># generate random numbers</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">r</span> <span class=\"o\">=</span> <span class=\"n\">r1</span> <span class=\"o\">=</span> <span class=\"n\">r2</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">zeros</span><span class=\"p\">((</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">N</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">r</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.8</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">fabs</span><span class=\"p\">(</span><span class=\"n\">i</span> <span class=\"o\">-</span> <span class=\"n\">j</span><span class=\"p\">))</span> <span class=\"c1\"># element in correlation matrix</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">errl</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sqrt</span><span class=\"p\">([</span><span class=\"mf\">3.4</span><span class=\"p\">,</span> <span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"mf\">3.6</span><span class=\"p\">])</span> <span class=\"c1\"># set y errors</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">r</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">*=</span> <span class=\"n\">errl</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">errl</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"c1\"># element in covariance matrix</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"n\">cholesky</span><span class=\"p\">(</span><span class=\"n\">r</span><span class=\"p\">,</span> <span class=\"n\">lower</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"n\">c</span><span class=\"p\">,</span> <span class=\"n\">x1</span><span class=\"p\">),</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"n\">c</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)}</span> <span class=\"c1\"># generate y data with the covariance matrix defined</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">chol_inv_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">data</span> <span class=\"o\">=</span> <span class=\"p\">[]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">key</span> <span class=\"ow\">in</span> <span class=\"n\">y</span><span class=\"o\">.</span><span class=\"n\">keys</span><span class=\"p\">():</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">x_dict</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([[</span><span class=\"n\">i</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\">+</span> <span class=\"n\">o</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">y</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">][</span><span class=\"n\">i</span><span class=\"p\">]]],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ens&#39;</span><span class=\"p\">]))</span> <span class=\"c1\"># generate y Obs from the y data</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"p\">[</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">data</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">covariance</span><span class=\"p\">(</span><span class=\"n\">data</span><span class=\"p\">,</span> <span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">inverrdiag</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">diag</span><span class=\"p\">(</span><span class=\"mi\">1</span> <span class=\"o\">/</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">asarray</span><span class=\"p\">([</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">dvalue</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">data</span><span class=\"p\">]))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">chol_inv</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">obs</span><span class=\"o\">.</span><span class=\"n\">invert_corr_cov_cholesky</span><span class=\"p\">(</span><span class=\"n\">corr</span><span class=\"p\">,</span> <span class=\"n\">inverrdiag</span><span class=\"p\">)</span> <span class=\"c1\"># gives form of the inverse covariance matrix needed for the combined correlated fit below</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y_dict</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">data</span><span class=\"p\">[:</span><span class=\"mi\">3</span><span class=\"p\">],</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"n\">data</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">:]}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># common fit parameter p[0] in combined fit</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">fit1</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">fit2</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fitf_dict</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">fit1</span><span class=\"p\">,</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span><span class=\"n\">fit2</span><span class=\"p\">}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fitp_inv_cov_combined_fit</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x_dict</span><span class=\"p\">,</span><span class=\"n\">y_dict</span><span class=\"p\">,</span> <span class=\"n\">fitf_dict</span><span class=\"p\">,</span> <span class=\"n\">correlated_fit</span> <span class=\"o\">=</span> <span class=\"kc\">True</span><span class=\"p\">,</span> <span class=\"n\">inv_chol_cov_matrix</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"n\">chol_inv</span><span class=\"p\">,[</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">,</span><span class=\"s1\">&#39;b&#39;</span><span class=\"p\">]])</span>\n<span class=\"go\">Fit with 3 parameters</span>\n<span class=\"go\">Method: Levenberg-Marquardt</span>\n<span class=\"go\">`ftol` termination condition is satisfied.</span>\n<span class=\"go\">chisquare/d.o.f.: 0.5388013574561786 # random</span>\n<span class=\"go\">fit parameters [1.11897846 0.96361162 0.92325319] # random</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">priors</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "<p>Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nlist of Obs, or a tuple of lists of Obs</li>\n<li><strong>y</strong> (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</li>\n<li><p><strong>func</strong> (object):\nfunc has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>silent</strong> (bool, optional):\nIf true all output to the console is omitted (default False).</li>\n<li><strong>initial_guess</strong> (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).</li>\n<li><strong>num_grad</strong> (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Based on the orthogonal distance regression module of scipy.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>output</strong> (Fit_result):\nParameters and information on the fitted result.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "<p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.</li>\n<li><strong>y</strong> (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>fit_parameters</strong> (list[Obs]):\nLIist of fitted observables.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "<p>Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">o_y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span>, </span><span class=\"param\"><span class=\"n\">title</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "<p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>\n\n<p>For uncorrelated data the residuals are expected to be distributed ~N(0,1).</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">fit_res</span>, </span><span class=\"param\"><span class=\"n\">title</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "<p>Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>err</strong> (np.array(Obs)):\nError band for an array of sample values x</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">beta</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "<p>Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>objects</strong> (list):\nList of fit results to include in the analysis (optional).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">objects</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "<p><code>pyerrors</code> includes an <code>input</code> submodule in which input routines and parsers for the output of various numerical programs are contained.</p>\n\n<h1 id=\"jackknife-samples\">Jackknife samples</h1>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can also generate jackknife samples from an <code>Obs</code> object or import jackknife samples into an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> and <code>pyerrors.obs.import_jackknife</code> for details.</p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "<p>Extract generic MCMC data from a bdio file</p>\n\n<p>read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path -- path to the bdio file</strong></li>\n<li><strong>bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (List[Obs]):\nExtracted data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "<p>Write Obs to a bdio file according to ADerrors conventions</p>\n\n<p>read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path -- path to the bdio file</strong></li>\n<li><strong>bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>success</strong> (int):\nreturns 0 is successful</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_list</span>, </span><span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "<p>Extract mesons data from a bdio file and return it as a dictionary</p>\n\n<p>The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)</p>\n\n<p>read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (dict):\nExtracted meson data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "<p>Extract dSdm data from a bdio file and return it as a dictionary</p>\n\n<p>The dictionary can be accessed with a tuple consisting of (type, kappa)</p>\n\n<p>read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>xml_str</strong> (str):\nXML formatted string of the input data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obsl</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>, </span><span class=\"param\"><span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "<p>Import a list of Obs from a string in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>content</strong> (str):\nXML string containing the data</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">content</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator |is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>xml_str</strong> (str):\nXML string generated from the data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "<p>Read hadrons hdf5 file and extract entry based on attributes.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filestem</strong> (str):\nFull namestem of the files to read, including the full path.</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>group</strong> (str):\nlabel of the group to be extracted.</li>\n<li><p><strong>attrs</strong> (dict or int):\nDictionary containing the attributes. For example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">attrs</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s2\">&quot;gamma_snk&quot;</span><span class=\"p\">:</span> <span class=\"s2\">&quot;Gamma5&quot;</span><span class=\"p\">,</span>\n         <span class=\"s2\">&quot;gamma_src&quot;</span><span class=\"p\">:</span> <span class=\"s2\">&quot;Gamma5&quot;</span><span class=\"p\">}</span>\n</code></pre>\n</div>\n\n<p>Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.</p></li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>part</strong> (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr</strong> (Corr):\nCorrelator of the source sink combination in question.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">group</span>, </span><span class=\"param\"><span class=\"n\">attrs</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">part</span><span class=\"o\">=</span><span class=\"s1\">&#39;real&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "<p>Read hadrons meson hdf5 file and extract the meson labeled 'meson'</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>meson</strong> (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.</li>\n<li><strong>gammas</strong> (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr</strong> (Corr):\nCorrelator of the source sink combination in question.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">meson</span><span class=\"o\">=</span><span class=\"s1\">&#39;meson_0&#39;</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">gammas</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "<p>Read hadrons FlowObservables hdf5 file and extract t0</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>obs</strong> (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">filestem</span>,</span><span class=\"param\">\t<span class=\"n\">ens_id</span>,</span><span class=\"param\">\t<span class=\"n\">obs</span><span class=\"o\">=</span><span class=\"s1\">&#39;Clover energy density&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "<p>Read hadrons DistillationContraction hdf5 files in given directory structure</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the directories to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>diagrams</strong> (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (dict):\nextracted DistillationContration data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">diagrams</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;direct&#39;</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "<p>ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)</p>\n\n<p>An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)</p>\n\n<p>Arrays should be constructed using <code>array</code>, <code>zeros</code> or <code>empty</code> (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (<code>ndarray(...)</code>) for instantiating an array.</p>\n\n<p>For more information, refer to the <code>numpy</code> module and examine the\nmethods and attributes of an array.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>(for the __new__ method; see Notes below)</strong></li>\n<li><strong>shape</strong> (tuple of ints):\nShape of created array.</li>\n<li><strong>dtype</strong> (data-type, optional):\nAny object that can be interpreted as a numpy data type.</li>\n<li><strong>buffer</strong> (object exposing buffer interface, optional):\nUsed to fill the array with data.</li>\n<li><strong>offset</strong> (int, optional):\nOffset of array data in buffer.</li>\n<li><strong>strides</strong> (tuple of ints, optional):\nStrides of data in memory.</li>\n<li><strong>order</strong> ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.</li>\n</ul>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>T</strong> (ndarray):\nTranspose of the array.</li>\n<li><strong>data</strong> (buffer):\nThe array's elements, in memory.</li>\n<li><strong>dtype</strong> (dtype object):\nDescribes the format of the elements in the array.</li>\n<li><strong>flags</strong> (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.</li>\n<li><strong>flat</strong> (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., <code>x.flat = 3</code> (See <code>ndarray.flat</code> for\nassignment examples; TODO).</li>\n<li><strong>imag</strong> (ndarray):\nImaginary part of the array.</li>\n<li><strong>real</strong> (ndarray):\nReal part of the array.</li>\n<li><strong>size</strong> (int):\nNumber of elements in the array.</li>\n<li><strong>itemsize</strong> (int):\nThe memory use of each array element in bytes.</li>\n<li><strong>nbytes</strong> (int):\nThe total number of bytes required to store the array data,\ni.e., <code>itemsize * size</code>.</li>\n<li><strong>ndim</strong> (int):\nThe array's number of dimensions.</li>\n<li><strong>shape</strong> (tuple of ints):\nShape of the array.</li>\n<li><strong>strides</strong> (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous <code>(3, 4)</code> array of type\n<code>int16</code> in C-order has strides <code>(8, 2)</code>.  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(<code>2 * 4</code>).</li>\n<li><strong>ctypes</strong> (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.</li>\n<li><strong>base</strong> (ndarray):\nIf the array is a view into another array, that array is its <code>base</code>\n(unless that array is also a view).  The <code>base</code> array is where the\narray data is actually stored.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>array</code>:  Construct an array.<br />\n<code>zeros</code>:  Create an array, each element of which is zero.<br />\n<code>empty</code>:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").<br />\n<code>dtype</code>:  Create a data-type.<br />\n<code>numpy.typing.NDArray</code>:  An ndarray alias :term:<code>generic &lt;generic type&gt;</code>\nw.r.t. its <code>dtype.type &lt;numpy.dtype.type&gt;</code>.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>There are two modes of creating an array using <code>__new__</code>:</p>\n\n<ol>\n<li>If <code>buffer</code> is None, then only <code>shape</code>, <code>dtype</code>, and <code>order</code>\nare used.</li>\n<li>If <code>buffer</code> is an object exposing the buffer interface, then\nall keywords are interpreted.</li>\n</ol>\n\n<p>No <code>__init__</code> method is needed because the array is fully initialized\nafter the <code>__new__</code> method.</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>These examples illustrate the low-level <code>ndarray</code> constructor.  Refer\nto the <code>See Also</code> section above for easier ways of constructing an\nndarray.</p>\n\n<p>First mode, <code>buffer</code> is None:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">(</span><span class=\"n\">shape</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">),</span> <span class=\"n\">dtype</span><span class=\"o\">=</span><span class=\"nb\">float</span><span class=\"p\">,</span> <span class=\"n\">order</span><span class=\"o\">=</span><span class=\"s1\">&#39;F&#39;</span><span class=\"p\">)</span>\n<span class=\"go\">array([[0.0e+000, 0.0e+000], # random</span>\n<span class=\"go\">       [     nan, 2.5e-323]])</span>\n</code></pre>\n</div>\n\n<p>Second mode:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">((</span><span class=\"mi\">2</span><span class=\"p\">,),</span> <span class=\"n\">buffer</span><span class=\"o\">=</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">]),</span>\n<span class=\"gp\">... </span>           <span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">int_</span><span class=\"p\">()</span><span class=\"o\">.</span><span class=\"n\">itemsize</span><span class=\"p\">,</span>\n<span class=\"gp\">... </span>           <span class=\"n\">dtype</span><span class=\"o\">=</span><span class=\"nb\">int</span><span class=\"p\">)</span> <span class=\"c1\"># offset = 1*itemsize, i.e. skip first element</span>\n<span class=\"go\">array([2, 3])</span>\n</code></pre>\n</div>\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "<p>Gamma_5 hermitean conjugate</p>\n\n<p>Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.</p>\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "<p>Read hadrons ExternalLeg hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (Npr_matrix):\nread Cobs-matrix</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "<p>Read hadrons Bilinear hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result_dict</strong> (dict[Npr_matrix]):\nextracted Bilinears</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "<p>Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>vertices</strong> (list):\nVertex functions to be extracted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result_dict</strong> (dict):\nextracted fourquark matrizes</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vertices</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;VA&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;AV&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ol</strong> (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>json_string</strong> (str):\nString for export to .json(.gz) file</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ol</strong> (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Null</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "<p>Reconstruct a list of Obs or structures containing Obs from a json string.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>json_string</strong> (str):\njson string containing the data.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nreconstructed list of observables from the json string</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (Obs):\nonly one observable if the list only has one entry</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (dict):\nif full_output=True</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">json_string</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "<p>Import a list of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nreconstructed list of observables from the json string</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (Obs):\nonly one observable if the list only has one entry</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (dict):\nif full_output=True</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "<p>Export a dict of Obs or structures containing Obs to a .json(.gz) file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>od</strong> (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">od</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "<p>Import a dict of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (Obs / list / Corr):\nRead data</li>\n<li><strong>or</strong></li>\n<li><strong>data</strong> (dict):\nRead data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "<p>Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).</p>\n\n<p>It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.</p>\n\n<p>A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t2E_dict</strong> (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)</li>\n<li><strong>observable</strong> (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>root</strong> (Obs):\nThe root of the data series.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">t2E_dict</span>, </span><span class=\"param\"><span class=\"n\">fit_range</span>, </span><span class=\"param\"><span class=\"n\">plot_fit</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">observable</span><span class=\"o\">=</span><span class=\"s1\">&#39;t0&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "<p>Read pbp format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nlist of observables read</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "<p>Read rwms format from given folder structure. Returns a list of length nrw</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath that contains the data files</li>\n<li><strong>prefix</strong> (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.</li>\n<li><strong>version</strong> (str):\nversion of openQCD, default 2.0</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>print_err</strong> (bool):\nPrint additional information that is useful for debugging.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>rwms</strong> (Obs):\nReweighting factors read</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;2.0&#39;</span>, </span><span class=\"param\"><span class=\"n\">names</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "<p>Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to .ms.dat files</li>\n<li><strong>prefix</strong> (str):\nEnsemble prefix</li>\n<li><strong>dtr_read</strong> (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.</li>\n<li><strong>xmin</strong> (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.</li>\n<li><strong>spatial_extent</strong> (int):\nspatial extent of the lattice, required for normalization.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>postfix</strong> (str):\nPostfix of measurement file (Default: ms)</li>\n<li><strong>c</strong> (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>t0</strong> (Obs):\nExtracted t0</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">dtr_read</span>,</span><span class=\"param\">\t<span class=\"n\">xmin</span>,</span><span class=\"param\">\t<span class=\"n\">spatial_extent</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">postfix</span><span class=\"o\">=</span><span class=\"s1\">&#39;ms&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">c</span><span class=\"o\">=</span><span class=\"mf\">0.3</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "<p>Extract w0/a from given .ms.dat files. Returns w0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2<E>)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to .ms.dat files</li>\n<li><strong>prefix</strong> (str):\nEnsemble prefix</li>\n<li><strong>dtr_read</strong> (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.</li>\n<li><strong>xmin</strong> (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.</li>\n<li><strong>spatial_extent</strong> (int):\nspatial extent of the lattice, required for normalization.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>postfix</strong> (str):\nPostfix of measurement file (Default: ms)</li>\n<li><strong>c</strong> (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of w0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>w0</strong> (Obs):\nExtracted w0</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">dtr_read</span>,</span><span class=\"param\">\t<span class=\"n\">xmin</span>,</span><span class=\"param\">\t<span class=\"n\">spatial_extent</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">postfix</span><span class=\"o\">=</span><span class=\"s1\">&#39;ms&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">c</span><span class=\"o\">=</span><span class=\"mf\">0.3</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "<p>Read the topologial charge based on openQCD gradient flow measurements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nEither openQCD or sfqcd, depending on the data.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n<li><strong>integer_charge</strong> (bool):\nIf True, the charge is rounded towards the nearest integer on each config.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (Obs):\nRead topological charge</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;openQCD&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "<p>Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.</p>\n\n<p>Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">Zeuthen_flow</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "<p>Returns the projection to the topological charge sector defined by target.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (Obs):\nTopological charge.</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>reto</strong> (Obs):\nprojection to the topological charge sector defined by target</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">qtop</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "<p>Constructs reweighting factors to a specified topological sector.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs</li>\n<li><strong>r_stop</strong> (list):\nlast configurations that need to be read (per replicum)</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>reto</strong> (Obs):\nprojection to the topological charge sector defined by target</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "<p>Read data from files in the specified directory with the specified prefix and quark combination extension, and return a <code>Corr</code> object containing the data.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nThe directory to search for the files in.</li>\n<li><strong>prefix</strong> (str):\nThe prefix to match the files against.</li>\n<li><strong>qc</strong> (str):\nThe quark combination extension to match the files against.</li>\n<li><strong>corr</strong> (str):\nThe correlator to extract data for.</li>\n<li><strong>sep</strong> (str, optional):\nThe separator to use when parsing the replika names.</li>\n<li><p><strong>**kwargs</strong>: Additional keyword arguments. The following keyword arguments are recognized:</p>\n\n<ul>\n<li>names (List[str]): A list of names to use for the replicas.</li>\n<li>files (List[str]): A list of files to read data from.</li>\n<li>idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.</li>\n</ul></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Corr</strong>: A complex valued <code>Corr</code> object containing the data read from the files. In case of boudary to bulk correlators.</li>\n<li><strong>or</strong></li>\n<li><strong>CObs</strong>: A complex valued <code>CObs</code> object containing the data read from the files. In case of boudary to boundary correlators.</li>\n</ul>\n\n<h6 id=\"raises\">Raises</h6>\n\n<ul>\n<li><strong>FileNotFoundError</strong>: If no files matching the specified prefix and quark combination extension are found in the specified directory.</li>\n<li><strong>IOError</strong>: If there is an error reading a file.</li>\n<li><strong>struct.error</strong>: If there is an error unpacking binary data.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">qc</span>, </span><span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">sep</span><span class=\"o\">=</span><span class=\"s1\">&#39;r&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "<p>Write DataFrame including Obs or Corr valued columns to sqlite database.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be written to the database.</li>\n<li><strong>table_name</strong> (str):\nName of the table in the database.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>if exists</strong> (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.</li>\n<li><strong>gz</strong> (bool):\nIf True the json strings are gzipped.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">table_name</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">if_exists</span><span class=\"o\">=</span><span class=\"s1\">&#39;fail&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "<p>Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sql</strong> (str):\nSQL query to be executed.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (pandas.DataFrame):\nDataframe with the content of the sqlite database.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">sql</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "<p>Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.</p>\n\n<p>Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be dumped to a file.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "<p>Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (pandas.DataFrame):\nDataframe with the content of the sqlite database.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "<p></p>\n", "default_value": "&#x27;/&#x27;"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "<p>Read sfcf files from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to the sfcf files.</li>\n<li><strong>prefix</strong> (str):\nPrefix of the sfcf files.</li>\n<li><strong>name</strong> (str):\nName of the correlation function to read.</li>\n<li><strong>quarks</strong> (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>corr_type</strong> (str):\nType of correlation function to read. Can be\n<ul>\n<li>'bi' for boundary-inner</li>\n<li>'bb' for boundary-boundary</li>\n<li>'bib' for boundary-inner-boundary</li>\n</ul></li>\n<li><strong>noffset</strong> (int):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf</strong> (int):\nID of wave function</li>\n<li><strong>wf2</strong> (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs</strong> (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">quarks</span><span class=\"o\">=</span><span class=\"s1\">&#39;.*&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type</span><span class=\"o\">=</span><span class=\"s1\">&#39;bi&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">noffset</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf2</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "<p>Read sfcf files from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to the sfcf files.</li>\n<li><strong>prefix</strong> (str):\nPrefix of the sfcf files.</li>\n<li><strong>name</strong> (str):\nName of the correlation function to read.</li>\n<li><strong>quarks_list</strong> (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>corr_type_list</strong> (list[str]):\nType of correlation function to read. Can be\n<ul>\n<li>'bi' for boundary-inner</li>\n<li>'bb' for boundary-boundary</li>\n<li>'bib' for boundary-inner-boundary</li>\n</ul></li>\n<li><strong>noffset_list</strong> (list[int]):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf_list</strong> (int):\nID of wave function</li>\n<li><strong>wf2_list</strong> (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs</strong> (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n<li><strong>rep_string</strong> (str):\nSeparator of ensemble name and replicum. Example: In \"ensAr0\", \"r\" would be the separator string.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name_list</span>,</span><span class=\"param\">\t<span class=\"n\">quarks_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;.*&#39;</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;bi&#39;</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">noffset_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">wf_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">wf2_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">keyed_out</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "<p>Utilities for the input</p>\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "<p>Sorts a list of names of replika with searches for <code>r</code> and <code>id</code> in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ll</strong> (list):\nlist to sort</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>ll</strong> (list):\nsorted list</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ll</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "<p>Checks if list of configurations is contained in an idl</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>idl</strong> (range or list):\nidl of the current replicum</li>\n<li><strong>che</strong> (list):\nlist of configurations to be checked against</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>miss_str</strong> (str):\nstring with integers of which idls are missing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">idl</span>, </span><span class=\"param\"><span class=\"n\">che</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "<p>Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nmeasurement path, same as for sfcf read method</li>\n<li><strong>param_hash</strong> (str):\nexpected parameter hash</li>\n<li><strong>prefix</strong> (str):\ndata prefix to find the appropriate replicum folders in path</li>\n<li><strong>param_prefix</strong> (str):\nprefix of the parameter file. Defaults to 'parameters_'</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>nums</strong> (dict):\ndictionary of faulty parameter files sorted by the replica paths</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">param_hash</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">param_prefix</span><span class=\"o\">=</span><span class=\"s1\">&#39;parameters_&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "<p>Performs a (one-dimensional) numeric integration of f(p, x) from a to b.</p>\n\n<p>The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><p><strong>func</strong> (object):\nfunction to integrate, has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is the integration variable.</p></li>\n<li><strong>p</strong> (list of floats or Obs):\nparameters of the function func.</li>\n<li><strong>a</strong> (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).</li>\n<li><strong>b</strong> (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).</li>\n<li><strong>All parameters of scipy.integrate.quad</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>y</strong> (Obs):\nThe integral of func from <code>a</code> to <code>b</code>.</li>\n<li><strong>abserr</strong> (float):\nAn estimate of the absolute error in the result.</li>\n<li><strong>infodict</strong> (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.</li>\n<li><strong>message</strong>: A convergence message.</li>\n<li><strong>explain</strong>: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span>, </span><span class=\"param\"><span class=\"n\">a</span>, </span><span class=\"param\"><span class=\"n\">b</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "<p>Matrix multiply all operands.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n<li><strong>This implementation is faster compared to standard multiplication via the @ operator.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "<p>Matrix multiply both operands making use of the jackknife approximation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n<li><strong>For large matrices this is considerably faster compared to matmul.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "<p>Wrapper for numpy.einsum</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>subscripts</strong> (str):\nSubscripts for summation (see numpy documentation for details)</li>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">subscripts</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "<p>Inverse of Obs or CObs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "<p>Cholesky decomposition of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "<p>Determinant of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "<p>Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "<p>Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "<p>Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "<p>Computes the Moore-Penrose pseudoinverse of a matrix of Obs.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "<p>Computes the singular value decomposition of a matrix of Obs.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "<p>Print information about version of python, pyerrors and dependencies.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "<p>pyerrors wrapper for the errorbars method of matplotlib</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nA list of x-values which can be Obs.</li>\n<li><strong>y</strong> (list):\nA list of y-values which can be Obs.</li>\n<li><strong>axes</strong> ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">x</span>,</span><span class=\"param\">\t<span class=\"n\">y</span>,</span><span class=\"param\">\t<span class=\"n\">axes</span><span class=\"o\">=&lt;</span><span class=\"n\">module</span> <span class=\"s1\">&#39;matplotlib.pyplot&#39;</span> <span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"s1\">&#39;/opt/hostedtoolcache/Python/3.10.16/x64/lib/python3.10/site-packages/matplotlib/pyplot.py&#39;</span><span class=\"o\">&gt;</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "<p>Dump object into pickle file.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obj</strong> (object):\nobject to be saved in the pickle file</li>\n<li><strong>name</strong> (str):\nname of the file</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obj</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "<p>Load object from pickle file.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the file</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>object</strong> (Obs):\nLoaded Object</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "<p>Generate an Obs object with given value, dvalue and name for test purposes</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>value</strong> (float):\ncentral value of the Obs to be generated.</li>\n<li><strong>dvalue</strong> (float):\nerror of the Obs to be generated.</li>\n<li><strong>name</strong> (str):\nname of the ensemble for which the Obs is to be generated.</li>\n<li><strong>samples</strong> (int):\nnumber of samples for the Obs (default 1000).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (Obs):\nGenerated Observable</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">value</span>, </span><span class=\"param\"><span class=\"n\">dvalue</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "<p>Generate observables with given covariance and autocorrelation times.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>means</strong> (list):\nlist containing the mean value of each observable.</li>\n<li><strong>cov</strong> (numpy.ndarray):\ncovariance matrix for the data to be generated.</li>\n<li><strong>name</strong> (str):\nensemble name for the data to be geneated.</li>\n<li><strong>tau</strong> (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.</li>\n<li><strong>samples</strong> (int):\nnumber of samples to be generated for each observable.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr_obs</strong> (list[Obs]):\nGenerated observable list</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">tau</span><span class=\"o\">=</span><span class=\"mf\">0.5</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "<p>Matrix pencil method to extract k energy levels from data</p>\n\n<p>Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data</strong> (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.</li>\n<li><strong>k</strong> (int):\nNumber of states to extract (default 1).</li>\n<li><strong>p</strong> (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>energy_levels</strong> (list[Obs]):\nExtracted energy levels</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corrs</span>, </span><span class=\"param\"><span class=\"n\">k</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">p</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "<p>Class for a general observable.</p>\n\n<p>Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.</p>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>S_global</strong> (float):\nStandard value for S (default 2.0)</li>\n<li><strong>S_dict</strong> (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.</li>\n<li><strong>tau_exp_global</strong> (float):\nStandard value for tau_exp (default 0.0)</li>\n<li><strong>tau_exp_dict</strong> (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.</li>\n<li><strong>N_sigma_global</strong> (float):\nStandard value for N_sigma (default 1.0)</li>\n<li><strong>N_sigma_dict</strong> (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.</li>\n</ul>\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "<p>Initialize Obs object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>samples</strong> (list):\nlist of numpy arrays containing the Monte Carlo samples</li>\n<li><strong>names</strong> (list):\nlist of strings labeling the individual samples</li>\n<li><strong>idl</strong> (list, optional):\nlist of ranges or lists on which the samples are defined</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">samples</span>, </span><span class=\"param\"><span class=\"n\">names</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span>)</span>"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "<p>Estimate the error and related properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>S</strong> (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.</li>\n<li><strong>tau_exp</strong> (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).</li>\n<li><strong>N_sigma</strong> (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).</li>\n<li><strong>fft</strong> (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "<p>Estimate the error and related properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>S</strong> (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.</li>\n<li><strong>tau_exp</strong> (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).</li>\n<li><strong>N_sigma</strong> (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).</li>\n<li><strong>fft</strong> (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "<p>Output detailed properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ens_content</strong> (bool):\nprint details about the ensembles and replica if true.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">ens_content</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "<p>Reweight the obs with given rewighting factors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "<p>Checks whether the observable is zero within 'sigma' standard errors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sigma</strong> (int):\nNumber of standard errors used for the check.</li>\n<li><strong>Works only properly when the gamma method was run.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">sigma</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "<p>Checks whether the observable is zero within a given tolerance.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">atol</span><span class=\"o\">=</span><span class=\"mf\">1e-10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "<p>Plot integrated autocorrelation time for each ensemble.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "<p>Plot normalized autocorrelation function time for each ensemble.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "<p>Plot replica distribution for each ensemble with more than one replicum.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "<p>Plot derived Monte Carlo history for each ensemble</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>expand</strong> (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">expand</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "<p>Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "<p>Dump the Obs to a file 'name' of chosen format.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nname of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>description</strong> (str):\nDescription for output file, only relevant for json.gz format.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "<p>Export jackknife samples from the Obs</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>numpy.ndarray</strong>: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "<p>Export bootstrap samples from the Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>samples</strong> (int):\nNumber of bootstrap samples to generate.</li>\n<li><strong>random_numbers</strong> (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.</li>\n<li><strong>save_rng</strong> (str):\nSave the random numbers to a file if a path is specified.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>numpy.ndarray</strong>: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">500</span>, </span><span class=\"param\"><span class=\"n\">random_numbers</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">save_rng</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "<p>Class for a complex valued observable.</p>\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">real</span>, </span><span class=\"param\"><span class=\"n\">imag</span><span class=\"o\">=</span><span class=\"mf\">0.0</span></span>)</span>"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "<p>Executes the gamma_method for the real and the imaginary part.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "<p>Checks whether both real and imaginary part are zero within machine precision.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "<p>Vectorized version of the gamma_method applicable to lists or arrays of Obs.</p>\n\n<p>See docstring of pe.Obs.gamma_method for details.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "<p>Vectorized version of the gamma_method applicable to lists or arrays of Obs.</p>\n\n<p>See docstring of pe.Obs.gamma_method for details.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "<p>Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>func</strong> (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').</li>\n<li><strong>data</strong> (list):\nlist of Obs, e.g. [obs1, obs2, obs3].</li>\n<li><strong>num_grad</strong> (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.</li>\n<li><strong>man_grad</strong> (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use</p>\n\n<p>new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">data</span>, </span><span class=\"param\"><span class=\"n\">array_mode</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "<p>Reweight a list of observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>obs</strong> (list):\nlist of Obs, e.g. [obs1, obs2, obs3].</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "<p>Correlate two observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs_a</strong> (Obs):\nFirst observable</li>\n<li><strong>obs_b</strong> (Obs):\nSecond observable</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nOnly works if a single ensemble is present in the Obs.\nCurrently only works if ensemble content is identical (this is not strictly necessary).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_a</span>, </span><span class=\"param\"><span class=\"n\">obs_b</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "<p>Calculates the error covariance matrix of a set of observables.</p>\n\n<p>WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.</p>\n\n<p>The gamma method has to be applied first to all observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs</strong> (list or numpy.ndarray):\nList or one dimensional array of Obs</li>\n<li><strong>visualize</strong> (bool):\nIf True plots the corresponding normalized correlation matrix (default False).</li>\n<li><strong>correlation</strong> (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).</li>\n<li><strong>smooth</strong> (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"n\">visualize</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">smooth</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "<p>Constructs a lower triangular matrix <code>chol</code> via the Cholesky decomposition of the correlation matrix <code>corr</code>\n   and then returns the inverse covariance matrix <code>chol_inv</code> as a lower triangular matrix by solving <code>chol * x = inverrdiag</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>corr</strong> (np.ndarray):\ncorrelation matrix</li>\n<li><strong>inverrdiag</strong> (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">inverrdiag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "<p>Reorders a correlation matrix to match the alphabetical order of its underlying y data.</p>\n\n<p>The ordering of the input correlation matrix <code>corr</code> is given by the list of keys <code>kl</code>.\nThe input dictionary <code>yd</code> (with the same keys <code>kl</code>) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys <code>kl</code> alphabetically and sorts the matrix <code>corr</code>\naccording to this alphabetical order such that the sorted matrix <code>corr_sorted</code> corresponds\nto the y data <code>yd</code> when arranged in an alphabetical order by its keys.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>corr</strong> (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by <code>kl</code>.\nThe dimensions of <code>corr</code> should match the total number of y data points in <code>yd</code> combined.</li>\n<li><strong>kl</strong> (list of str):\nA list of keys that denotes the order in which the y data from <code>yd</code> was used to build the\ninput correlation matrix <code>corr</code>.</li>\n<li><strong>yd</strong> (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof <code>corr</code>. The lists in the dictionary can be lists of Obs.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>np.ndarray</strong>: A new, sorted correlation matrix that corresponds to the y data from <code>yd</code> when arranged alphabetically by its keys.</li>\n</ul>\n\n<h6 id=\"example\">Example</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">corr</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mf\">0.3</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mf\">0.3</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">kl</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"s1\">&#39;b&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;a&#39;</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yd</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">],</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">]}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sorted_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">obs</span><span class=\"o\">.</span><span class=\"n\">sort_corr</span><span class=\"p\">(</span><span class=\"n\">corr</span><span class=\"p\">,</span> <span class=\"n\">kl</span><span class=\"p\">,</span> <span class=\"n\">yd</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">sorted_corr</span><span class=\"p\">)</span>\n<span class=\"go\">array([[1. , 0.3, 0.4],</span>\n<span class=\"go\">       [0.3, 1. , 0.2],</span>\n<span class=\"go\">       [0.4, 0.2, 1. ]])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">kl</span>, </span><span class=\"param\"><span class=\"n\">yd</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "<p>Imports jackknife samples and returns an Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>jacks</strong> (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.</li>\n<li><strong>name</strong> (str):\nname of the ensemble the samples are defined on.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">jacks</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "<p>Imports bootstrap samples and returns an Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>boots</strong> (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.</li>\n<li><strong>name</strong> (str):\nname of the ensemble the samples are defined on.</li>\n<li><strong>random_numbers</strong> (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">boots</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">random_numbers</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "<p>Combine all observables in list_of_obs into one new observable.\nThis allows to merge Obs that have been computed on multiple replica\nof the same ensemble.\nIf you like to merge Obs that are based on several ensembles, please\naverage them yourself.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>list_of_obs</strong> (list):\nlist of the Obs object to be combined</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is not possible to combine obs which are based on the same replicum</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">list_of_obs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "<p>Create an Obs based on mean(s) and a covariance matrix</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>mean</strong> (list of floats or float):\nN mean value(s) of the new Obs</li>\n<li><strong>cov</strong> (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance</li>\n<li><strong>name</strong> (str):\nidentifier for the covariance matrix</li>\n<li><strong>grad</strong> (list or array):\nGradient of the Covobs wrt. the means belonging to cov.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "<p>Finds the root of the function func(x, d) where d is an <code>Obs</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>d</strong> (Obs):\nObs passed to the function.</li>\n<li><p><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">root_func</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">x</span> <span class=\"o\">**</span> <span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">d</span>\n</code></pre>\n</div></li>\n<li><p><strong>guess</strong> (float):\nInitial guess for the minimization.</p></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (Obs):\n<code>Obs</code> valued root of the function.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">d</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "<p>beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>beta(a, b, out=None)</p>\n\n<p>Beta function.</p>\n\n<p>This function is defined in <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> as</p>\n\n<p>$$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nReal-valued arguments</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function result</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the beta function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>betainc</code>:   the regularized incomplete beta function<br />\n<code>betaln</code>:  the natural logarithm of the absolute\nvalue of the beta function  </p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>The beta function relates to the gamma function by the\ndefinition given above:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"go\">0.08333333333333333</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span><span class=\"o\">*</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"go\">0.08333333333333333</span>\n</code></pre>\n</div>\n\n<p>As this relationship demonstrates, the beta function\nis symmetric:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mf\">1.7</span><span class=\"p\">,</span> <span class=\"mf\">2.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.16567527689031739</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mf\">2.4</span><span class=\"p\">,</span> <span class=\"mf\">1.7</span><span class=\"p\">)</span>\n<span class=\"go\">0.16567527689031739</span>\n</code></pre>\n</div>\n\n<p>This function satisfies \\( B(1, b) = 1/b \\):</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">)</span>\n<span class=\"go\">0.25</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. <a href=\"https://dlmf.nist.gov/5.12\">https://dlmf.nist.gov/5.12</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "<p>betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>betainc(a, b, x, out=None)</p>\n\n<p>Regularized incomplete beta function.</p>\n\n<p>Computes the regularized incomplete beta function, defined as <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>:</p>\n\n<p>$$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$</p>\n\n<p>for \\( 0 \\leq x \\leq 1 \\).</p>\n\n<p>This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nPositive, real-valued parameters</li>\n<li><strong>x</strong> (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the regularized incomplete beta function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>beta</code>:  beta function<br />\n<code>betaincinv</code>:  inverse of the regularized incomplete beta function<br />\n<code>betaincc</code>:  complement of the regularized incomplete beta function<br />\n<code>scipy.stats.beta</code>:  beta distribution  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The term <em>regularized</em> in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as <em>regularized</em>, the name <em>incomplete\nbeta function</em> often refers to just the integral expression,\nwithout the gamma terms.  One can use the function <code>beta</code> from\n<code>scipy.special</code> to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of <code>betainc(a, b, x)</code> by\n<code>beta(a, b)</code>.</p>\n\n<p>This function wraps the <code>ibeta</code> routine from the\nBoost Math C++ library <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">2</a></sup>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Let \\( B(a, b) \\) be the <code>beta</code> function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>The coefficient in terms of <code>gamma</code> is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">1.0</span><span class=\"p\">)</span>\n<span class=\"go\">1.0</span>\n</code></pre>\n</div>\n\n<p>It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function <code>hyp2f1</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">1.4</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span><span class=\"o\">**</span><span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">hyp2f1</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">a</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">))</span>\n<span class=\"go\">0.8148904036225295</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.8148904036225296</span>\n</code></pre>\n</div>\n\n<p>This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">2.2</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.49339638807619446</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">2.2</span><span class=\"p\">,</span> <span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"mf\">0.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.49339638807619446</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/8.17\">https://dlmf.nist.gov/8.17</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>The Boost Developers. \"Boost C++ Libraries\". <a href=\"https://www.boost.org/\">https://www.boost.org/</a>.&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "<p>betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>betaln(a, b, out=None)</p>\n\n<p>Natural logarithm of absolute value of beta function.</p>\n\n<p>Computes <code>ln(abs(beta(a, b)))</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nPositive, real-valued parameters</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the betaln function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>betainc</code>:   the regularized incomplete beta function<br />\n<code>beta</code>:  the beta function  </p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">betaln</span><span class=\"p\">,</span> <span class=\"n\">beta</span>\n</code></pre>\n</div>\n\n<p>Verify that, for moderate values of <code>a</code> and <code>b</code>, <code>betaln(a, b)</code>\nis the same as <code>log(beta(a, b))</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">betaln</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">)</span>\n<span class=\"go\">-4.0943445622221</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">))</span>\n<span class=\"go\">-4.0943445622221</span>\n</code></pre>\n</div>\n\n<p>In the following <code>beta(a, b)</code> underflows to 0, so we can't compute\nthe logarithm of the actual value.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"mi\">400</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"mi\">900</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">0.0</span>\n</code></pre>\n</div>\n\n<p>We can compute the logarithm of <code>beta(a, b)</code> by using <code>betaln</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">betaln</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">-804.3069951764146</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "<p>Polygamma functions.</p>\n\n<p>Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\n<code>digamma</code> function. See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>n</strong> (array_like):\nThe order of the derivative of the digamma function; must be\nintegral</li>\n<li><strong>x</strong> (array_like):\nReal valued input</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>ndarray</strong>: Function results</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>digamma</code>  </p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    <a href=\"https://dlmf.nist.gov/5.15\">https://dlmf.nist.gov/5.15</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">25.5</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">polygamma</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.64493407,  0.39493407,  0.03999467])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">polygamma</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ True,  True,  True], dtype=bool)</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "<p>psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>psi(z, out=None)</p>\n\n<p>The digamma function.</p>\n\n<p>The logarithmic derivative of the gamma function evaluated at <code>z</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex argument.</li>\n<li><strong>out</strong> (ndarray, optional):\nArray for the computed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>digamma</strong> (scalar or ndarray):\nComputed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For large values not close to the negative real axis, <code>psi</code> is\ncomputed using the asymptotic series (5.11.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">2</a></sup> is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">3</a></sup> is\nused first. Note that <code>psi</code> has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">4</a></sup>, so the\nfunction should maintain full accuracy around the origin.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">psi</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mi\">3</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<p>Verify psi(z) = psi(z + 1) - 1/z:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"o\">/</span><span class=\"n\">z</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 3 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) <a href=\"http://mpmath.org/\">http://mpmath.org/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 4 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "<p>psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>psi(z, out=None)</p>\n\n<p>The digamma function.</p>\n\n<p>The logarithmic derivative of the gamma function evaluated at <code>z</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex argument.</li>\n<li><strong>out</strong> (ndarray, optional):\nArray for the computed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>digamma</strong> (scalar or ndarray):\nComputed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For large values not close to the negative real axis, <code>psi</code> is\ncomputed using the asymptotic series (5.11.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">2</a></sup> is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">3</a></sup> is\nused first. Note that <code>psi</code> has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">4</a></sup>, so the\nfunction should maintain full accuracy around the origin.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">psi</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mi\">3</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<p>Verify psi(z) = psi(z + 1) - 1/z:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"o\">/</span><span class=\"n\">z</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 3 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) <a href=\"http://mpmath.org/\">http://mpmath.org/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 4 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "<p>gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gamma(z, out=None)</p>\n\n<p>gamma function.</p>\n\n<p>The gamma function is defined as</p>\n\n<p>$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$</p>\n\n<p>for \\( \\Re(z) &gt; 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex valued argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the gamma function</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).</p>\n\n<p>The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.</p>\n\n<p>Prior to SciPy version 1.15, <code>scipy.special.gamma(z)</code> returned <code>+inf</code>\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as</p>\n\n<p><code>gamma(u) * gamma(v) / (gamma(w) * gamma(x))</code></p>\n\n<p>no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function <code>rgamma</code> for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas</p>\n\n<p><code>gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))</code></p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5.2#E1\">https://dlmf.nist.gov/5.2#E1</a>\n.. [isoc99] <a href=\"https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf\">https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">gamma</span><span class=\"p\">,</span> <span class=\"n\">factorial</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">5</span><span class=\"p\">])</span>\n<span class=\"go\">array([         inf,   1.77245385,   1.        ,  24.        ])</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mf\">2.5</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(0.77476210455108352+0.70763120437959293j)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"n\">z</span><span class=\"o\">*</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>  <span class=\"c1\"># Recurrence property</span>\n<span class=\"go\">((1.2292740569981171+2.5438401155000685j),</span>\n<span class=\"go\"> (1.2292740569981158+2.5438401155000658j))</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mi\">2</span>  <span class=\"c1\"># gamma(0.5) = sqrt(pi)</span>\n<span class=\"go\">3.1415926535897927</span>\n</code></pre>\n</div>\n\n<p>Plot gamma(x) for real x</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">5.5</span><span class=\"p\">,</span> <span class=\"mi\">2251</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">,</span> <span class=\"n\">alpha</span><span class=\"o\">=</span><span class=\"mf\">0.6</span><span class=\"p\">,</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"s1\">&#39;gamma(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">k</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">7</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">k</span><span class=\"p\">,</span> <span class=\"n\">factorial</span><span class=\"p\">(</span><span class=\"n\">k</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"s1\">&#39;k*&#39;</span><span class=\"p\">,</span> <span class=\"n\">alpha</span><span class=\"o\">=</span><span class=\"mf\">0.6</span><span class=\"p\">,</span>\n<span class=\"gp\">... </span>         <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"s1\">&#39;(x-1)!, x = 1, 2, ...&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">5.5</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">(</span><span class=\"n\">loc</span><span class=\"o\">=</span><span class=\"s1\">&#39;lower right&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "<p>gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammaln(x, out=None)</p>\n\n<p>Logarithm of the absolute value of the gamma function.</p>\n\n<p>Defined as</p>\n\n<p>$$\\ln(\\lvert\\Gamma(x)\\rvert)$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the log of the absolute value of gamma</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammasgn</code>:  sign of the gamma function<br />\n<code>loggamma</code>:  principal branch of the logarithm of the gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is the same function as the Python standard library function\n<code>math.lgamma()</code>.</p>\n\n<p>When used in conjunction with <code>gammasgn</code>, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation <code>exp(gammaln(x)) =\ngammasgn(x) * gamma(x)</code>.</p>\n\n<p>For complex-valued log-gamma, use <code>loggamma</code> instead of <code>gammaln</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It has two positive zeros.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">])</span>\n<span class=\"go\">array([0., 0.])</span>\n</code></pre>\n</div>\n\n<p>It has poles at nonpositive integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([inf, inf, inf, inf, inf])</span>\n</code></pre>\n</div>\n\n<p>It asymptotically approaches <code>x * log(x)</code> (Stirling's formula).</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">1e10</span><span class=\"p\">,</span> <span class=\"mf\">1e20</span><span class=\"p\">,</span> <span class=\"mf\">1e40</span><span class=\"p\">,</span> <span class=\"mf\">1e80</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "<p>gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammainc(a, x, out=None)</p>\n\n<p>Regularized lower incomplete gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$</p>\n\n<p>for \\( a &gt; 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nPositive parameter</li>\n<li><strong>x</strong> (array_like):\nNonnegative argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the lower incomplete gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammaincc</code>:  regularized upper incomplete gamma function<br />\n<code>gammaincinv</code>:  inverse of the regularized lower incomplete gamma function<br />\n<code>gammainccinv</code>:  inverse of the regularized upper incomplete gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The function satisfies the relation <code>gammainc(a, x) +\ngammaincc(a, x) = 1</code> where <code>gammaincc</code> is the regularized upper\nincomplete gamma function.</p>\n\n<p>The implementation largely follows that of [boost]_.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical functions\n          <a href=\"https://dlmf.nist.gov/8.2#E4\">https://dlmf.nist.gov/8.2#E4</a>\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   <a href=\"https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html\">https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">])</span>\n<span class=\"go\">array([0.        , 0.84270079, 0.99999226, 1.        ])</span>\n</code></pre>\n</div>\n\n<p>It is equal to one minus the upper incomplete gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.6289066304773024</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.6289066304773024</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "<p>gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammaincc(a, x, out=None)</p>\n\n<p>Regularized upper incomplete gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$</p>\n\n<p>for \\( a &gt; 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nPositive parameter</li>\n<li><strong>x</strong> (array_like):\nNonnegative argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the upper incomplete gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammainc</code>:  regularized lower incomplete gamma function<br />\n<code>gammaincinv</code>:  inverse of the regularized lower incomplete gamma function<br />\n<code>gammainccinv</code>:  inverse of the regularized upper incomplete gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The function satisfies the relation <code>gammainc(a, x) +\ngammaincc(a, x) = 1</code> where <code>gammainc</code> is the regularized lower\nincomplete gamma function.</p>\n\n<p>The implementation largely follows that of [boost]_.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical functions\n          <a href=\"https://dlmf.nist.gov/8.2#E4\">https://dlmf.nist.gov/8.2#E4</a>\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   <a href=\"https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html\">https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,</span>\n<span class=\"go\">       0.00000000e+00])</span>\n</code></pre>\n</div>\n\n<p>It is equal to one minus the lower incomplete gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.37109336952269756</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.37109336952269756</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "<p>gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammasgn(x, out=None)</p>\n\n<p>Sign of the gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 &amp; \\Gamma(x) &gt; 0 \\\n  -1 &amp; \\Gamma(x) &lt; 0\n\\end{cases}$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function; see <code>gamma</code>. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Sign of the gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>gammaln</code>:  log of the absolute value of the gamma function<br />\n<code>loggamma</code>:  analytic continuation of the log of the gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function can be computed as <code>gammasgn(x) *\nnp.exp(gammaln(x))</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5.2#E1\">https://dlmf.nist.gov/5.2#E1</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is 1 for <code>x &gt; 0</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1., 1., 1., 1.])</span>\n</code></pre>\n</div>\n\n<p>It alternates between -1 and 1 for negative integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">])</span>\n<span class=\"go\">array([-1.,  1., -1.,  1.])</span>\n</code></pre>\n</div>\n\n<p>It can be used to compute the gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"go\">array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "<p>rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>rgamma(z, out=None)</p>\n\n<p>Reciprocal of the gamma function.</p>\n\n<p>Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see <code>gamma</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex valued input</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Function results</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma,</code>, <code>gammaln,</code>, <code>loggamma</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function has no zeros and has simple poles at\nnonpositive integers, so <code>rgamma</code> is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] Nist, Digital Library of Mathematical functions,\n    <a href=\"https://dlmf.nist.gov/5.2#i\">https://dlmf.nist.gov/5.2#i</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the reciprocal of the gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.        , 1.        , 0.5       , 0.16666667])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">/</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.        , 1.        , 0.5       , 0.16666667])</span>\n</code></pre>\n</div>\n\n<p>It is zero at nonpositive integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"go\">array([0., 0., 0., 0.])</span>\n</code></pre>\n</div>\n\n<p>It rapidly underflows to zero along the positive real axis.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">,</span> <span class=\"mi\">179</span><span class=\"p\">])</span>\n<span class=\"go\">array([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "<p>Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (ndarray):\nThe multivariate gamma is computed for each item of <code>a</code>.</li>\n<li><strong>d</strong> (int):\nThe dimension of the space of integration.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (ndarray):\nThe values of the log multivariate gamma at the given points <code>a</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The formal definition of the multivariate gamma of dimension d for a real\n<code>a</code> is</p>\n\n<p>$$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$</p>\n\n<p>with the condition \\( a &gt; (d-1)/2 \\), and \\( A &gt; 0 \\) being the set of\nall the positive definite matrices of dimension <code>d</code>.  Note that <code>a</code> is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).</p>\n\n<p>This can be proven to be equal to the much friendlier equation</p>\n\n<p>$$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">multigammaln</span><span class=\"p\">,</span> <span class=\"n\">gammaln</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"mf\">23.5</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">d</span> <span class=\"o\">=</span> <span class=\"mi\">10</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">multigammaln</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">)</span>\n<span class=\"go\">454.1488605074416</span>\n</code></pre>\n</div>\n\n<p>Verify that the result agrees with the logarithm of the equation\nshown above:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">d</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">d</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">pi</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">))</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">()</span>\n<span class=\"go\">454.1488605074416</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "<p>Modified Bessel function of the second kind of integer order n</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "<p>j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>j0(x, out=None)</p>\n\n<p>Bessel function of the first kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jv</code>:  Bessel function of real order and complex argument.<br />\n<code>spherical_jn</code>:  spherical Bessel functions.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:</p>\n\n<p>$$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$</p>\n\n<p>where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.</p>\n\n<p>In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>j0</code>.\nIt should not be confused with the spherical Bessel functions (see\n<code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">j0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.7651976865579665</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">4.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([ 0.22389078,  1.        , -0.39714981])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -20 to 20.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "<p>y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>y0(x, out=None)</p>\n\n<p>Bessel function of the second kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>j0</code>:  Bessel function of the first kind of order 0<br />\n<code>yv</code>:  Bessel function of the first kind  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,</p>\n\n<p>$$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$</p>\n\n<p>where \\( J_0 \\) is the Bessel function of the first kind of order 0.</p>\n\n<p>In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>y0</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">y0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.08825696421567697</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-0.44451873,  0.51037567,  0.37685001])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "<p>j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>j1(x, out=None)</p>\n\n<p>Bessel function of the first kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jv</code>:  Bessel function of the first kind<br />\n<code>spherical_jn</code>:  spherical Bessel functions.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>j1</code>.\nIt should not be confused with the spherical Bessel functions (see\n<code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">j1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.44005058574493355</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">4.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-0.57672481,  0.        , -0.06604333])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -20 to 20.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "<p>y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>y1(x, out=None)</p>\n\n<p>Bessel function of the second kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>j1</code>:  Bessel function of the first kind of order 1<br />\n<code>yn</code>:  Bessel function of the second kind<br />\n<code>yv</code>:  Bessel function of the second kind  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>y1</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">y1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">-0.7812128213002888</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-1.47147239, -0.10703243,  0.32467442])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "<p>jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>jv(v, z, out=None)</p>\n\n<p>Bessel function of the first kind of real order and complex argument.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like):\nOrder (float).</li>\n<li><strong>z</strong> (array_like):\nArgument (float or complex).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jve</code>:  \\( J_v \\) with leading exponential behavior stripped off.<br />\n<code>spherical_jn</code>:  spherical Bessel functions.<br />\n<code>j0</code>:  faster version of this function for order 0.<br />\n<code>j1</code>:  faster version of this function for order 1.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For positive <code>v</code> values, the computation is carried out using the AMOS\n<sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> <code>zbesj</code> routine, which exploits the connection to the modified\nBessel function \\( I_v \\),</p>\n\n<p>$$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z &gt; 0)</p>\n\n<p>J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z &lt; 0)$$</p>\n\n<p>For negative <code>v</code> values the formula,</p>\n\n<p>$$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$</p>\n\n<p>is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine <code>zbesy</code>.  Note that the second\nterm is exactly zero for integer <code>v</code>; to improve accuracy the second\nterm is explicitly omitted for <code>v</code> values such that <code>v = floor(v)</code>.</p>\n\n<p>Not to be confused with the spherical Bessel functions (see <code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">jv</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.7651976865579666</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.76519769, 0.44005059, 0.24029784])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.22389078,  1.        , -0.26005195])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 0.22389078,  1.        , -0.26005195],</span>\n<span class=\"go\">       [-0.57672481,  0.        ,  0.33905896]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -10 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$J_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "<p>yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>yn(n, x, out=None)</p>\n\n<p>Bessel function of the second kind of integer order and real argument.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>n</strong> (array_like):\nOrder (integer).</li>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>yv</code>:  For real order and real or complex argument.<br />\n<code>y0</code>:  faster implementation of this function for order 0<br />\n<code>y1</code>:  faster implementation of this function for order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>yn</code>.</p>\n\n<p>The function is evaluated by forward recurrence on <code>n</code>, starting with\nvalues computed by the Cephes routines <code>y0</code> and <code>y1</code>. If <code>n = 0</code> or 1,\nthe routine for <code>y0</code> or <code>y1</code> is called directly.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">yn</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.08825696421567697</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.08825696, -0.78121282, -1.65068261])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">,</span> <span class=\"mf\">8.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([-0.44451873,  0.37685001,  0.22352149])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[-0.44451873,  0.37685001,  0.22352149],</span>\n<span class=\"go\">       [-1.47147239,  0.32467442, -0.15806046]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$Y_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "<p>i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>i0(x, out=None)</p>\n\n<p>Modified Bessel function of order 0.</p>\n\n<p>Defined as,</p>\n\n<p>$$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$</p>\n\n<p>where \\( J_0 \\) is the Bessel function of the first kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float)</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>I</strong> (scalar or ndarray):\nValue of the modified Bessel function of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of any order<br />\n<code>i0e</code>:  Exponentially scaled modified Bessel function of order 0  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>i0</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">i0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">1.2660658777520082</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.5</span><span class=\"p\">]))</span>\n<span class=\"go\">array([2.2795853 , 1.        , 7.37820343])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -10 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "<p>i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>i1(x, out=None)</p>\n\n<p>Modified Bessel function of order 1.</p>\n\n<p>Defined as,</p>\n\n<p>$$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$</p>\n\n<p>where \\( J_1 \\) is the Bessel function of the first kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float)</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>I</strong> (scalar or ndarray):\nValue of the modified Bessel function of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of the first kind<br />\n<code>i1e</code>:  Exponentially scaled modified Bessel function of order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>i1</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">i1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.5651591039924851</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">6.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-1.59063685,  0.        , 61.34193678])</span>\n</code></pre>\n</div>\n\n<p>Plot the function between -10 and 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "<p>iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>iv(v, z, out=None)</p>\n\n<p>Modified Bessel function of the first kind of real order.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like):\nOrder. If <code>z</code> is of real type and negative, <code>v</code> must be integer\nvalued.</li>\n<li><strong>z</strong> (array_like of float or complex):\nArgument.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the modified Bessel function.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>ive</code>:  This function with leading exponential behavior stripped off.<br />\n<code>i0</code>:  Faster version of this function for order 0.<br />\n<code>i1</code>:  Faster version of this function for order 1.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For real <code>z</code> and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>.  For larger orders, uniform asymptotic\nexpansions are applied.</p>\n\n<p>For complex <code>z</code> and positive <code>v</code>, the AMOS <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">2</a></sup> <code>zbesi</code> routine is\ncalled. It uses a power series for small <code>z</code>, the asymptotic expansion\nfor large <code>abs(z)</code>, the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.</p>\n\n<p>The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,</p>\n\n<p>$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$</p>\n\n<p>(valid when the real part of <code>z</code> is positive).  For negative <code>v</code>, the\nformula</p>\n\n<p>$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$</p>\n\n<p>is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine <code>zbesk</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">iv</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">1.2660658777520084</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(1.2660658777520084, 0.565159103992485, 0.2935253263474798)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([1.26606588, 0.5651591 , 0.29352533])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.2795853 , 1.        , 4.88079259])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 2.2795853 ,  1.        ,  4.88079259],</span>\n<span class=\"go\">       [-1.59063685,  0.        ,  3.95337022]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -5 to 5.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$I_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Temme, Journal of Computational Physics, vol 21, 343 (1976)&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "<p>ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>ive(v, z, out=None)</p>\n\n<p>Exponentially scaled modified Bessel function of the first kind.</p>\n\n<p>Defined as::</p>\n\n<pre><code>ive(v, z) = iv(v, z) * exp(-abs(z.real))\n</code></pre>\n\n<p>For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind <code>iv</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like of float):\nOrder.</li>\n<li><strong>z</strong> (array_like of float or complex):\nArgument.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the exponentially scaled modified Bessel function.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of the first kind<br />\n<code>i0e</code>:  Faster implementation of this function for order 0<br />\n<code>i1e</code>:  Faster implementation of this function for order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For positive <code>v</code>, the AMOS <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> <code>zbesi</code> routine is called. It uses a\npower series for small <code>z</code>, the asymptotic expansion for large\n<code>abs(z)</code>, the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.</p>\n\n<p>The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,</p>\n\n<p>$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$</p>\n\n<p>(valid when the real part of <code>z</code> is positive).  For negative <code>v</code>, the\nformula</p>\n\n<p>$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$</p>\n\n<p>is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine <code>zbesk</code>.</p>\n\n<p><code>ive</code> is useful for large arguments <code>z</code>: for these, <code>iv</code> easily overflows,\nwhile <code>ive</code> does not due to the exponential scaling.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>In the following example <code>iv</code> returns infinity whereas <code>ive</code> still returns\na finite number.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">iv</span><span class=\"p\">,</span> <span class=\"n\">ive</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">1000.</span><span class=\"p\">),</span> <span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">1000.</span><span class=\"p\">)</span>\n<span class=\"go\">(inf, 0.01256056218254712)</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.46575961, 0.20791042, 0.10798193])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.30850832, 1.        , 0.24300035])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for different orders by\nproviding arrays for both <code>v</code> for <code>z</code>. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]],</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 0.30850832,  1.        ,  0.24300035],</span>\n<span class=\"go\">       [-0.21526929,  0.        ,  0.19682671],</span>\n<span class=\"go\">       [ 0.09323903,  0.        ,  0.11178255]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -5 to 5.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">fr</span><span class=\"s1\">&#39;$I_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">(z)\\cdot e^</span><span class=\"se\">{{</span><span class=\"s1\">-|z|</span><span class=\"se\">}}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"sa\">r</span><span class=\"s2\">&quot;$z$&quot;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "<p>erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erf(z, out=None)</p>\n\n<p>Returns the error function of complex argument.</p>\n\n<p>It is defined as <code>2/sqrt(pi)*integral(exp(-t**2), t=0..z)</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nInput array.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (scalar or ndarray):\nThe values of the error function at the given points <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erfc,</code>, <code>erfinv,</code>, <code>erfcinv,</code>, <code>wofz,</code>, <code>erfcx,</code>, <code>erfi</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The cumulative of the unit normal distribution is given by\n<code>Phi(z) = 1/2[1 + erf(z/sqrt(2))]</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">erf</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$x$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$erf(x)$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "<p>erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfc(x, out=None)</p>\n\n<p>Complementary error function, <code>1 - erf(x)</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal or complex valued argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the complementary error function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf,</code>, <code>erfi,</code>, <code>erfcx,</code>, <code>dawsn,</code>, <code>wofz</code>  </p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">erfc</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$x$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$erfc(x)$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "<p>erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfinv(y, out=None)</p>\n\n<p>Inverse of the error function.</p>\n\n<p>Computes the inverse of the error function.</p>\n\n<p>In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 &lt; x &lt; 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>y</strong> (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>erfinv</strong> (scalar or ndarray):\nThe inverse of erf of y, element-wise</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf</code>:  Error function of a complex argument<br />\n<code>erfc</code>:  Complementary error function, <code>1 - erf(x)</code><br />\n<code>erfcinv</code>:  Inverse of the complementary error function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>This function wraps the <code>erf_inv</code> routine from the\nBoost Math C++ library <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">erfinv</span><span class=\"p\">,</span> <span class=\"n\">erf</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span>\n<span class=\"go\">0.4769362762044699</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">1.0</span><span class=\"p\">,</span> <span class=\"mf\">1.0</span><span class=\"p\">,</span> <span class=\"n\">num</span><span class=\"o\">=</span><span class=\"mi\">9</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span>\n<span class=\"go\">array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,</span>\n<span class=\"go\">        0.22531206,  0.47693628,  0.81341985,         inf])</span>\n</code></pre>\n</div>\n\n<p>Verify that <code>erf(erfinv(y))</code> is <code>y</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erf</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])</span>\n</code></pre>\n</div>\n\n<p>Plot the function:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">200</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">(</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;y&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_title</span><span class=\"p\">(</span><span class=\"s1\">&#39;erfinv(y)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>The Boost Developers. \"Boost C++ Libraries\". <a href=\"https://www.boost.org/\">https://www.boost.org/</a>.&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "<p>erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfcinv(y, out=None)</p>\n\n<p>Inverse of the complementary error function.</p>\n\n<p>Computes the inverse of the complementary error function.</p>\n\n<p>In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 &lt; x &lt; 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).</p>\n\n<p>It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>y</strong> (ndarray):\nArgument at which to evaluate. Domain: [0, 2]</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>erfcinv</strong> (scalar or ndarray):\nThe inverse of erfc of y, element-wise</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf</code>:  Error function of a complex argument<br />\n<code>erfc</code>:  Complementary error function, <code>1 - erf(x)</code><br />\n<code>erfinv</code>:  Inverse of the error function  </p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">erfcinv</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span>\n<span class=\"go\">0.4769362762044699</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">2.0</span><span class=\"p\">,</span> <span class=\"n\">num</span><span class=\"o\">=</span><span class=\"mi\">11</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"go\">array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,</span>\n<span class=\"go\">       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,</span>\n<span class=\"go\">              -inf])</span>\n</code></pre>\n</div>\n\n<p>Plot the function:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">200</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">(</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;y&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_title</span><span class=\"p\">(</span><span class=\"s1\">&#39;erfcinv(y)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "<p>logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>logit(x, out=None)</p>\n\n<p>Logit ufunc for ndarrays.</p>\n\n<p>The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p&lt;0 or p>1 yields nan.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nThe ndarray to apply logit to element-wise.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>expit</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee <a href=\"https://docs.scipy.org/doc/numpy/reference/ufuncs.html\">ufuncs </a></p>\n\n<p><em>New in version 0.10.0.</em></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">logit</span><span class=\"p\">,</span> <span class=\"n\">expit</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logit</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">0.25</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.75</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"go\">array([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])</span>\n</code></pre>\n</div>\n\n<p><code>expit</code> is the inverse of <code>logit</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">expit</span><span class=\"p\">(</span><span class=\"n\">logit</span><span class=\"p\">([</span><span class=\"mf\">0.1</span><span class=\"p\">,</span> <span class=\"mf\">0.75</span><span class=\"p\">,</span> <span class=\"mf\">0.999</span><span class=\"p\">]))</span>\n<span class=\"go\">array([ 0.1  ,  0.75 ,  0.999])</span>\n</code></pre>\n</div>\n\n<p>Plot logit(x) for x in [0, 1]:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">501</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">logit</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">title</span><span class=\"p\">(</span><span class=\"s1\">&#39;logit(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "<p>expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>expit(x, out=None)</p>\n\n<p>Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.</p>\n\n<p>The expit function, also known as the logistic sigmoid function, is\ndefined as <code>expit(x) = 1/(1+exp(-x))</code>.  It is the inverse of the\nlogit function.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nThe ndarray to apply expit to element-wise.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: An ndarray of the same shape as x. Its entries\nare <code>expit</code> of the corresponding entry of x.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>logit</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee <a href=\"https://docs.scipy.org/doc/numpy/reference/ufuncs.html\">ufuncs </a></p>\n\n<p><em>New in version 0.10.0.</em></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">expit</span><span class=\"p\">,</span> <span class=\"n\">logit</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">expit</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">inf</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">inf</span><span class=\"p\">])</span>\n<span class=\"go\">array([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])</span>\n</code></pre>\n</div>\n\n<p><code>logit</code> is the inverse of <code>expit</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logit</span><span class=\"p\">(</span><span class=\"n\">expit</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">5.0</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-2.5,  0. ,  3.1,  5. ])</span>\n</code></pre>\n</div>\n\n<p>Plot expit(x) for x in [-6, 6]:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">121</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">expit</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">title</span><span class=\"p\">(</span><span class=\"s1\">&#39;expit(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "<p>Compute the log of the sum of exponentials of input elements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nInput array.</li>\n<li><p><strong>axis</strong> (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default <code>axis</code> is None,\nand all elements are summed.</p>\n\n<p><em>New in version 0.11.0.</em></p></li>\n<li><p><strong>b</strong> (array-like, optional):\nScaling factor for exp(<code>a</code>) must be of the same shape as <code>a</code> or\nbroadcastable to <code>a</code>. These values may be negative in order to\nimplement subtraction.</p>\n\n<p><em>New in version 0.12.0.</em></p></li>\n<li><p><strong>keepdims</strong> (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.</p>\n\n<p><em>New in version 0.15.0.</em></p></li>\n<li><p><strong>return_sign</strong> (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).</p>\n\n<p><em>New in version 0.16.0.</em></p></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (ndarray):\nThe result, <code>np.log(np.sum(np.exp(a)))</code> calculated in a numerically\nmore stable way. If <code>b</code> is given then <code>np.log(np.sum(b*np.exp(a)))</code>\nis returned. If <code>return_sign</code> is True, <code>res</code> contains the log of\nthe absolute value of the argument.</li>\n<li><strong>sgn</strong> (ndarray):\nIf <code>return_sign</code> is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in <code>res</code>.\nIf <code>return_sign</code> is False, only one result is returned.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>numpy.logaddexp,</code>, <code>numpy.logaddexp2</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>NumPy has a logaddexp function which is very similar to <code>logsumexp</code>, but\nonly handles two arguments. <code>logaddexp.reduce</code> is similar to this\nfunction, but may be less stable.</p>\n\n<p>The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">logsumexp</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"go\">9.4586297444267107</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)))</span>\n<span class=\"go\">9.4586297444267107</span>\n</code></pre>\n</div>\n\n<p>With weights</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"o\">=</span><span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">9.9170178533034665</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">(</span><span class=\"n\">b</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)))</span>\n<span class=\"go\">9.9170178533034647</span>\n</code></pre>\n</div>\n\n<p>Returning a sign flag</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">],</span><span class=\"n\">b</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">],</span><span class=\"n\">return_sign</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"go\">(1.5413248546129181, -1.0)</span>\n</code></pre>\n</div>\n\n<p>Notice that <code>logsumexp</code> does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ma</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">),</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)],</span>\n<span class=\"gp\">... </span>                 <span class=\"n\">mask</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"kc\">False</span><span class=\"p\">,</span> <span class=\"kc\">True</span><span class=\"p\">,</span> <span class=\"kc\">False</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"o\">~</span><span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">mask</span><span class=\"p\">)</span><span class=\"o\">.</span><span class=\"n\">astype</span><span class=\"p\">(</span><span class=\"nb\">int</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"o\">=</span><span class=\"n\">b</span><span class=\"p\">),</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">)</span>\n<span class=\"go\">1.6094379124341005, 1.6094379124341005</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8400}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 367}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, 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Some of its features are:</p>\n\n<ul>\n<li>automatic differentiation for exact linear error propagation as suggested in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a> (partly based on the <a href=\"https://github.com/HIPS/autograd\">autograd</a> package).</li>\n<li>treatment of slow modes in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>.</li>\n<li>coherent error propagation for data from different Markov chains.</li>\n<li>non-linear fits with x- and y-errors and exact linear error propagation based on automatic differentiation as introduced in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</li>\n<li>real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).</li>\n</ul>\n\n<p>More detailed examples can found in the <a href=\"https://github.com/fjosw/pyerrors/tree/develop/examples\">GitHub repository</a> <a href=\"https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples\"><img src=\"https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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\" alt=\"badge\" /></a>.</p>\n\n<p>If you use <code>pyerrors</code> for research that leads to a publication please consider citing:</p>\n\n<ul>\n<li>Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, <em>pyerrors: a python framework for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 288 (2023) 108750.</li>\n<li>Ulli Wolff, <em>Monte Carlo errors with less errors</em>. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</li>\n<li>Alberto Ramos, <em>Automatic differentiation for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 238 (2019) 19-35.</li>\n</ul>\n\n<p>and</p>\n\n<ul>\n<li>Stefan Schaefer, Rainer Sommer, Francesco Virotta, <em>Critical slowing down and error analysis in lattice QCD simulations</em>. Nucl.Phys.B 845 (2011) 93-119.</li>\n</ul>\n\n<p>where applicable.</p>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a>, <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a> and <a href=\"https://github.com/mbruno46/pyobs\">Python</a>.</p>\n\n<h2 id=\"installation\">Installation</h2>\n\n<p>Install the most recent release using pip and <a href=\"https://pypi.org/project/pyerrors/\">pypi</a>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>python<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>pyerrors<span class=\"w\">     </span><span class=\"c1\"># Fresh install</span>\npython<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>-U<span class=\"w\"> </span>pyerrors<span class=\"w\">  </span><span class=\"c1\"># Update</span>\n</code></pre>\n</div>\n\n<p>Install the most recent release using conda and <a href=\"https://anaconda.org/conda-forge/pyerrors\">conda-forge</a>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>conda<span class=\"w\"> </span>install<span class=\"w\"> </span>-c<span class=\"w\"> </span>conda-forge<span class=\"w\"> </span>pyerrors<span class=\"w\">  </span><span class=\"c1\"># Fresh install</span>\nconda<span class=\"w\"> </span>update<span class=\"w\"> </span>-c<span class=\"w\"> </span>conda-forge<span class=\"w\"> </span>pyerrors<span class=\"w\">   </span><span class=\"c1\"># Update</span>\n</code></pre>\n</div>\n\n<p>Install the current <code>develop</code> version:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code>python<span class=\"w\"> </span>-m<span class=\"w\"> </span>pip<span class=\"w\"> </span>install<span class=\"w\"> </span>-U<span class=\"w\"> </span>--no-deps<span class=\"w\"> </span>--force-reinstall<span class=\"w\"> </span>git+https://github.com/fjosw/pyerrors.git@develop\n</code></pre>\n</div>\n\n<p>(Also works for any feature branch).</p>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span> <span class=\"c1\"># Initialize an Obs object</span>\n<span class=\"n\">my_new_obs</span> <span class=\"o\">=</span> <span class=\"mi\">2</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">)</span> <span class=\"o\">/</span> <span class=\"n\">my_obs</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"c1\"># Construct derived Obs object</span>\n<span class=\"n\">my_new_obs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>                     <span class=\"c1\"># Estimate the statistical error</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_new_obs</span><span class=\"p\">)</span>                             <span class=\"c1\"># Print the result to stdout</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.31498</span><span class=\"p\">(</span><span class=\"mi\">72</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h1 id=\"the-obs-class\">The <code>Obs</code> class</h1>\n\n<p><code>pyerrors</code> introduces a new datatype, <code>Obs</code>, which simplifies error propagation and estimation for auto- and cross-correlated data.\nAn <code>Obs</code> object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.\nThe samples can either be provided as python list or as numpy array.\nThe second argument is a list containing the names of the respective Monte Carlo chains as strings. These strings uniquely identify a Monte Carlo chain/ensemble. <strong>It is crucial for the correct error propagation that observations from the same Monte Carlo history are labeled with the same name. See <a href=\"#multiple-ensemblesreplica\">Multiple ensembles/replica</a> for details.</strong></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<h2 id=\"error-propagation\">Error propagation</h2>\n\n<p>When performing mathematical operations on <code>Obs</code> objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion\n$$\\delta_f^i=\\sum_\\alpha \\bar{f}_\\alpha \\delta_\\alpha^i\\,,\\quad \\delta_\\alpha^i=a_\\alpha^i-\\bar{a}_\\alpha\\,,$$\nas introduced in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nThe required derivatives $\\bar{f}_\\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<p>The <code>Obs</code> class is designed such that mathematical numpy functions can be used on <code>Obs</code> just as for regular floats.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">my_obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble_name&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">my_obs1</span> <span class=\"o\">+</span> <span class=\"n\">my_obs2</span>\n\n<span class=\"n\">my_m_eff</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">my_obs1</span> <span class=\"o\">/</span> <span class=\"n\">my_obs2</span><span class=\"p\">)</span>\n\n<span class=\"n\">iamzero</span> <span class=\"o\">=</span> <span class=\"n\">my_m_eff</span> <span class=\"o\">-</span> <span class=\"n\">my_m_eff</span>\n<span class=\"c1\"># Check that value and fluctuations are zero within machine precision</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">iamzero</span> <span class=\"o\">==</span> <span class=\"mf\">0.0</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<h2 id=\"error-estimation\">Error estimation</h2>\n\n<p>The error estimation within <code>pyerrors</code> is based on the gamma method introduced in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nAfter having arrived at the derived quantity of interest the <code>gamma_method</code> can be called as detailed in the following example.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_sum</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">1.70</span><span class=\"p\">(</span><span class=\"mi\">57</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.72046658e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">7.56746598e-02</span> <span class=\"p\">(</span><span class=\"mf\">33.650</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">2.71422900e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.40320983e-01</span> <span class=\"n\">S</span> <span class=\"o\">=</span> <span class=\"mf\">2.00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>The <code>gamma_method</code> is not automatically called after every intermediate step in order to prevent computational overhead.</p>\n\n<p>We use the following definition of the integrated autocorrelation time established in <a href=\"https://link.springer.com/article/10.1007/BF01022990\">Madras &amp; Sokal 1988</a>\n$$\\tau_\\mathrm{int}=\\frac{1}{2}+\\sum_{t=1}^{W}\\rho(t)\\geq \\frac{1}{2}\\,.$$\nThe window $W$ is determined via the automatic windowing procedure described in <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>.\nThe standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the <code>gamma_method</code> as parameter.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">(</span><span class=\"n\">S</span><span class=\"o\">=</span><span class=\"mf\">3.0</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.30675201e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">1.04585650e-01</span> <span class=\"p\">(</span><span class=\"mf\">37.099</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">3.29909703e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">9.77310102e-01</span> <span class=\"n\">S</span> <span class=\"o\">=</span> <span class=\"mf\">3.00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>The integrated autocorrelation time $\\tau_\\mathrm{int}$ and the autocorrelation function $\\rho(W)$ can be monitored via the methods <code>pyerrors.obs.Obs.plot_tauint</code> and <code>pyerrors.obs.Obs.plot_rho</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.\nIn this case the error estimate is identical to the sample standard error.</p>\n\n<h3 id=\"exponential-tails\">Exponential tails</h3>\n\n<p>Slow modes in the Monte Carlo history can be accounted for by attaching an exponential tail to the autocorrelation function $\\rho$ as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>. The longest autocorrelation time in the history, $\\tau_\\mathrm{exp}$, can be passed to the <code>gamma_method</code> as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">(</span><span class=\"n\">tau_exp</span><span class=\"o\">=</span><span class=\"mf\">7.2</span><span class=\"p\">)</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.70000000e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">6.28097762e-01</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.79077524e-02</span> <span class=\"p\">(</span><span class=\"mf\">36.947</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">t_int</span>         <span class=\"mf\">3.27218667e+00</span> <span class=\"o\">+/-</span> <span class=\"mf\">7.99583654e-01</span> <span class=\"n\">tau_exp</span> <span class=\"o\">=</span> <span class=\"mf\">7.20</span><span class=\"p\">,</span>  <span class=\"n\">N_sigma</span> <span class=\"o\">=</span> <span class=\"mi\">1</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1000</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble_name&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For the full API see <code>pyerrors.obs.Obs.gamma_method</code>.</p>\n\n<h2 id=\"multiple-ensemblesreplica\">Multiple ensembles/replica</h2>\n\n<p>Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their <code>name</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble2&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">obs1</span> <span class=\"o\">+</span> <span class=\"n\">obs2</span>\n<span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>   <span class=\"mf\">2.00697958e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">2</span> <span class=\"n\">ensembles</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble2&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Observables from the <strong>same Monte Carlo chain</strong> have to be initialized with the <strong>same name</strong> for correct error propagation. If different names were used in this case the data would be treated as statistically independent resulting in loss of relevant information and a potential over or under estimate of the statistical error.</p>\n\n<p><code>pyerrors</code> identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar <code>|</code> in the name of the data set.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1|r01&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1|r02&#39;</span><span class=\"p\">])</span>\n\n<span class=\"o\">&gt;</span> <span class=\"n\">my_sum</span> <span class=\"o\">=</span> <span class=\"n\">obs1</span> <span class=\"o\">+</span> <span class=\"n\">obs2</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">my_sum</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>   <span class=\"mf\">2.00697958e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span>\n<span class=\"o\">&gt;</span>     <span class=\"err\">\u00b7</span> <span class=\"n\">Replicum</span> <span class=\"s1\">&#39;r01&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">1000</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>     <span class=\"err\">\u00b7</span> <span class=\"n\">Replicum</span> <span class=\"s1\">&#39;r02&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h3 id=\"error-estimation-for-multiple-ensembles\">Error estimation for multiple ensembles</h3>\n\n<p>In order to keep track of different error analysis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">S_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">2.5</span>\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">tau_exp_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble2&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">8.0</span>\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"o\">.</span><span class=\"n\">tau_exp_dict</span><span class=\"p\">[</span><span class=\"s1\">&#39;ensemble3&#39;</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"mf\">2.0</span>\n</code></pre>\n</div>\n\n<p>In case the <code>gamma_method</code> is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.\nPassing arguments to the <code>gamma_method</code> still dominates over the dictionaries.</p>\n\n<h2 id=\"irregular-monte-carlo-chains\">Irregular Monte Carlo chains</h2>\n\n<p><code>Obs</code> objects defined on irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"c1\"># Observable defined on configurations 20 to 519</span>\n<span class=\"n\">obs1</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">20</span><span class=\"p\">,</span> <span class=\"mi\">520</span><span class=\"p\">)])</span>\n<span class=\"n\">obs1</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">9.98319881e-01</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">20</span> <span class=\"n\">to</span> <span class=\"mi\">519</span><span class=\"p\">)</span>\n\n<span class=\"c1\"># Observable defined on every second configuration between 5 and 1003</span>\n<span class=\"n\">obs2</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">,</span> <span class=\"mi\">1005</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">)])</span>\n<span class=\"n\">obs2</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">9.99100712e-01</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">500</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">500</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"mi\">5</span> <span class=\"n\">to</span> <span class=\"mi\">1003</span> <span class=\"ow\">in</span> <span class=\"n\">steps</span> <span class=\"n\">of</span> <span class=\"mi\">2</span><span class=\"p\">)</span>\n\n<span class=\"c1\"># Observable defined on configurations 2, 9, 28, 29 and 501</span>\n<span class=\"n\">obs3</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples3</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">],</span> <span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"p\">[[</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">9</span><span class=\"p\">,</span> <span class=\"mi\">28</span><span class=\"p\">,</span> <span class=\"mi\">29</span><span class=\"p\">,</span> <span class=\"mi\">501</span><span class=\"p\">]])</span>\n<span class=\"n\">obs3</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.01718064e+00</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Ensemble</span> <span class=\"s1\">&#39;ensemble1&#39;</span> <span class=\"p\">:</span> <span class=\"mi\">5</span> <span class=\"n\">configurations</span> <span class=\"p\">(</span><span class=\"n\">irregular</span> <span class=\"nb\">range</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><code>Obs</code> objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</p>\n\n<p><strong>Warning:</strong> Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.\nMake sure to check the autocorrelation time with e.g. <code>pyerrors.obs.Obs.plot_rho</code> or <code>pyerrors.obs.Obs.plot_tauint</code>.</p>\n\n<p>For the full API see <code>pyerrors.obs.Obs</code>.</p>\n\n<h1 id=\"correlators\">Correlators</h1>\n\n<p>When one is not interested in single observables but correlation functions, <code>pyerrors</code> offers the <code>Corr</code> class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a <code>Corr</code> objects one needs to arrange the data as a list of <code>Obs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">],</span> <span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">4</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span>\n</code></pre>\n</div>\n\n<p>The individual entries of a correlator can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Error propagation with the <code>Corr</code> class works very similar to <code>Obs</code> objects. Mathematical operations are overloaded and <code>Corr</code> objects can be computed together with other <code>Corr</code> objects, <code>Obs</code> objects or real numbers and integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_new_corr</span> <span class=\"o\">=</span> <span class=\"mf\">0.3</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">+</span> <span class=\"mi\">12</span> <span class=\"o\">/</span> <span class=\"n\">my_corr</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>\n\n<ul>\n<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>\n<li><code>Corr.m_eff</code> to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</li>\n<li><code>Corr.deriv</code> returns the first derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.second_deriv</code> returns the second derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.symmetric</code> symmetrizes parity even correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.anti_symmetric</code> anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.T_symmetry</code> averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</li>\n<li><code>Corr.plateau</code> extracts a plateau value from the correlator in a given range.</li>\n<li><code>Corr.roll</code> periodically shifts the correlator.</li>\n<li><code>Corr.reverse</code> reverses the time ordering of the correlator.</li>\n<li><code>Corr.correlate</code> constructs a disconnected correlation function from the correlator and another <code>Corr</code> or <code>Obs</code> object.</li>\n<li><code>Corr.reweight</code> reweights the correlator.</li>\n</ul>\n\n<p><code>pyerrors</code> can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see <code>pyerrors.correlators.Corr.GEVP</code>).</p>\n\n<p>For the full API see <code>pyerrors.correlators.Corr</code>.</p>\n\n<h1 id=\"complex-valued-observables\">Complex valued observables</h1>\n\n<p><code>pyerrors</code> can handle complex valued observables via the class <code>pyerrors.obs.CObs</code>.\n<code>CObs</code> are initialized with a real and an imaginary part which both can be <code>Obs</code> valued.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_real_part</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n<span class=\"n\">my_imag_part</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples2</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ensemble1&#39;</span><span class=\"p\">])</span>\n\n<span class=\"n\">my_cobs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">CObs</span><span class=\"p\">(</span><span class=\"n\">my_real_part</span><span class=\"p\">,</span> <span class=\"n\">my_imag_part</span><span class=\"p\">)</span>\n<span class=\"n\">my_cobs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_cobs</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">(</span><span class=\"mf\">0.9959</span><span class=\"p\">(</span><span class=\"mi\">91</span><span class=\"p\">)</span><span class=\"o\">+</span><span class=\"mf\">0.659</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span><span class=\"n\">j</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Elementary mathematical operations are overloaded and samples are properly propagated as for the <code>Obs</code> class.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_derived_cobs</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"n\">my_cobs</span> <span class=\"o\">+</span> <span class=\"n\">my_cobs</span><span class=\"o\">.</span><span class=\"n\">conjugate</span><span class=\"p\">())</span> <span class=\"o\">/</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">abs</span><span class=\"p\">(</span><span class=\"n\">my_cobs</span><span class=\"p\">)</span>\n<span class=\"n\">my_derived_cobs</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_derived_cobs</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">(</span><span class=\"mf\">1.668</span><span class=\"p\">(</span><span class=\"mi\">23</span><span class=\"p\">)</span><span class=\"o\">+</span><span class=\"mf\">0.0</span><span class=\"n\">j</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<h1 id=\"the-covobs-class\">The <code>Covobs</code> class</h1>\n\n<p>In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The <code>Covobs</code> class allows to define such quantities in <code>pyerrors</code>. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</p>\n\n<p>This concept is built into the definition of <code>Covobs</code>. In <code>pyerrors</code>, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). <strong>Note, that the square of the error enters <code>cov_Obs</code></strong>, since the second argument of this function is the covariance matrix of the <code>Covobs</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors.obs</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n\n<span class=\"n\">mpi</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">(</span><span class=\"mf\">134.9768</span><span class=\"p\">,</span> <span class=\"mf\">0.0005</span><span class=\"o\">**</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s1\">&#39;pi^0 mass&#39;</span><span class=\"p\">)</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">details</span><span class=\"p\">()</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Result</span>         <span class=\"mf\">1.34976800e+02</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.00000000e-04</span> <span class=\"o\">+/-</span> <span class=\"mf\">0.00000000e+00</span> <span class=\"p\">(</span><span class=\"mf\">0.000</span><span class=\"o\">%</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span>  <span class=\"n\">pi</span><span class=\"o\">^</span><span class=\"mi\">0</span> <span class=\"n\">mass</span>     <span class=\"mf\">5.00000000e-04</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span> <span class=\"n\">samples</span> <span class=\"ow\">in</span> <span class=\"mi\">1</span> <span class=\"n\">ensemble</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span>   <span class=\"err\">\u00b7</span> <span class=\"n\">Covobs</span>   <span class=\"s1\">&#39;pi^0 mass&#39;</span>\n</code></pre>\n</div>\n\n<p>The resulting object <code>mpi</code> is an <code>Obs</code> that contains a <code>Covobs</code>. In the following, it may be handled as any other <code>Obs</code>. The contribution of the covariance matrix to the error of an <code>Obs</code> is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the <code>Obs</code> with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.</p>\n\n<p>Correlated auxiliary data is defined similarly to above, e.g., via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">RAP</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">([</span><span class=\"mf\">16.7457</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">19.0475</span><span class=\"p\">],</span> <span class=\"p\">[[</span><span class=\"mf\">3.49591</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">,</span> <span class=\"mf\">10.5834</span><span class=\"p\">]],</span> <span class=\"s1\">&#39;R_AP, 1906.03445, (5.3a)&#39;</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">RAP</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">[</span><span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"mf\">16.7</span><span class=\"p\">(</span><span class=\"mf\">1.9</span><span class=\"p\">)],</span> <span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">19.0</span><span class=\"p\">(</span><span class=\"mf\">3.3</span><span class=\"p\">)]]</span>\n</code></pre>\n</div>\n\n<p>where <code>RAP</code> now is a list of two <code>Obs</code> that contains the two correlated parameters.</p>\n\n<p>Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the <code>Covobs</code> class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an <code>Obs</code> <code>o</code> with respect to a covariance matrix with the identifying string <code>k</code> may be accessed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">covobs</span><span class=\"p\">[</span><span class=\"n\">k</span><span class=\"p\">]</span><span class=\"o\">.</span><span class=\"n\">grad</span>\n</code></pre>\n</div>\n\n<h1 id=\"error-propagation-in-iterative-algorithms\">Error propagation in iterative algorithms</h1>\n\n<p><code>pyerrors</code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<h2 id=\"least-squares-fits\">Least squares fits</h2>\n\n<p>Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with <code>pyerrors.fits.least_squares</code>. As default solver the Levenberg-Marquardt algorithm implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html\">scipy</a> is used.</p>\n\n<p>Fit functions have to be of the following form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><strong>It is important that numerical functions refer to <code>autograd.numpy</code> instead of <code>numpy</code> for the automatic differentiation in iterative algorithms to work properly.</strong></p>\n\n<p>Fits can then be performed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">fits</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">func</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"s2\">&quot;</span><span class=\"se\">\\n</span><span class=\"s2\">&quot;</span><span class=\"p\">,</span> <span class=\"n\">fit_result</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"k\">with</span> <span class=\"mi\">2</span> <span class=\"n\">parameters</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Method</span><span class=\"p\">:</span> <span class=\"n\">Levenberg</span><span class=\"o\">-</span><span class=\"n\">Marquardt</span>\n<span class=\"o\">&gt;</span> <span class=\"err\">`</span><span class=\"n\">ftol</span><span class=\"err\">`</span> <span class=\"n\">termination</span> <span class=\"n\">condition</span> <span class=\"ow\">is</span> <span class=\"n\">satisfied</span><span class=\"o\">.</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">chisquare</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span><span class=\"p\">:</span> <span class=\"mf\">0.9593035785160936</span>\n\n<span class=\"o\">&gt;</span>  <span class=\"n\">Goodness</span> <span class=\"n\">of</span> <span class=\"n\">fit</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">\u03c7</span><span class=\"err\">\u00b2</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span> <span class=\"o\">=</span> <span class=\"mf\">0.959304</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">p</span><span class=\"o\">-</span><span class=\"n\">value</span>   <span class=\"o\">=</span> <span class=\"mf\">0.5673</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"n\">parameters</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.0548</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">1.933</span><span class=\"p\">(</span><span class=\"mi\">64</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is a <code>list</code> or <code>numpy.array</code> of <code>floats</code> and y is a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>Data stored in <code>Corr</code> objects can be fitted directly using the <code>Corr.fit</code> method.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">my_corr</span><span class=\"o\">.</span><span class=\"n\">fit</span><span class=\"p\">(</span><span class=\"n\">func</span><span class=\"p\">,</span> <span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">12</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<p>this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</p>\n\n<p>For fit functions with multiple independent variables the fit function can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.\nDetails about how the required covariance matrix is estimated can be found in <code>pyerrors.obs.covariance</code>.\nDirect visualizations of the performed fits can be triggered via <code>resplot=True</code> or <code>qqplot=True</code>.</p>\n\n<p>For all available options including combined fits to multiple datasets see <code>pyerrors.fits.least_squares</code>.</p>\n\n<h2 id=\"total-least-squares-fits\">Total least squares fits</h2>\n\n<p><code>pyerrors</code> can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to as orthogonal distance regression as implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/odr.html\">scipy</a>, see <code>pyerrors.fits.least_squares</code>. The syntax is identical to the standard least squares case, the only difference being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors</code> provides wrappers for <code>Obs</code>- and <code>CObs</code>-valued matrix operations based on <code>numpy.linalg</code>. The supported functions include:</p>\n\n<ul>\n<li><code>inv</code> for the matrix inverse.</li>\n<li><code>cholseky</code> for the Cholesky decomposition.</li>\n<li><code>det</code> for the matrix determinant.</li>\n<li><code>eigh</code> for eigenvalues and eigenvectors of hermitean matrices.</li>\n<li><code>eig</code> for eigenvalues of general matrices.</li>\n<li><code>pinv</code> for the Moore-Penrose pseudoinverse.</li>\n<li><code>svd</code> for the singular-value-decomposition.</li>\n</ul>\n\n<p>For the full API see <code>pyerrors.linalg</code>.</p>\n\n<h1 id=\"export-data\">Export data</h1>\n\n<p><a href=\"https://xkcd.com/927/\"><img src=\"https://imgs.xkcd.com/comics/standards_2x.png\" width=\"75%\" height=\"75%\"></a></p>\n\n<p>The preferred exported file format within <code>pyerrors</code> is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</p>\n\n<ul>\n<li>What observables are stored? Possibly: How exactly are they defined.</li>\n<li>How does each single ensemble or external quantity contribute to the error of the observable?</li>\n<li>Who did write the file when and on which machine?</li>\n</ul>\n\n<p>This can be achieved by storing all information in one single file. The export routines of <code>pyerrors</code> are written such that as much information as possible is written automatically as described in the following example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_obs</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([</span><span class=\"n\">samples</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"s2\">&quot;test_ensemble&quot;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">tag</span> <span class=\"o\">=</span> <span class=\"s2\">&quot;My observable&quot;</span>\n\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">dump_to_json</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">,</span> <span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n<span class=\"c1\"># For a single observable one can equivalently use the class method dump</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">dump</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n\n<span class=\"n\">check</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">load_json</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">)</span>\n\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_obs</span> <span class=\"o\">==</span> <span class=\"n\">check</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<p>The format also allows to directly write out the content of <code>Corr</code> objects or lists and arrays of <code>Obs</code> objects by passing the desired data to <code>pyerrors.input.json.dump_to_json</code>.</p>\n\n<h2 id=\"jsongz-format-specification\">json.gz format specification</h2>\n\n<p>The first entries of the file provide optional auxiliary information:</p>\n\n<ul>\n<li><code>program</code> is a string that indicates which program was used to write the file.</li>\n<li><code>version</code> is a string that specifies the version of the format.</li>\n<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>\n<li><code>date</code> is a string and contains the creation date of the file.</li>\n<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>\n<li><code>description</code> contains information on the content of the file. This field is not filled automatically in <code>pyerrors</code>. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</li>\n</ul>\n\n<p>The only necessary entry of the file is the field\n-<code>obsdata</code>, an array that contains the actual data.</p>\n\n<p>Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of <code>Obs</code>, <code>list</code>, <code>numpy.ndarray</code>, <code>Corr</code>. All <code>Obs</code> inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array <code>obsdata</code>, are treated independently. Each entry of the array <code>obsdata</code> has the following required entries:</p>\n\n<ul>\n<li><code>type</code> is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</li>\n<li><code>value</code> is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:</li>\n<li><code>layout</code> is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</li>\n<li><code>tag</code> is any JSON type. It contains additional information concerning the structure. The <code>tag</code> of an <code>Obs</code> in <code>pyerrors</code> is written here.</li>\n<li><code>reweighted</code> is a Bool that may be used to specify, whether the <code>Obs</code> in the structure have been reweighted.</li>\n<li><code>data</code> is an array that contains the data from MC chains. We will define it below.</li>\n<li><code>cdata</code> is an array that contains the data from external quantities with an error (<code>Covobs</code> in <code>pyerrors</code>). We will define it below.</li>\n</ul>\n\n<p>The array <code>data</code> contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that contains the name of the ensemble</li>\n<li><code>replica</code>, an array that contains an entry per replica of the ensemble.</li>\n</ul>\n\n<p>Each entry of <code>replica</code> contains\n<code>name</code>, a string that contains the name of the replica\n<code>deltas</code>, an array that contains the actual data.</p>\n\n<p>Each entry in <code>deltas</code> corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each <code>Obs</code> inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</p>\n\n<p>The array <code>cdata</code> contains information about the contribution of auxiliary observables, represented by <code>Covobs</code> in <code>pyerrors</code>, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that identifies the covariance matrix</li>\n<li><code>layout</code>, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").</li>\n<li><code>cov</code>, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.</li>\n<li><code>grad</code>, an array that contains N entries, one for each <code>Obs</code> inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</li>\n</ul>\n\n<p>A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</p>\n\n<p>Julia I/O routines for the json.gz format, compatible with <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">ADerrors.jl</a>, can be found <a href=\"https://github.com/fjosw/ADjson.jl\">here</a>.</p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "kind": "class", "doc": "<p>The class for a correlator (time dependent sequence of pe.Obs).</p>\n\n<p>Everything, this class does, can be achieved using lists or arrays of Obs.\nBut it is simply more convenient to have a dedicated object for correlators.\nOne often wants to add or multiply correlators of the same length at every timeslice and it is inconvenient\nto iterate over all timeslices for every operation. This is especially true, when dealing with matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a matrix at every timeslice.\nOther dependency (eg. spatial) are not supported.</p>\n\n<p>The Corr class can also deal with missing measurements or paddings for fixed boundary conditions.\nThe missing entries are represented via the <code>None</code> object.</p>\n\n<h6 id=\"initialization\">Initialization</h6>\n\n<p>A simple correlator can be initialized with a list or a one-dimensional array of <code>Obs</code> or <code>Cobs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">corr11</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs1</span><span class=\"p\">,</span> <span class=\"n\">obs2</span><span class=\"p\">])</span>\n<span class=\"n\">corr11</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"n\">obs1</span><span class=\"p\">,</span> <span class=\"n\">obs2</span><span class=\"p\">]))</span>\n</code></pre>\n</div>\n\n<p>A matrix-valued correlator can either be initialized via a two-dimensional array of <code>Corr</code> objects</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">matrix_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"n\">corr11</span><span class=\"p\">,</span> <span class=\"n\">corr12</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"n\">corr21</span><span class=\"p\">,</span> <span class=\"n\">corr22</span><span class=\"p\">]]))</span>\n</code></pre>\n</div>\n\n<p>or alternatively via a three-dimensional array of <code>Obs</code> or <code>CObs</code> of shape (T, N, N) where T is\nthe temporal extent of the correlator and N is the dimension of the matrix.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "kind": "function", "doc": "<p>Initialize a Corr object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data_input</strong> (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs (see class docstring for details).</li>\n<li><strong>padding</strong> (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.</li>\n<li><strong>prange</strong> (list, optional):\nList containing the first and last timeslice of the plateau\nregion identified for this correlator.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">data_input</span>, </span><span class=\"param\"><span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">prange</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "pyerrors.correlators.Corr.tag": {"fullname": "pyerrors.correlators.Corr.tag", "modulename": "pyerrors.correlators", "qualname": "Corr.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.content": {"fullname": "pyerrors.correlators.Corr.content", "modulename": "pyerrors.correlators", "qualname": "Corr.content", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.T": {"fullname": "pyerrors.correlators.Corr.T", "modulename": "pyerrors.correlators", "qualname": "Corr.T", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.prange": {"fullname": "pyerrors.correlators.Corr.prange", "modulename": "pyerrors.correlators", "qualname": "Corr.prange", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "kind": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.gm": {"fullname": "pyerrors.correlators.Corr.gm", "modulename": "pyerrors.correlators", "qualname": "Corr.gm", "kind": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "kind": "function", "doc": "<p>We need to project the Correlator with a Vector to get a single value at each timeslice.</p>\n\n<p>The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">vector_l</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vector_r</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">normalize</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "kind": "function", "doc": "<p>Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>i</strong> (int):\nFirst index to be picked.</li>\n<li><strong>j</strong> (int):\nSecond index to be picked.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "kind": "function", "doc": "<p>Outputs the correlator in a plotable format.</p>\n\n<p>Outputs three lists containing the timeslice index, the value on each\ntimeslice and the error on each timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "kind": "function", "doc": "<p>Symmetrize the correlator around x0=0.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "kind": "function", "doc": "<p>Anti-symmetrize the correlator around x0=0.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "kind": "function", "doc": "<p>Checks whether a correlator matrices is symmetric on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.trace": {"fullname": "pyerrors.correlators.Corr.trace", "modulename": "pyerrors.correlators", "qualname": "Corr.trace", "kind": "function", "doc": "<p>Calculates the per-timeslice trace of a correlator matrix.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "kind": "function", "doc": "<p>Symmetrizes the correlator matrices on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "kind": "function", "doc": "<p>Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.</p>\n\n<p>The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[</span><span class=\"mi\">0</span><span class=\"p\">]</span>  <span class=\"c1\"># Ground state vector(s)</span>\n<span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[:</span><span class=\"mi\">3</span><span class=\"p\">]</span>  <span class=\"c1\"># Vectors for the lowest three states</span>\n</code></pre>\n</div>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t0</strong> (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$</li>\n<li><strong>ts</strong> (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.</li>\n<li><strong>sort</strong> (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n<ul>\n<li>\"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice. (default)</li>\n<li>\"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.</li>\n<li>None: The GEVP is solved only at ts, no sorting is necessary</li>\n</ul></li>\n<li><strong>vector_obs</strong> (bool):\nIf True, uncertainties are propagated in the eigenvector computation (default False).</li>\n</ul>\n\n<h6 id=\"other-parameters\">Other Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.</li>\n<li><strong>method</strong> (str):\nMethod used to solve the GEVP.\n<ul>\n<li>\"eigh\": Use scipy.linalg.eigh to solve the GEVP. (default for vector_obs=False)</li>\n<li>\"cholesky\": Use manually implemented solution via the Cholesky decomposition. Automatically chosen if vector_obs==True.</li>\n</ul></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"n\">vector_obs</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "kind": "function", "doc": "<p>Determines the eigenvalue of the GEVP by solving and projecting the correlator</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nThe state one is interested in ordered by energy. The lowest state is zero.</li>\n<li><strong>All other parameters are identical to the ones of Corr.GEVP.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">state</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "kind": "function", "doc": "<p>Constructs an NxN Hankel matrix</p>\n\n<p>C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>N</strong> (int):\nDimension of the Hankel matrix</li>\n<li><strong>periodic</strong> (bool, optional):\ndetermines whether the matrix is extended periodically</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">N</span>, </span><span class=\"param\"><span class=\"n\">periodic</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "kind": "function", "doc": "<p>Periodically shift the correlator by dt timeslices</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>dt</strong> (int):\nnumber of timeslices</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">dt</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "kind": "function", "doc": "<p>Reverse the time ordering of the Corr</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "kind": "function", "doc": "<p>Thin out a correlator to suppress correlations</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>spacing</strong> (int):\nKeep only every 'spacing'th entry of the correlator</li>\n<li><strong>offset</strong> (int):\nOffset the equal spacing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">spacing</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "kind": "function", "doc": "<p>Correlate the correlator with another correlator or Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>partner</strong> (Obs or Corr):\npartner to correlate the correlator with.\nCan either be an Obs which is correlated with all entries of the\ncorrelator or a Corr of same length.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "kind": "function", "doc": "<p>Reweight the correlator.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "kind": "function", "doc": "<p>Return the time symmetry average of the correlator and its partner</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>partner</strong> (Corr):\nTime symmetry partner of the Corr</li>\n<li><strong>parity</strong> (int):\nParity quantum number of the correlator, can be +1 or -1</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span>, </span><span class=\"param\"><span class=\"n\">parity</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "kind": "function", "doc": "<p>Return the first derivative of the correlator with respect to x0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, log, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "kind": "function", "doc": "<p>Return the second derivative of the correlator with respect to x0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice:\n    - symmetric (default)\n        $$\\tilde{\\partial}^2_0 f(x_0) = f(x_0+1)-2f(x_0)+f(x_0-1)$$\n    - big_symmetric\n        $$\\partial^2_0 f(x_0) = \\frac{f(x_0+2)-2f(x_0)+f(x_0-2)}{4}$$\n    - improved\n        $$\\partial^2_0 f(x_0) = \\frac{-f(x_0+2) + 16 * f(x_0+1) - 30 * f(x_0) + 16 * f(x_0-1) - f(x_0-2)}{12}$$\n    - log\n        $$f(x) = \\tilde{\\partial}^2_0 log(f(x_0))+(\\tilde{\\partial}_0 log(f(x_0)))^2$$</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "kind": "function", "doc": "<p>Returns the effective mass of the correlator as correlator object</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\nlog : uses the standard effective mass log(C(t) / C(t+1))\ncosh, periodic : Use periodicity of the correlator by solving C(t) / C(t+1) = cosh(m * (t - T/2)) / cosh(m * (t + 1 - T/2)) for m.\nsinh : Use anti-periodicity of the correlator by solving C(t) / C(t+1) = sinh(m * (t - T/2)) / sinh(m * (t + 1 - T/2)) for m.\nSee, e.g., arXiv:1205.5380\narccosh : Uses the explicit form of the symmetrized correlator (not recommended)\nlogsym: uses the symmetric effective mass log(C(t-1) / C(t+1))/2</li>\n<li><strong>guess</strong> (float):\nguess for the root finder, only relevant for the root variant</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;log&#39;</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "kind": "function", "doc": "<p>Fits function to the data</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>function</strong> (obj):\nfunction to fit to the data. See fits.least_squares for details.</li>\n<li><strong>fitrange</strong> (list):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\n<code>fitrange=[4, 6]</code> corresponds to the three entries 4, 5 and 6.\nIf not specified, self.prange or all timeslices are used.</li>\n<li><strong>silent</strong> (bool):\nDecides whether output is printed to the standard output.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">function</span>, </span><span class=\"param\"><span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "kind": "function", "doc": "<p>Extract a plateau value from a Corr object</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>plateau_range</strong> (list):\nlist with two entries, indicating the first and the last timeslice\nof the plateau region.</li>\n<li><strong>method</strong> (str):\nmethod to extract the plateau.\n    'fit' fits a constant to the plateau region\n    'avg', 'average' or 'mean' just average over the given timeslices.</li>\n<li><strong>auto_gamma</strong> (bool):\napply gamma_method with default parameters to the Corr. Defaults to None</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">plateau_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">method</span><span class=\"o\">=</span><span class=\"s1\">&#39;fit&#39;</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "kind": "function", "doc": "<p>Sets the attribute prange of the Corr object.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">prange</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "kind": "function", "doc": "<p>Plots the correlator using the tag of the correlator as label if available.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x_range</strong> (list):\nlist of two values, determining the range of the x-axis e.g. [4, 8].</li>\n<li><strong>comp</strong> (Corr or list of Corr):\nCorrelator or list of correlators which are plotted for comparison.\nThe tags of these correlators are used as labels if available.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale.</li>\n<li><strong>plateau</strong> (Obs):\nPlateau value to be visualized in the figure.</li>\n<li><strong>fit_res</strong> (Fit_result):\nFit_result object to be visualized.</li>\n<li><strong>fit_key</strong> (str):\nKey for the fit function in Fit_result.fit_function (for combined fits).</li>\n<li><strong>ylabel</strong> (str):\nLabel for the y-axis.</li>\n<li><strong>save</strong> (str):\npath to file in which the figure should be saved.</li>\n<li><strong>auto_gamma</strong> (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.</li>\n<li><strong>hide_sigma</strong> (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.</li>\n<li><strong>references</strong> (list):\nList of floating point values that are displayed as horizontal lines for reference.</li>\n<li><strong>title</strong> (string):\nOptional title of the figure.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"bp\">self</span>,</span><span class=\"param\">\t<span class=\"n\">x_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">comp</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">y_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">plateau</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_res</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_key</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">ylabel</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">hide_sigma</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">references</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">title</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "kind": "function", "doc": "<p>Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>logscale</strong> (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "kind": "function", "doc": "<p>Dumps the Corr into a file of chosen type</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">print_range</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.real": {"fullname": "pyerrors.correlators.Corr.real", "modulename": "pyerrors.correlators", "qualname": "Corr.real", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.imag": {"fullname": "pyerrors.correlators.Corr.imag", "modulename": "pyerrors.correlators", "qualname": "Corr.imag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "kind": "function", "doc": "<p>Project large correlation matrix to lowest states</p>\n\n<p>This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>Ntrunc</strong> (int):\nRank of the target matrix.</li>\n<li><strong>tproj</strong> (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.</li>\n<li><strong>t0proj</strong> (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.</li>\n<li><strong>basematrix</strong> (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">Ntrunc</span>, </span><span class=\"param\"><span class=\"n\">tproj</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">t0proj</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">basematrix</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.N": {"fullname": "pyerrors.correlators.Corr.N", "modulename": "pyerrors.correlators", "qualname": "Corr.N", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "kind": "class", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "kind": "function", "doc": "<p>Initialize Covobs object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>mean</strong> (float):\nMean value of the new Obs</li>\n<li><strong>cov</strong> (list or array):\n2d Covariance matrix or 1d diagonal entries</li>\n<li><strong>name</strong> (str):\nidentifier for the covariance matrix</li>\n<li><strong>pos</strong> (int):\nPosition of the variance belonging to mean in cov.\nIs taken to be 1 if cov is 0-dimensional</li>\n<li><strong>grad</strong> (list or array):\nGradient of the Covobs wrt. the means belonging to cov.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">mean</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">pos</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "pyerrors.covobs.Covobs.name": {"fullname": "pyerrors.covobs.Covobs.name", "modulename": "pyerrors.covobs", "qualname": "Covobs.name", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.value": {"fullname": "pyerrors.covobs.Covobs.value", "modulename": "pyerrors.covobs", "qualname": "Covobs.value", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "kind": "function", "doc": "<p>Return the variance (= square of the error) of the Covobs</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.covobs.Covobs.cov": {"fullname": "pyerrors.covobs.Covobs.cov", "modulename": "pyerrors.covobs", "qualname": "Covobs.cov", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.grad": {"fullname": "pyerrors.covobs.Covobs.grad", "modulename": "pyerrors.covobs", "qualname": "Covobs.grad", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.gammaX": {"fullname": "pyerrors.dirac.gammaX", "modulename": "pyerrors.dirac", "qualname": "gammaX", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n       [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaY": {"fullname": "pyerrors.dirac.gammaY", "modulename": "pyerrors.dirac", "qualname": "gammaY", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n       [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaZ": {"fullname": "pyerrors.dirac.gammaZ", "modulename": "pyerrors.dirac", "qualname": "gammaZ", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n       [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]])"}, "pyerrors.dirac.gammaT": {"fullname": "pyerrors.dirac.gammaT", "modulename": "pyerrors.dirac", "qualname": "gammaT", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j],\n       [1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j]])"}, "pyerrors.dirac.gamma": {"fullname": "pyerrors.dirac.gamma", "modulename": "pyerrors.dirac", "qualname": "gamma", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[[ 0.+0.j,  0.+0.j,  0.+0.j,  0.+1.j],\n        [ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j, -0.-1.j,  0.+0.j,  0.+0.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j],\n        [ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n        [-1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  0.+1.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j, -0.-1.j],\n        [-0.-1.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+1.j,  0.+0.j,  0.+0.j]],\n\n       [[ 0.+0.j,  0.+0.j,  1.+0.j,  0.+0.j],\n        [ 0.+0.j,  0.+0.j,  0.+0.j,  1.+0.j],\n        [ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n        [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j]]])"}, "pyerrors.dirac.gamma5": {"fullname": "pyerrors.dirac.gamma5", "modulename": "pyerrors.dirac", "qualname": "gamma5", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[ 1.+0.j,  0.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  1.+0.j,  0.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j, -1.+0.j,  0.+0.j],\n       [ 0.+0.j,  0.+0.j,  0.+0.j, -1.+0.j]])"}, "pyerrors.dirac.identity": {"fullname": "pyerrors.dirac.identity", "modulename": "pyerrors.dirac", "qualname": "identity", "kind": "variable", "doc": "<p></p>\n", "default_value": "array([[1.+0.j, 0.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 1.+0.j, 0.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 1.+0.j, 0.+0.j],\n       [0.+0.j, 0.+0.j, 0.+0.j, 1.+0.j]])"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "kind": "function", "doc": "<p>Rank-3 epsilon tensor</p>\n\n<p>Based on <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>elem</strong> (int):\nElement (i,j,k) of the epsilon tensor of rank 3</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "kind": "function", "doc": "<p>Rank-4 epsilon tensor</p>\n\n<p>Extension of <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>elem</strong> (int):\nElement (i,j,k,o) of the epsilon tensor of rank 4</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span>, </span><span class=\"param\"><span class=\"n\">o</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "kind": "function", "doc": "<p>Returns gamma matrix in Grid labeling.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">gamma_tag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "kind": "class", "doc": "<p>Represents fit results.</p>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>fit_parameters</strong> (list):\nresults for the individual fit parameters,\nalso accessible via indices.</li>\n<li><strong>chisquare_by_dof</strong> (float):\nreduced chisquare.</li>\n<li><strong>p_value</strong> (float):\np-value of the fit</li>\n<li><strong>t2_p_value</strong> (float):\nHotelling t-squared p-value for correlated fits.</li>\n</ul>\n", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.fit_parameters": {"fullname": "pyerrors.fits.Fit_result.fit_parameters", "modulename": "pyerrors.fits", "qualname": "Fit_result.fit_parameters", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "kind": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.Fit_result.gm": {"fullname": "pyerrors.fits.Fit_result.gm", "modulename": "pyerrors.fits", "qualname": "Fit_result.gm", "kind": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "kind": "function", "doc": "<p>Performs a non-linear fit to y = func(x).\n    ```</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>For an uncombined fit:</strong></li>\n<li><strong>x</strong> (list):\nlist of floats.</li>\n<li><strong>y</strong> (list):\nlist of Obs.</li>\n<li><p><strong>func</strong> (object):\nfit function, has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>OR For a combined fit:</strong></li>\n<li><strong>x</strong> (dict):\ndict of lists.</li>\n<li><strong>y</strong> (dict):\ndict of lists of Obs.</li>\n<li><p><strong>funcs</strong> (dict):\ndict of objects\nfit functions have to be of the form (here a[0] is the common fit parameter)\n```python\nimport autograd.numpy as anp\nfuncs = {\"a\": func_a,\n        \"b\": func_b}</p>\n\n<p>def func_a(a, x):\n    return a[1] * anp.exp(-a[0] * x)</p>\n\n<p>def func_b(a, x):\n    return a[2] * anp.exp(-a[0] * x)</p>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>priors</strong> (dict or list, optional):\npriors can either be a dictionary with integer keys and the corresponding priors as values or\na list with an entry for every parameter in the fit. The entries can either be\nObs (e.g. results from a previous fit) or strings containing a value and an error formatted like\n0.548(23), 500(40) or 0.5(0.4)</li>\n<li><strong>silent</strong> (bool, optional):\nIf true all output to the console is omitted (default False).</li>\n<li><strong>initial_guess</strong> (list):\ncan provide an initial guess for the input parameters. Relevant for\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.</li>\n<li><strong>method</strong> (str, optional):\ncan be used to choose an alternative method for the minimization of chisquare.\nThe possible methods are the ones which can be used for scipy.optimize.minimize and\nmigrad of iminuit. If no method is specified, Levenberg-Marquard is used.\nReliable alternatives are migrad, Powell and Nelder-Mead.</li>\n<li><strong>tol</strong> (float, optional):\ncan be used (only for combined fits and methods other than Levenberg-Marquard) to set the tolerance for convergence\nto a different value to either speed up convergence at the cost of a larger error on the fitted parameters (and possibly\ninvalid estimates for parameter uncertainties) or smaller values to get more accurate parameter values\nThe stopping criterion depends on the method, e.g. migrad: edm_max = 0.002 * tol * errordef (EDM criterion: edm &lt; edm_max)</li>\n<li><strong>correlated_fit</strong> (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see <code>pyerrors.obs.covariance</code>.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).</li>\n<li><strong>inv_chol_cov_matrix [array,list], optional</strong>: array: shape = (no of y values) X (no of y values)\nlist:   for an uncombined fit: [\"\"]\nfor a combined fit: list of keys belonging to the corr_matrix saved in the array, must be the same as the keys of the y dict in alphabetical order\nIf correlated_fit=True is set as well, can provide an inverse covariance matrix (y errors, dy_f included!) of your own choosing for a correlated fit.\nThe matrix must be a lower triangular matrix constructed from a Cholesky decomposition: The function invert_corr_cov_cholesky(corr, inverrdiag) can be\nused to construct it from a correlation matrix (corr) and the errors dy_f of the data points (inverrdiag = np.diag(1 / np.asarray(dy_f))). For the correct\nordering the correlation matrix (corr) can be sorted via the function sort_corr(corr, kl, yd) where kl is the list of keys and yd the y dict.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).</li>\n<li><strong>resplot</strong> (bool):\nIf True, a plot which displays fit, data and residuals is generated (default False).</li>\n<li><strong>qqplot</strong> (bool):\nIf True, a quantile-quantile plot of the fit result is generated (default False).</li>\n<li><strong>num_grad</strong> (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>output</strong> (Fit_result):\nParameters and information on the fitted result.</li>\n</ul>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># Example of a correlated (correlated_fit = True, inv_chol_cov_matrix handed over) combined fit, based on a randomly generated data set</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.stats</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">norm</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.linalg</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">cholesky</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># generating the random data set</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">num_samples</span> <span class=\"o\">=</span> <span class=\"mi\">400</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">N</span> <span class=\"o\">=</span> <span class=\"mi\">3</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x1</span> <span class=\"o\">=</span> <span class=\"n\">norm</span><span class=\"o\">.</span><span class=\"n\">rvs</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">num_samples</span><span class=\"p\">))</span> <span class=\"c1\"># generate random numbers</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x2</span> <span class=\"o\">=</span> <span class=\"n\">norm</span><span class=\"o\">.</span><span class=\"n\">rvs</span><span class=\"p\">(</span><span class=\"n\">size</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">num_samples</span><span class=\"p\">))</span> <span class=\"c1\"># generate random numbers</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">r</span> <span class=\"o\">=</span> <span class=\"n\">r1</span> <span class=\"o\">=</span> <span class=\"n\">r2</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">zeros</span><span class=\"p\">((</span><span class=\"n\">N</span><span class=\"p\">,</span> <span class=\"n\">N</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">r</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">0.8</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">fabs</span><span class=\"p\">(</span><span class=\"n\">i</span> <span class=\"o\">-</span> <span class=\"n\">j</span><span class=\"p\">))</span> <span class=\"c1\"># element in correlation matrix</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">errl</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sqrt</span><span class=\"p\">([</span><span class=\"mf\">3.4</span><span class=\"p\">,</span> <span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"mf\">3.6</span><span class=\"p\">])</span> <span class=\"c1\"># set y errors</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">j</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">r</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"o\">*=</span> <span class=\"n\">errl</span><span class=\"p\">[</span><span class=\"n\">i</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">errl</span><span class=\"p\">[</span><span class=\"n\">j</span><span class=\"p\">]</span> <span class=\"c1\"># element in covariance matrix</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">c</span> <span class=\"o\">=</span> <span class=\"n\">cholesky</span><span class=\"p\">(</span><span class=\"n\">r</span><span class=\"p\">,</span> <span class=\"n\">lower</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"n\">c</span><span class=\"p\">,</span> <span class=\"n\">x1</span><span class=\"p\">),</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">dot</span><span class=\"p\">(</span><span class=\"n\">c</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)}</span> <span class=\"c1\"># generate y data with the covariance matrix defined</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># random data set has been generated, now the dictionaries and the inverse covariance matrix to be handed over are built</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">chol_inv_dict</span> <span class=\"o\">=</span> <span class=\"p\">{}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">data</span> <span class=\"o\">=</span> <span class=\"p\">[]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">key</span> <span class=\"ow\">in</span> <span class=\"n\">y</span><span class=\"o\">.</span><span class=\"n\">keys</span><span class=\"p\">():</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">x_dict</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">]</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"n\">N</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>       <span class=\"n\">data</span><span class=\"o\">.</span><span class=\"n\">append</span><span class=\"p\">(</span><span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Obs</span><span class=\"p\">([[</span><span class=\"n\">i</span> <span class=\"o\">+</span> <span class=\"mi\">1</span> <span class=\"o\">+</span> <span class=\"n\">o</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">y</span><span class=\"p\">[</span><span class=\"n\">key</span><span class=\"p\">][</span><span class=\"n\">i</span><span class=\"p\">]]],</span> <span class=\"p\">[</span><span class=\"s1\">&#39;ens&#39;</span><span class=\"p\">]))</span> <span class=\"c1\"># generate y Obs from the y data</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"p\">[</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">data</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">covariance</span><span class=\"p\">(</span><span class=\"n\">data</span><span class=\"p\">,</span> <span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">inverrdiag</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">diag</span><span class=\"p\">(</span><span class=\"mi\">1</span> <span class=\"o\">/</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">asarray</span><span class=\"p\">([</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">dvalue</span> <span class=\"k\">for</span> <span class=\"n\">o</span> <span class=\"ow\">in</span> <span class=\"n\">data</span><span class=\"p\">]))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"n\">chol_inv</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">obs</span><span class=\"o\">.</span><span class=\"n\">invert_corr_cov_cholesky</span><span class=\"p\">(</span><span class=\"n\">corr</span><span class=\"p\">,</span> <span class=\"n\">inverrdiag</span><span class=\"p\">)</span> <span class=\"c1\"># gives form of the inverse covariance matrix needed for the combined correlated fit below</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y_dict</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">data</span><span class=\"p\">[:</span><span class=\"mi\">3</span><span class=\"p\">],</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"n\">data</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">:]}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"c1\"># common fit parameter p[0] in combined fit</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">fit1</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">fit2</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n<span class=\"gp\">&gt;&gt;&gt; </span>   <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fitf_dict</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"n\">fit1</span><span class=\"p\">,</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span><span class=\"n\">fit2</span><span class=\"p\">}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fitp_inv_cov_combined_fit</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x_dict</span><span class=\"p\">,</span><span class=\"n\">y_dict</span><span class=\"p\">,</span> <span class=\"n\">fitf_dict</span><span class=\"p\">,</span> <span class=\"n\">correlated_fit</span> <span class=\"o\">=</span> <span class=\"kc\">True</span><span class=\"p\">,</span> <span class=\"n\">inv_chol_cov_matrix</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"n\">chol_inv</span><span class=\"p\">,[</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">,</span><span class=\"s1\">&#39;b&#39;</span><span class=\"p\">]])</span>\n<span class=\"go\">Fit with 3 parameters</span>\n<span class=\"go\">Method: Levenberg-Marquardt</span>\n<span class=\"go\">`ftol` termination condition is satisfied.</span>\n<span class=\"go\">chisquare/d.o.f.: 0.5388013574561786 # random</span>\n<span class=\"go\">fit parameters [1.11897846 0.96361162 0.92325319] # random</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">priors</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "kind": "function", "doc": "<p>Performs a non-linear fit to y = func(x) and returns a list of Obs corresponding to the fit parameters.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nlist of Obs, or a tuple of lists of Obs</li>\n<li><strong>y</strong> (list):\nlist of Obs. The dvalues of the Obs are used as x- and yerror for the fit.</li>\n<li><p><strong>func</strong> (object):\nfunc has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"p\">(</span><span class=\"n\">x1</span><span class=\"p\">,</span> <span class=\"n\">x2</span><span class=\"p\">)</span> <span class=\"o\">=</span> <span class=\"n\">x</span>\n    <span class=\"k\">return</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x1</span> <span class=\"o\">**</span> <span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"n\">a</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x2</span>\n</code></pre>\n</div>\n\n<p>It is important that all numpy functions refer to autograd.numpy, otherwise the differentiation\nwill not work.</p></li>\n<li><strong>silent</strong> (bool, optional):\nIf true all output to the console is omitted (default False).</li>\n<li><strong>initial_guess</strong> (list):\ncan provide an initial guess for the input parameters. Relevant for non-linear\nfits with many parameters.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf true prints the expected chisquare which is\ncorrected by effects caused by correlated input data.\nThis can take a while as the full correlation matrix\nhas to be calculated (default False).</li>\n<li><strong>num_grad</strong> (bool):\nUse numerical differentation instead of automatic differentiation to perform the error propagation (default False).</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Based on the orthogonal distance regression module of scipy.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>output</strong> (Fit_result):\nParameters and information on the fitted result.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "kind": "function", "doc": "<p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nCan either be a list of floats in which case no xerror is assumed, or\na list of Obs, where the dvalues of the Obs are used as xerror for the fit.</li>\n<li><strong>y</strong> (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>fit_parameters</strong> (list[Obs]):\nLIist of fitted observables.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "kind": "function", "doc": "<p>Generates a quantile-quantile plot of the fit result which can be used to\n   check if the residuals of the fit are gaussian distributed.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">o_y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span>, </span><span class=\"param\"><span class=\"n\">title</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "kind": "function", "doc": "<p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>\n\n<p>For uncorrelated data the residuals are expected to be distributed ~N(0,1).</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">fit_res</span>, </span><span class=\"param\"><span class=\"n\">title</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "kind": "function", "doc": "<p>Calculate the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>err</strong> (np.array(Obs)):\nError band for an array of sample values x</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">beta</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "kind": "function", "doc": "<p>Performs a Kolmogorov\u2013Smirnov test for the p-values of all fit object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>objects</strong> (list):\nList of fit results to include in the analysis (optional).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">objects</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "kind": "module", "doc": "<p><code>pyerrors</code> includes an <code>input</code> submodule in which input routines and parsers for the output of various numerical programs are contained.</p>\n\n<h1 id=\"jackknife-samples\">Jackknife samples</h1>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can also generate jackknife samples from an <code>Obs</code> object or import jackknife samples into an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> and <code>pyerrors.obs.import_jackknife</code> for details.</p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "kind": "function", "doc": "<p>Extract generic MCMC data from a bdio file</p>\n\n<p>read_ADerrors requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path -- path to the bdio file</strong></li>\n<li><strong>bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (List[Obs]):\nExtracted data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "kind": "function", "doc": "<p>Write Obs to a bdio file according to ADerrors conventions</p>\n\n<p>read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path -- path to the bdio file</strong></li>\n<li><strong>bdio_path -- path to the shared bdio library libbdio.so (default ./libbdio.so)</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>success</strong> (int):\nreturns 0 is successful</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_list</span>, </span><span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "kind": "function", "doc": "<p>Extract mesons data from a bdio file and return it as a dictionary</p>\n\n<p>The dictionary can be accessed with a tuple consisting of (type, source_position, kappa1, kappa2)</p>\n\n<p>read_mesons requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (dict):\nExtracted meson data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "kind": "function", "doc": "<p>Extract dSdm data from a bdio file and return it as a dictionary</p>\n\n<p>The dictionary can be accessed with a tuple consisting of (type, kappa)</p>\n\n<p>read_dSdm requires bdio to be compiled into a shared library. This can be achieved by\nadding the flag -fPIC to CC and changing the all target to</p>\n\n<p>all:                bdio.o $(LIBDIR)\n            gcc -shared -Wl,-soname,libbdio.so -o $(BUILDDIR)/libbdio.so $(BUILDDIR)/bdio.o\n            cp $(BUILDDIR)/libbdio.so $(LIBDIR)/</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>file_path</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>xml_str</strong> (str):\nXML formatted string of the input data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obsl</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>, </span><span class=\"param\"><span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "kind": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "kind": "function", "doc": "<p>Import a list of Obs from a string in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>content</strong> (str):\nXML string containing the data</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">content</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "kind": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (list[Obs]):\nImported data</li>\n<li><strong>or</strong></li>\n<li><strong>res</strong> (dict):\nImported data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "kind": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator |is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>xml_str</strong> (str):\nXML string generated from the data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.hadrons.read_hd5": {"fullname": "pyerrors.input.hadrons.read_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_hd5", "kind": "function", "doc": "<p>Read hadrons hdf5 file and extract entry based on attributes.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filestem</strong> (str):\nFull namestem of the files to read, including the full path.</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>group</strong> (str):\nlabel of the group to be extracted.</li>\n<li><p><strong>attrs</strong> (dict or int):\nDictionary containing the attributes. For example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">attrs</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s2\">&quot;gamma_snk&quot;</span><span class=\"p\">:</span> <span class=\"s2\">&quot;Gamma5&quot;</span><span class=\"p\">,</span>\n         <span class=\"s2\">&quot;gamma_src&quot;</span><span class=\"p\">:</span> <span class=\"s2\">&quot;Gamma5&quot;</span><span class=\"p\">}</span>\n</code></pre>\n</div>\n\n<p>Alternatively an integer can be specified to identify the sub group.\nThis is discouraged as the order in the file is not guaranteed.</p></li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>part</strong> (str):\nstring specifying whether to extract the real part ('real'),\nthe imaginary part ('imag') or a complex correlator ('complex').\nDefault 'real'.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr</strong> (Corr):\nCorrelator of the source sink combination in question.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">group</span>, </span><span class=\"param\"><span class=\"n\">attrs</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">part</span><span class=\"o\">=</span><span class=\"s1\">&#39;real&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "kind": "function", "doc": "<p>Read hadrons meson hdf5 file and extract the meson labeled 'meson'</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>meson</strong> (str):\nlabel of the meson to be extracted, standard value meson_0 which\ncorresponds to the pseudoscalar pseudoscalar two-point function.</li>\n<li><strong>gammas</strong> (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at sink and source (gamma_snk, gamma_src).\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr</strong> (Corr):\nCorrelator of the source sink combination in question.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">meson</span><span class=\"o\">=</span><span class=\"s1\">&#39;meson_0&#39;</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">gammas</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.extract_t0_hd5": {"fullname": "pyerrors.input.hadrons.extract_t0_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "extract_t0_hd5", "kind": "function", "doc": "<p>Read hadrons FlowObservables hdf5 file and extract t0</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>obs</strong> (str):\nlabel of the observable from which t0 should be extracted.\nOptions: 'Clover energy density' and 'Plaquette energy density'</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">filestem</span>,</span><span class=\"param\">\t<span class=\"n\">ens_id</span>,</span><span class=\"param\">\t<span class=\"n\">obs</span><span class=\"o\">=</span><span class=\"s1\">&#39;Clover energy density&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "kind": "function", "doc": "<p>Read hadrons DistillationContraction hdf5 files in given directory structure</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the directories to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>diagrams</strong> (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (dict):\nextracted DistillationContration data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">diagrams</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;direct&#39;</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "kind": "class", "doc": "<p>ndarray(shape, dtype=float, buffer=None, offset=0,\n        strides=None, order=None)</p>\n\n<p>An array object represents a multidimensional, homogeneous array\nof fixed-size items.  An associated data-type object describes the\nformat of each element in the array (its byte-order, how many bytes it\noccupies in memory, whether it is an integer, a floating point number,\nor something else, etc.)</p>\n\n<p>Arrays should be constructed using <code>array</code>, <code>zeros</code> or <code>empty</code> (refer\nto the See Also section below).  The parameters given here refer to\na low-level method (<code>ndarray(...)</code>) for instantiating an array.</p>\n\n<p>For more information, refer to the <code>numpy</code> module and examine the\nmethods and attributes of an array.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>(for the __new__ method; see Notes below)</strong></li>\n<li><strong>shape</strong> (tuple of ints):\nShape of created array.</li>\n<li><strong>dtype</strong> (data-type, optional):\nAny object that can be interpreted as a numpy data type.</li>\n<li><strong>buffer</strong> (object exposing buffer interface, optional):\nUsed to fill the array with data.</li>\n<li><strong>offset</strong> (int, optional):\nOffset of array data in buffer.</li>\n<li><strong>strides</strong> (tuple of ints, optional):\nStrides of data in memory.</li>\n<li><strong>order</strong> ({'C', 'F'}, optional):\nRow-major (C-style) or column-major (Fortran-style) order.</li>\n</ul>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>T</strong> (ndarray):\nTranspose of the array.</li>\n<li><strong>data</strong> (buffer):\nThe array's elements, in memory.</li>\n<li><strong>dtype</strong> (dtype object):\nDescribes the format of the elements in the array.</li>\n<li><strong>flags</strong> (dict):\nDictionary containing information related to memory use, e.g.,\n'C_CONTIGUOUS', 'OWNDATA', 'WRITEABLE', etc.</li>\n<li><strong>flat</strong> (numpy.flatiter object):\nFlattened version of the array as an iterator.  The iterator\nallows assignments, e.g., <code>x.flat = 3</code> (See <code>ndarray.flat</code> for\nassignment examples; TODO).</li>\n<li><strong>imag</strong> (ndarray):\nImaginary part of the array.</li>\n<li><strong>real</strong> (ndarray):\nReal part of the array.</li>\n<li><strong>size</strong> (int):\nNumber of elements in the array.</li>\n<li><strong>itemsize</strong> (int):\nThe memory use of each array element in bytes.</li>\n<li><strong>nbytes</strong> (int):\nThe total number of bytes required to store the array data,\ni.e., <code>itemsize * size</code>.</li>\n<li><strong>ndim</strong> (int):\nThe array's number of dimensions.</li>\n<li><strong>shape</strong> (tuple of ints):\nShape of the array.</li>\n<li><strong>strides</strong> (tuple of ints):\nThe step-size required to move from one element to the next in\nmemory. For example, a contiguous <code>(3, 4)</code> array of type\n<code>int16</code> in C-order has strides <code>(8, 2)</code>.  This implies that\nto move from element to element in memory requires jumps of 2 bytes.\nTo move from row-to-row, one needs to jump 8 bytes at a time\n(<code>2 * 4</code>).</li>\n<li><strong>ctypes</strong> (ctypes object):\nClass containing properties of the array needed for interaction\nwith ctypes.</li>\n<li><strong>base</strong> (ndarray):\nIf the array is a view into another array, that array is its <code>base</code>\n(unless that array is also a view).  The <code>base</code> array is where the\narray data is actually stored.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>array</code>:  Construct an array.<br />\n<code>zeros</code>:  Create an array, each element of which is zero.<br />\n<code>empty</code>:  Create an array, but leave its allocated memory unchanged (i.e.,\nit contains \"garbage\").<br />\n<code>dtype</code>:  Create a data-type.<br />\n<code>numpy.typing.NDArray</code>:  An ndarray alias :term:<code>generic &lt;generic type&gt;</code>\nw.r.t. its <code>dtype.type &lt;numpy.dtype.type&gt;</code>.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>There are two modes of creating an array using <code>__new__</code>:</p>\n\n<ol>\n<li>If <code>buffer</code> is None, then only <code>shape</code>, <code>dtype</code>, and <code>order</code>\nare used.</li>\n<li>If <code>buffer</code> is an object exposing the buffer interface, then\nall keywords are interpreted.</li>\n</ol>\n\n<p>No <code>__init__</code> method is needed because the array is fully initialized\nafter the <code>__new__</code> method.</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>These examples illustrate the low-level <code>ndarray</code> constructor.  Refer\nto the <code>See Also</code> section above for easier ways of constructing an\nndarray.</p>\n\n<p>First mode, <code>buffer</code> is None:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">(</span><span class=\"n\">shape</span><span class=\"o\">=</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">),</span> <span class=\"n\">dtype</span><span class=\"o\">=</span><span class=\"nb\">float</span><span class=\"p\">,</span> <span class=\"n\">order</span><span class=\"o\">=</span><span class=\"s1\">&#39;F&#39;</span><span class=\"p\">)</span>\n<span class=\"go\">array([[0.0e+000, 0.0e+000], # random</span>\n<span class=\"go\">       [     nan, 2.5e-323]])</span>\n</code></pre>\n</div>\n\n<p>Second mode:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ndarray</span><span class=\"p\">((</span><span class=\"mi\">2</span><span class=\"p\">,),</span> <span class=\"n\">buffer</span><span class=\"o\">=</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">,</span><span class=\"mi\">3</span><span class=\"p\">]),</span>\n<span class=\"gp\">... </span>           <span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">int_</span><span class=\"p\">()</span><span class=\"o\">.</span><span class=\"n\">itemsize</span><span class=\"p\">,</span>\n<span class=\"gp\">... </span>           <span class=\"n\">dtype</span><span class=\"o\">=</span><span class=\"nb\">int</span><span class=\"p\">)</span> <span class=\"c1\"># offset = 1*itemsize, i.e. skip first element</span>\n<span class=\"go\">array([2, 3])</span>\n</code></pre>\n</div>\n", "bases": "numpy.ndarray"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "kind": "variable", "doc": "<p>Gamma_5 hermitean conjugate</p>\n\n<p>Uses the fact that the propagator is gamma5 hermitean, so just the\nin and out momenta of the propagator are exchanged.</p>\n"}, "pyerrors.input.hadrons.read_ExternalLeg_hd5": {"fullname": "pyerrors.input.hadrons.read_ExternalLeg_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_ExternalLeg_hd5", "kind": "function", "doc": "<p>Read hadrons ExternalLeg hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (Npr_matrix):\nread Cobs-matrix</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "kind": "function", "doc": "<p>Read hadrons Bilinear hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result_dict</strong> (dict[Npr_matrix]):\nextracted Bilinears</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "kind": "function", "doc": "<p>Read hadrons FourquarkFullyConnected hdf5 file and output an array of CObs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the files to read</li>\n<li><strong>filestem</strong> (str):\nnamestem of the files to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n<li><strong>vertices</strong> (list):\nVertex functions to be extracted.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result_dict</strong> (dict):\nextracted fourquark matrizes</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vertices</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;VA&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;AV&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.json.create_json_string": {"fullname": "pyerrors.input.json.create_json_string", "modulename": "pyerrors.input.json", "qualname": "create_json_string", "kind": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .json(.gz) file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ol</strong> (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>json_string</strong> (str):\nString for export to .json(.gz) file</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "kind": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .json(.gz) file.\nDict keys that are not JSON-serializable such as floats are converted to strings.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ol</strong> (list):\nList of objects that will be exported. At the moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Null</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "kind": "function", "doc": "<p>Reconstruct a list of Obs or structures containing Obs from a json string.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>json_string</strong> (str):\njson string containing the data.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nreconstructed list of observables from the json string</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (Obs):\nonly one observable if the list only has one entry</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (dict):\nif full_output=True</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">json_string</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "kind": "function", "doc": "<p>Import a list of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\nIf the list contains only one element, it is unpacked from the list.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nreconstructed list of observables from the json string</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (Obs):\nonly one observable if the list only has one entry</li>\n<li><strong>or</strong></li>\n<li><strong>result</strong> (dict):\nif full_output=True</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "kind": "function", "doc": "<p>Export a dict of Obs or structures containing Obs to a .json(.gz) file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>od</strong> (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\nAll Obs inside a structure have to be defined on the same set of configurations.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>description</strong> (str):\nOptional string that describes the contents of the json file.</li>\n<li><strong>indent</strong> (int):\nSpecify the indentation level of the json file. None or 0 is permissible and\nsaves disk space.</li>\n<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped json. If False, the output is a json file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">od</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "kind": "function", "doc": "<p>Import a dict of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the file.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n<li><strong>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned.</li>\n<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (Obs / list / Corr):\nRead data</li>\n<li><strong>or</strong></li>\n<li><strong>data</strong> (dict):\nRead data and meta-data</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.misc.fit_t0": {"fullname": "pyerrors.input.misc.fit_t0", "modulename": "pyerrors.input.misc", "qualname": "fit_t0", "kind": "function", "doc": "<p>Compute the root of (flow-based) data based on a dictionary that contains\nthe necessary information in key-value pairs a la (flow time: observable at flow time).</p>\n\n<p>It is assumed that the data is monotonically increasing and passes zero from below.\nNo exception is thrown if this is not the case (several roots, no monotonic increase).\nAn exception is thrown if no root can be found in the data.</p>\n\n<p>A linear fit in the vicinity of the root is performed to exctract the root from the\ntwo fit parameters.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t2E_dict</strong> (dict):\nDictionary with pairs of (flow time: observable at flow time) where the flow times\nare of type float and the observables of type Obs.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data. (Default: False)</li>\n<li><strong>observable</strong> (str):\nKeyword to identify the observable to print the correct ylabel (if plot_fit is True)\nfor the observables 't0' and 'w0'. No y label is printed otherwise. (Default: 't0')</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>root</strong> (Obs):\nThe root of the data series.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">t2E_dict</span>, </span><span class=\"param\"><span class=\"n\">fit_range</span>, </span><span class=\"param\"><span class=\"n\">plot_fit</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">observable</span><span class=\"o\">=</span><span class=\"s1\">&#39;t0&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "kind": "function", "doc": "<p>Read pbp format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nlist of observables read</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "kind": "function", "doc": "<p>Read rwms format from given folder structure. Returns a list of length nrw</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath that contains the data files</li>\n<li><strong>prefix</strong> (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.</li>\n<li><strong>version</strong> (str):\nversion of openQCD, default 2.0</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>print_err</strong> (bool):\nPrint additional information that is useful for debugging.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>rwms</strong> (Obs):\nReweighting factors read</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;2.0&#39;</span>, </span><span class=\"param\"><span class=\"n\">names</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "kind": "function", "doc": "<p>Extract t0/a^2 from given .ms.dat files. Returns t0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - c (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to .ms.dat files</li>\n<li><strong>prefix</strong> (str):\nEnsemble prefix</li>\n<li><strong>dtr_read</strong> (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.</li>\n<li><strong>xmin</strong> (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.</li>\n<li><strong>spatial_extent</strong> (int):\nspatial extent of the lattice, required for normalization.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>postfix</strong> (str):\nPostfix of measurement file (Default: ms)</li>\n<li><strong>c</strong> (float):\nConstant that defines the flow scale. Default 0.3 for t_0, choose 2./3 for t_1.</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>t0</strong> (Obs):\nExtracted t0</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">dtr_read</span>,</span><span class=\"param\">\t<span class=\"n\">xmin</span>,</span><span class=\"param\">\t<span class=\"n\">spatial_extent</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">postfix</span><span class=\"o\">=</span><span class=\"s1\">&#39;ms&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">c</span><span class=\"o\">=</span><span class=\"mf\">0.3</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.extract_w0": {"fullname": "pyerrors.input.openQCD.extract_w0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_w0", "kind": "function", "doc": "<p>Extract w0/a from given .ms.dat files. Returns w0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t d(t^2<E>)/dt -  (where c=0.3 by default)\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to .ms.dat files</li>\n<li><strong>prefix</strong> (str):\nEnsemble prefix</li>\n<li><strong>dtr_read</strong> (int):\nDetermines how many trajectories should be skipped\nwhen reading the ms.dat files.\nCorresponds to dtr_cnfg / dtr_ms in the openQCD input file.</li>\n<li><strong>xmin</strong> (int):\nFirst timeslice where the boundary\neffects have sufficiently decayed.</li>\n<li><strong>spatial_extent</strong> (int):\nspatial extent of the lattice, required for normalization.</li>\n<li><strong>fit_range</strong> (int):\nNumber of data points left and right of the zero\ncrossing to be included in the linear fit. (Default: 5)</li>\n<li><strong>postfix</strong> (str):\nPostfix of measurement file (Default: ms)</li>\n<li><strong>c</strong> (float):\nConstant that defines the flow scale. Default 0.3 for w_0, choose 2./3 for w_1.</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of w0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of w0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>w0</strong> (Obs):\nExtracted w0</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">dtr_read</span>,</span><span class=\"param\">\t<span class=\"n\">xmin</span>,</span><span class=\"param\">\t<span class=\"n\">spatial_extent</span>,</span><span class=\"param\">\t<span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>,</span><span class=\"param\">\t<span class=\"n\">postfix</span><span class=\"o\">=</span><span class=\"s1\">&#39;ms&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">c</span><span class=\"o\">=</span><span class=\"mf\">0.3</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "kind": "function", "doc": "<p>Read the topologial charge based on openQCD gradient flow measurements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nEither openQCD or sfqcd, depending on the data.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n<li><strong>integer_charge</strong> (bool):\nIf True, the charge is rounded towards the nearest integer on each config.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (Obs):\nRead topological charge</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;openQCD&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "kind": "function", "doc": "<p>Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.</p>\n\n<p>Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>r_start</strong> (list):\nlist which contains the first config to be read for each replicum.</li>\n<li><strong>r_stop</strong> (list):\nlist which contains the last config to be read for each replicum.</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.gfms.dat' for openQCD-files</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">Zeuthen_flow</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "kind": "function", "doc": "<p>Returns the projection to the topological charge sector defined by target.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (Obs):\nTopological charge.</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>reto</strong> (Obs):\nprojection to the topological charge sector defined by target</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">qtop</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "kind": "function", "doc": "<p>Constructs reweighting factors to a specified topological sector.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs</li>\n<li><strong>r_stop</strong> (list):\nlast configurations that need to be read (per replicum)</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>reto</strong> (Obs):\nprojection to the topological charge sector defined by target</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_ms5_xsf": {"fullname": "pyerrors.input.openQCD.read_ms5_xsf", "modulename": "pyerrors.input.openQCD", "qualname": "read_ms5_xsf", "kind": "function", "doc": "<p>Read data from files in the specified directory with the specified prefix and quark combination extension, and return a <code>Corr</code> object containing the data.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nThe directory to search for the files in.</li>\n<li><strong>prefix</strong> (str):\nThe prefix to match the files against.</li>\n<li><strong>qc</strong> (str):\nThe quark combination extension to match the files against.</li>\n<li><strong>corr</strong> (str):\nThe correlator to extract data for.</li>\n<li><strong>sep</strong> (str, optional):\nThe separator to use when parsing the replika names.</li>\n<li><p><strong>**kwargs</strong>: Additional keyword arguments. The following keyword arguments are recognized:</p>\n\n<ul>\n<li>names (List[str]): A list of names to use for the replicas.</li>\n<li>files (List[str]): A list of files to read data from.</li>\n<li>idl (List[List[int]]): A list of idls per replicum, resticting data to the idls given.</li>\n</ul></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Corr</strong>: A complex valued <code>Corr</code> object containing the data read from the files. In case of boudary to bulk correlators.</li>\n<li><strong>or</strong></li>\n<li><strong>CObs</strong>: A complex valued <code>CObs</code> object containing the data read from the files. In case of boudary to boundary correlators.</li>\n</ul>\n\n<h6 id=\"raises\">Raises</h6>\n\n<ul>\n<li><strong>FileNotFoundError</strong>: If no files matching the specified prefix and quark combination extension are found in the specified directory.</li>\n<li><strong>IOError</strong>: If there is an error reading a file.</li>\n<li><strong>struct.error</strong>: If there is an error unpacking binary data.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">qc</span>, </span><span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">sep</span><span class=\"o\">=</span><span class=\"s1\">&#39;r&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "kind": "function", "doc": "<p>Write DataFrame including Obs or Corr valued columns to sqlite database.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be written to the database.</li>\n<li><strong>table_name</strong> (str):\nName of the table in the database.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>if exists</strong> (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.</li>\n<li><strong>gz</strong> (bool):\nIf True the json strings are gzipped.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">table_name</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">if_exists</span><span class=\"o\">=</span><span class=\"s1\">&#39;fail&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "kind": "function", "doc": "<p>Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sql</strong> (str):\nSQL query to be executed.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (pandas.DataFrame):\nDataframe with the content of the sqlite database.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">sql</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "kind": "function", "doc": "<p>Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.</p>\n\n<p>Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be dumped to a file.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "kind": "function", "doc": "<p>Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>fname</strong> (str):\nFilename of the input file.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>data</strong> (pandas.DataFrame):\nDataframe with the content of the sqlite database.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.input.sfcf.sep": {"fullname": "pyerrors.input.sfcf.sep", "modulename": "pyerrors.input.sfcf", "qualname": "sep", "kind": "variable", "doc": "<p></p>\n", "default_value": "&#x27;/&#x27;"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "kind": "function", "doc": "<p>Read sfcf files from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to the sfcf files.</li>\n<li><strong>prefix</strong> (str):\nPrefix of the sfcf files.</li>\n<li><strong>name</strong> (str):\nName of the correlation function to read.</li>\n<li><strong>quarks</strong> (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>corr_type</strong> (str):\nType of correlation function to read. Can be\n<ul>\n<li>'bi' for boundary-inner</li>\n<li>'bb' for boundary-boundary</li>\n<li>'bib' for boundary-inner-boundary</li>\n</ul></li>\n<li><strong>noffset</strong> (int):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf</strong> (int):\nID of wave function</li>\n<li><strong>wf2</strong> (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs</strong> (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (list[Obs]):\nlist of Observables with length T, observable per timeslice.\nbb-type correlators have length 1.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">quarks</span><span class=\"o\">=</span><span class=\"s1\">&#39;.*&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type</span><span class=\"o\">=</span><span class=\"s1\">&#39;bi&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">noffset</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf2</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_multi": {"fullname": "pyerrors.input.sfcf.read_sfcf_multi", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_multi", "kind": "function", "doc": "<p>Read sfcf files from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nPath to the sfcf files.</li>\n<li><strong>prefix</strong> (str):\nPrefix of the sfcf files.</li>\n<li><strong>name</strong> (str):\nName of the correlation function to read.</li>\n<li><strong>quarks_list</strong> (list[str]):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>corr_type_list</strong> (list[str]):\nType of correlation function to read. Can be\n<ul>\n<li>'bi' for boundary-inner</li>\n<li>'bb' for boundary-boundary</li>\n<li>'bib' for boundary-inner-boundary</li>\n</ul></li>\n<li><strong>noffset_list</strong> (list[int]):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf_list</strong> (int):\nID of wave function</li>\n<li><strong>wf2_list</strong> (list[int]):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list[list[int]]):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs</strong> (list[list[int]]):\nlist of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n<li><strong>rep_string</strong> (str):\nSeparator of ensemble name and replicum. Example: In \"ensAr0\", \"r\" would be the separator string.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>result</strong> (dict[list[Obs]]):\ndict with one of the following properties:\nif keyed_out:\n    dict[key] = list[Obs]\n    where key has the form name/quarks/offset/wf/wf2\nif not keyed_out:\n    dict[name][quarks][offset][wf][wf2] = list[Obs]</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name_list</span>,</span><span class=\"param\">\t<span class=\"n\">quarks_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;.*&#39;</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;bi&#39;</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">noffset_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">wf_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">wf2_list</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">keyed_out</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "kind": "module", "doc": "<p>Utilities for the input</p>\n"}, "pyerrors.input.utils.sort_names": {"fullname": "pyerrors.input.utils.sort_names", "modulename": "pyerrors.input.utils", "qualname": "sort_names", "kind": "function", "doc": "<p>Sorts a list of names of replika with searches for <code>r</code> and <code>id</code> in the replikum string.\nIf this search fails, a fallback method is used,\nwhere the strings are simply compared and the first diffeing numeral is used for differentiation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ll</strong> (list):\nlist to sort</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>ll</strong> (list):\nsorted list</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ll</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "kind": "function", "doc": "<p>Checks if list of configurations is contained in an idl</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>idl</strong> (range or list):\nidl of the current replicum</li>\n<li><strong>che</strong> (list):\nlist of configurations to be checked against</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>miss_str</strong> (str):\nstring with integers of which idls are missing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">idl</span>, </span><span class=\"param\"><span class=\"n\">che</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils.check_params": {"fullname": "pyerrors.input.utils.check_params", "modulename": "pyerrors.input.utils", "qualname": "check_params", "kind": "function", "doc": "<p>Check if, for sfcf, the parameter hashes at the end of the parameter files are in fact the expected one.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\nmeasurement path, same as for sfcf read method</li>\n<li><strong>param_hash</strong> (str):\nexpected parameter hash</li>\n<li><strong>prefix</strong> (str):\ndata prefix to find the appropriate replicum folders in path</li>\n<li><strong>param_prefix</strong> (str):\nprefix of the parameter file. Defaults to 'parameters_'</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>nums</strong> (dict):\ndictionary of faulty parameter files sorted by the replica paths</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">param_hash</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">param_prefix</span><span class=\"o\">=</span><span class=\"s1\">&#39;parameters_&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.integrate": {"fullname": "pyerrors.integrate", "modulename": "pyerrors.integrate", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.integrate.quad": {"fullname": "pyerrors.integrate.quad", "modulename": "pyerrors.integrate", "qualname": "quad", "kind": "function", "doc": "<p>Performs a (one-dimensional) numeric integration of f(p, x) from a to b.</p>\n\n<p>The integration is performed using scipy.integrate.quad().\nAll parameters that can be passed to scipy.integrate.quad may also be passed to this function.\nThe output is the same as for scipy.integrate.quad, the first element being an Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><p><strong>func</strong> (object):\nfunction to integrate, has to be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">func</span><span class=\"p\">(</span><span class=\"n\">p</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">]</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">x</span> <span class=\"o\">+</span> <span class=\"n\">p</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">sinh</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is the integration variable.</p></li>\n<li><strong>p</strong> (list of floats or Obs):\nparameters of the function func.</li>\n<li><strong>a</strong> (float or Obs):\nLower limit of integration (use -numpy.inf for -infinity).</li>\n<li><strong>b</strong> (float or Obs):\nUpper limit of integration (use -numpy.inf for -infinity).</li>\n<li><strong>All parameters of scipy.integrate.quad</strong></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>y</strong> (Obs):\nThe integral of func from <code>a</code> to <code>b</code>.</li>\n<li><strong>abserr</strong> (float):\nAn estimate of the absolute error in the result.</li>\n<li><strong>infodict</strong> (dict):\nA dictionary containing additional information.\nRun scipy.integrate.quad_explain() for more information.</li>\n<li><strong>message</strong>: A convergence message.</li>\n<li><strong>explain</strong>: Appended only with 'cos' or 'sin' weighting and infinite\nintegration limits, it contains an explanation of the codes in\ninfodict['ierlst']</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span>, </span><span class=\"param\"><span class=\"n\">a</span>, </span><span class=\"param\"><span class=\"n\">b</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "kind": "function", "doc": "<p>Matrix multiply all operands.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n<li><strong>This implementation is faster compared to standard multiplication via the @ operator.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "kind": "function", "doc": "<p>Matrix multiply both operands making use of the jackknife approximation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n<li><strong>For large matrices this is considerably faster compared to matmul.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "kind": "function", "doc": "<p>Wrapper for numpy.einsum</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>subscripts</strong> (str):\nSubscripts for summation (see numpy documentation for details)</li>\n<li><strong>operands</strong> (numpy.ndarray):\nArbitrary number of 2d-numpy arrays which can be real or complex\nObs valued.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">subscripts</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "kind": "function", "doc": "<p>Inverse of Obs or CObs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "kind": "function", "doc": "<p>Cholesky decomposition of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "kind": "function", "doc": "<p>Determinant of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "kind": "function", "doc": "<p>Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "kind": "function", "doc": "<p>Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.eigv": {"fullname": "pyerrors.linalg.eigv", "modulename": "pyerrors.linalg", "qualname": "eigv", "kind": "function", "doc": "<p>Computes the eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "kind": "function", "doc": "<p>Computes the Moore-Penrose pseudoinverse of a matrix of Obs.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "kind": "function", "doc": "<p>Computes the singular value decomposition of a matrix of Obs.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.misc.print_config": {"fullname": "pyerrors.misc.print_config", "modulename": "pyerrors.misc", "qualname": "print_config", "kind": "function", "doc": "<p>Print information about version of python, pyerrors and dependencies.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.errorbar": {"fullname": "pyerrors.misc.errorbar", "modulename": "pyerrors.misc", "qualname": "errorbar", "kind": "function", "doc": "<p>pyerrors wrapper for the errorbars method of matplotlib</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nA list of x-values which can be Obs.</li>\n<li><strong>y</strong> (list):\nA list of y-values which can be Obs.</li>\n<li><strong>axes</strong> ((matplotlib.pyplot.axes)):\nThe axes to plot on. default is plt.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">x</span>,</span><span class=\"param\">\t<span class=\"n\">y</span>,</span><span class=\"param\">\t<span class=\"n\">axes</span><span class=\"o\">=&lt;</span><span class=\"n\">module</span> <span class=\"s1\">&#39;matplotlib.pyplot&#39;</span> <span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"s1\">&#39;/opt/hostedtoolcache/Python/3.10.17/x64/lib/python3.10/site-packages/matplotlib/pyplot.py&#39;</span><span class=\"o\">&gt;</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "kind": "function", "doc": "<p>Dump object into pickle file.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obj</strong> (object):\nobject to be saved in the pickle file</li>\n<li><strong>name</strong> (str):\nname of the file</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>None</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obj</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "kind": "function", "doc": "<p>Load object from pickle file.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the file</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>object</strong> (Obs):\nLoaded Object</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "kind": "function", "doc": "<p>Generate an Obs object with given value, dvalue and name for test purposes</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>value</strong> (float):\ncentral value of the Obs to be generated.</li>\n<li><strong>dvalue</strong> (float):\nerror of the Obs to be generated.</li>\n<li><strong>name</strong> (str):\nname of the ensemble for which the Obs is to be generated.</li>\n<li><strong>samples</strong> (int):\nnumber of samples for the Obs (default 1000).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (Obs):\nGenerated Observable</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">value</span>, </span><span class=\"param\"><span class=\"n\">dvalue</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "kind": "function", "doc": "<p>Generate observables with given covariance and autocorrelation times.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>means</strong> (list):\nlist containing the mean value of each observable.</li>\n<li><strong>cov</strong> (numpy.ndarray):\ncovariance matrix for the data to be generated.</li>\n<li><strong>name</strong> (str):\nensemble name for the data to be geneated.</li>\n<li><strong>tau</strong> (float or list):\ncan either be a real number or a list with an entry for\nevery dataset.</li>\n<li><strong>samples</strong> (int):\nnumber of samples to be generated for each observable.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>corr_obs</strong> (list[Obs]):\nGenerated observable list</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">tau</span><span class=\"o\">=</span><span class=\"mf\">0.5</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "kind": "function", "doc": "<p>Matrix pencil method to extract k energy levels from data</p>\n\n<p>Implementation of the matrix pencil method based on\neq. (2.17) of Y. Hua, T. K. Sarkar, IEEE Trans. Acoust. 38, 814-824 (1990)</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data</strong> (list):\ncan be a list of Obs for the analysis of a single correlator, or a list of lists\nof Obs if several correlators are to analyzed at once.</li>\n<li><strong>k</strong> (int):\nNumber of states to extract (default 1).</li>\n<li><strong>p</strong> (int):\nmatrix pencil parameter which filters noise. The optimal value is expected between\nlen(data)/3 and 2*len(data)/3. The computation is more expensive the closer p is\nto len(data)/2 but could possibly suppress more noise (default len(data)//2).</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>energy_levels</strong> (list[Obs]):\nExtracted energy levels</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corrs</span>, </span><span class=\"param\"><span class=\"n\">k</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">p</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "kind": "class", "doc": "<p>Class for a general observable.</p>\n\n<p>Instances of Obs are the basic objects of a pyerrors error analysis.\nThey are initialized with a list which contains arrays of samples for\ndifferent ensembles/replica and another list of same length which contains\nthe names of the ensembles/replica. Mathematical operations can be\nperformed on instances. The result is another instance of Obs. The error of\nan instance can be computed with the gamma_method. Also contains additional\nmethods for output and visualization of the error calculation.</p>\n\n<h6 id=\"attributes\">Attributes</h6>\n\n<ul>\n<li><strong>S_global</strong> (float):\nStandard value for S (default 2.0)</li>\n<li><strong>S_dict</strong> (dict):\nDictionary for S values. If an entry for a given ensemble\nexists this overwrites the standard value for that ensemble.</li>\n<li><strong>tau_exp_global</strong> (float):\nStandard value for tau_exp (default 0.0)</li>\n<li><strong>tau_exp_dict</strong> (dict):\nDictionary for tau_exp values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.</li>\n<li><strong>N_sigma_global</strong> (float):\nStandard value for N_sigma (default 1.0)</li>\n<li><strong>N_sigma_dict</strong> (dict):\nDictionary for N_sigma values. If an entry for a given ensemble exists\nthis overwrites the standard value for that ensemble.</li>\n</ul>\n"}, "pyerrors.obs.Obs.__init__": {"fullname": "pyerrors.obs.Obs.__init__", "modulename": "pyerrors.obs", "qualname": "Obs.__init__", "kind": "function", "doc": "<p>Initialize Obs object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>samples</strong> (list):\nlist of numpy arrays containing the Monte Carlo samples</li>\n<li><strong>names</strong> (list):\nlist of strings labeling the individual samples</li>\n<li><strong>idl</strong> (list, optional):\nlist of ranges or lists on which the samples are defined</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">samples</span>, </span><span class=\"param\"><span class=\"n\">names</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span>)</span>"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "2.0"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "0.0"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "kind": "variable", "doc": "<p></p>\n", "default_value": "1.0"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "kind": "variable", "doc": "<p></p>\n", "default_value": "{}"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "kind": "function", "doc": "<p>Estimate the error and related properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>S</strong> (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.</li>\n<li><strong>tau_exp</strong> (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).</li>\n<li><strong>N_sigma</strong> (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).</li>\n<li><strong>fft</strong> (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.gm": {"fullname": "pyerrors.obs.Obs.gm", "modulename": "pyerrors.obs", "qualname": "Obs.gm", "kind": "function", "doc": "<p>Estimate the error and related properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>S</strong> (float):\nspecifies a custom value for the parameter S (default 2.0).\nIf set to 0 it is assumed that the data exhibits no\nautocorrelation. In this case the error estimates coincides\nwith the sample standard error.</li>\n<li><strong>tau_exp</strong> (float):\npositive value triggers the critical slowing down analysis\n(default 0.0).</li>\n<li><strong>N_sigma</strong> (float):\nnumber of standard deviations from zero until the tail is\nattached to the autocorrelation function (default 1).</li>\n<li><strong>fft</strong> (bool):\ndetermines whether the fft algorithm is used for the computation\nof the autocorrelation function (default True)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "kind": "function", "doc": "<p>Output detailed properties of the Obs.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>ens_content</strong> (bool):\nprint details about the ensembles and replica if true.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">ens_content</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "kind": "function", "doc": "<p>Reweight the obs with given rewighting factors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero_within_error": {"fullname": "pyerrors.obs.Obs.is_zero_within_error", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero_within_error", "kind": "function", "doc": "<p>Checks whether the observable is zero within 'sigma' standard errors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sigma</strong> (int):\nNumber of standard errors used for the check.</li>\n<li><strong>Works only properly when the gamma method was run.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">sigma</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "kind": "function", "doc": "<p>Checks whether the observable is zero within a given tolerance.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">atol</span><span class=\"o\">=</span><span class=\"mf\">1e-10</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "kind": "function", "doc": "<p>Plot integrated autocorrelation time for each ensemble.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "kind": "function", "doc": "<p>Plot normalized autocorrelation function time for each ensemble.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "kind": "function", "doc": "<p>Plot replica distribution for each ensemble with more than one replicum.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "kind": "function", "doc": "<p>Plot derived Monte Carlo history for each ensemble</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>expand</strong> (bool):\nshow expanded history for irregular Monte Carlo chains (default: True).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">expand</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "kind": "function", "doc": "<p>Plot piechart which shows the fractional contribution of each\nensemble to the error and returns a dictionary containing the fractions.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>save</strong> (str):\nsaves the figure to a file named 'save' if.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "kind": "function", "doc": "<p>Dump the Obs to a file 'name' of chosen format.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nname of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>description</strong> (str):\nDescription for output file, only relevant for json.gz format.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "kind": "function", "doc": "<p>Export jackknife samples from the Obs</p>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>numpy.ndarray</strong>: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N jackknife samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived jackknife samples\nshould agree with samples from a full jackknife analysis up to O(1/N).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.export_bootstrap": {"fullname": "pyerrors.obs.Obs.export_bootstrap", "modulename": "pyerrors.obs", "qualname": "Obs.export_bootstrap", "kind": "function", "doc": "<p>Export bootstrap samples from the Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>samples</strong> (int):\nNumber of bootstrap samples to generate.</li>\n<li><strong>random_numbers</strong> (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples.\nIf not provided the bootstrap samples are generated bashed on the md5 hash of the enesmble name.</li>\n<li><strong>save_rng</strong> (str):\nSave the random numbers to a file if a path is specified.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>numpy.ndarray</strong>: Returns a numpy array of length N + 1 where N is the number of samples\nfor the given ensemble and replicum. The zeroth entry of the array contains\nthe mean value of the Obs, entries 1 to N contain the N import_bootstrap samples\nderived from the Obs. The current implementation only works for observables\ndefined on exactly one ensemble and replicum. The derived bootstrap samples\nshould agree with samples from a full bootstrap analysis up to O(1/N).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">500</span>, </span><span class=\"param\"><span class=\"n\">random_numbers</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">save_rng</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_n_dtauint": {"fullname": "pyerrors.obs.Obs.e_n_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_dtauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_n_tauint": {"fullname": "pyerrors.obs.Obs.e_n_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_n_tauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "kind": "class", "doc": "<p>Class for a complex valued observable.</p>\n"}, "pyerrors.obs.CObs.__init__": {"fullname": "pyerrors.obs.CObs.__init__", "modulename": "pyerrors.obs", "qualname": "CObs.__init__", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">real</span>, </span><span class=\"param\"><span class=\"n\">imag</span><span class=\"o\">=</span><span class=\"mf\">0.0</span></span>)</span>"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "kind": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "kind": "function", "doc": "<p>Executes the gamma_method for the real and the imaginary part.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "kind": "function", "doc": "<p>Checks whether both real and imaginary part are zero within machine precision.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "kind": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.gamma_method": {"fullname": "pyerrors.obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "gamma_method", "kind": "function", "doc": "<p>Vectorized version of the gamma_method applicable to lists or arrays of Obs.</p>\n\n<p>See docstring of pe.Obs.gamma_method for details.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.gm": {"fullname": "pyerrors.obs.gm", "modulename": "pyerrors.obs", "qualname": "gm", "kind": "function", "doc": "<p>Vectorized version of the gamma_method applicable to lists or arrays of Obs.</p>\n\n<p>See docstring of pe.Obs.gamma_method for details.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "kind": "function", "doc": "<p>Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>func</strong> (object):\narbitrary function of the form func(data, **kwargs). For the\nautomatic differentiation to work, all numpy functions have to have\nthe autograd wrapper (use 'import autograd.numpy as anp').</li>\n<li><strong>data</strong> (list):\nlist of Obs, e.g. [obs1, obs2, obs3].</li>\n<li><strong>num_grad</strong> (bool):\nif True, numerical derivatives are used instead of autograd\n(default False). To control the numerical differentiation the\nkwargs of numdifftools.step_generators.MaxStepGenerator\ncan be used.</li>\n<li><strong>man_grad</strong> (list):\nmanually supply a list or an array which contains the jacobian\nof func. Use cautiously, supplying the wrong derivative will\nnot be intercepted.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For simple mathematical operations it can be practical to use anonymous\nfunctions. For the ratio of two observables one can e.g. use</p>\n\n<p>new_obs = derived_observable(lambda x: x[0] / x[1], [obs1, obs2])</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">data</span>, </span><span class=\"param\"><span class=\"n\">array_mode</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "kind": "function", "doc": "<p>Reweight a list of observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>weight</strong> (Obs):\nReweighting factor. An Observable that has to be defined on a superset of the\nconfigurations in obs[i].idl for all i.</li>\n<li><strong>obs</strong> (list):\nlist of Obs, e.g. [obs1, obs2, obs3].</li>\n<li><strong>all_configs</strong> (bool):\nif True, the reweighted observables are normalized by the average of\nthe reweighting factor on all configurations in weight.idl and not\non the configurations in obs[i].idl. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "kind": "function", "doc": "<p>Correlate two observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs_a</strong> (Obs):\nFirst observable</li>\n<li><strong>obs_b</strong> (Obs):\nSecond observable</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nOnly works if a single ensemble is present in the Obs.\nCurrently only works if ensemble content is identical (this is not strictly necessary).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_a</span>, </span><span class=\"param\"><span class=\"n\">obs_b</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "kind": "function", "doc": "<p>Calculates the error covariance matrix of a set of observables.</p>\n\n<p>WARNING: This function should be used with care, especially for observables with support on multiple\n         ensembles with differing autocorrelations. See the notes below for details.</p>\n\n<p>The gamma method has to be applied first to all observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs</strong> (list or numpy.ndarray):\nList or one dimensional array of Obs</li>\n<li><strong>visualize</strong> (bool):\nIf True plots the corresponding normalized correlation matrix (default False).</li>\n<li><strong>correlation</strong> (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).</li>\n<li><strong>smooth</strong> (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"n\">visualize</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">smooth</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.invert_corr_cov_cholesky": {"fullname": "pyerrors.obs.invert_corr_cov_cholesky", "modulename": "pyerrors.obs", "qualname": "invert_corr_cov_cholesky", "kind": "function", "doc": "<p>Constructs a lower triangular matrix <code>chol</code> via the Cholesky decomposition of the correlation matrix <code>corr</code>\n   and then returns the inverse covariance matrix <code>chol_inv</code> as a lower triangular matrix by solving <code>chol * x = inverrdiag</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>corr</strong> (np.ndarray):\ncorrelation matrix</li>\n<li><strong>inverrdiag</strong> (np.ndarray):\ndiagonal matrix, the entries are the inverse errors of the data points considered</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">inverrdiag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.sort_corr": {"fullname": "pyerrors.obs.sort_corr", "modulename": "pyerrors.obs", "qualname": "sort_corr", "kind": "function", "doc": "<p>Reorders a correlation matrix to match the alphabetical order of its underlying y data.</p>\n\n<p>The ordering of the input correlation matrix <code>corr</code> is given by the list of keys <code>kl</code>.\nThe input dictionary <code>yd</code> (with the same keys <code>kl</code>) must contain the corresponding y data\nthat the correlation matrix is based on.\nThis function sorts the list of keys <code>kl</code> alphabetically and sorts the matrix <code>corr</code>\naccording to this alphabetical order such that the sorted matrix <code>corr_sorted</code> corresponds\nto the y data <code>yd</code> when arranged in an alphabetical order by its keys.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>corr</strong> (np.ndarray):\nA square correlation matrix constructed using the order of the y data specified by <code>kl</code>.\nThe dimensions of <code>corr</code> should match the total number of y data points in <code>yd</code> combined.</li>\n<li><strong>kl</strong> (list of str):\nA list of keys that denotes the order in which the y data from <code>yd</code> was used to build the\ninput correlation matrix <code>corr</code>.</li>\n<li><strong>yd</strong> (dict of list):\nA dictionary where each key corresponds to a unique identifier, and its value is a list of\ny data points. The total number of y data points across all keys must match the dimensions\nof <code>corr</code>. The lists in the dictionary can be lists of Obs.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>np.ndarray</strong>: A new, sorted correlation matrix that corresponds to the y data from <code>yd</code> when arranged alphabetically by its keys.</li>\n</ul>\n\n<h6 id=\"example\">Example</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">pyerrors</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">pe</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">corr</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mf\">0.3</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mf\">0.3</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">kl</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"s1\">&#39;b&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;a&#39;</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yd</span> <span class=\"o\">=</span> <span class=\"p\">{</span><span class=\"s1\">&#39;a&#39;</span><span class=\"p\">:</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">],</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">:</span> <span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">]}</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sorted_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">obs</span><span class=\"o\">.</span><span class=\"n\">sort_corr</span><span class=\"p\">(</span><span class=\"n\">corr</span><span class=\"p\">,</span> <span class=\"n\">kl</span><span class=\"p\">,</span> <span class=\"n\">yd</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">sorted_corr</span><span class=\"p\">)</span>\n<span class=\"go\">array([[1. , 0.3, 0.4],</span>\n<span class=\"go\">       [0.3, 1. , 0.2],</span>\n<span class=\"go\">       [0.4, 0.2, 1. ]])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corr</span>, </span><span class=\"param\"><span class=\"n\">kl</span>, </span><span class=\"param\"><span class=\"n\">yd</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "kind": "function", "doc": "<p>Imports jackknife samples and returns an Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>jacks</strong> (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N jackknife samples as first to Nth entry.</li>\n<li><strong>name</strong> (str):\nname of the ensemble the samples are defined on.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">jacks</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.import_bootstrap": {"fullname": "pyerrors.obs.import_bootstrap", "modulename": "pyerrors.obs", "qualname": "import_bootstrap", "kind": "function", "doc": "<p>Imports bootstrap samples and returns an Obs</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>boots</strong> (numpy.ndarray):\nnumpy array containing the mean value as zeroth entry and\nthe N bootstrap samples as first to Nth entry.</li>\n<li><strong>name</strong> (str):\nname of the ensemble the samples are defined on.</li>\n<li><strong>random_numbers</strong> (np.ndarray):\nArray of shape (samples, length) containing the random numbers to generate the bootstrap samples,\nwhere samples is the number of bootstrap samples and length is the length of the original Monte Carlo\nchain to be reconstructed.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">boots</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">random_numbers</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "kind": "function", "doc": "<p>Combine all observables in list_of_obs into one new observable.\nThis allows to merge Obs that have been computed on multiple replica\nof the same ensemble.\nIf you like to merge Obs that are based on several ensembles, please\naverage them yourself.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>list_of_obs</strong> (list):\nlist of the Obs object to be combined</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is not possible to combine obs which are based on the same replicum</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">list_of_obs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "kind": "function", "doc": "<p>Create an Obs based on mean(s) and a covariance matrix</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>mean</strong> (list of floats or float):\nN mean value(s) of the new Obs</li>\n<li><strong>cov</strong> (list or array):\n2d (NxN) Covariance matrix, 1d diagonal entries or 0d covariance</li>\n<li><strong>name</strong> (str):\nidentifier for the covariance matrix</li>\n<li><strong>grad</strong> (list or array):\nGradient of the Covobs wrt. the means belonging to cov.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "kind": "function", "doc": "<p>Finds the root of the function func(x, d) where d is an <code>Obs</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>d</strong> (Obs):\nObs passed to the function.</li>\n<li><p><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">autograd.numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">anp</span>\n<span class=\"k\">def</span><span class=\"w\"> </span><span class=\"nf\">root_func</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">):</span>\n    <span class=\"k\">return</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">x</span> <span class=\"o\">**</span> <span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">d</span>\n</code></pre>\n</div></li>\n<li><p><strong>guess</strong> (float):\nInitial guess for the minimization.</p></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (Obs):\n<code>Obs</code> valued root of the function.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">d</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special": {"fullname": "pyerrors.special", "modulename": "pyerrors.special", "kind": "module", "doc": "<p></p>\n"}, "pyerrors.special.beta": {"fullname": "pyerrors.special.beta", "modulename": "pyerrors.special", "qualname": "beta", "kind": "function", "doc": "<p>beta(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>beta(a, b, out=None)</p>\n\n<p>Beta function.</p>\n\n<p>This function is defined in <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> as</p>\n\n<p>$$B(a, b) = \\int_0^1 t^{a-1}(1-t)^{b-1}dt\n        = \\frac{\\Gamma(a)\\Gamma(b)}{\\Gamma(a+b)},$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nReal-valued arguments</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function result</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the beta function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>betainc</code>:   the regularized incomplete beta function<br />\n<code>betaln</code>:  the natural logarithm of the absolute\nvalue of the beta function  </p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>The beta function relates to the gamma function by the\ndefinition given above:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"go\">0.08333333333333333</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">)</span><span class=\"o\">*</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mi\">2</span> <span class=\"o\">+</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"go\">0.08333333333333333</span>\n</code></pre>\n</div>\n\n<p>As this relationship demonstrates, the beta function\nis symmetric:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mf\">1.7</span><span class=\"p\">,</span> <span class=\"mf\">2.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.16567527689031739</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mf\">2.4</span><span class=\"p\">,</span> <span class=\"mf\">1.7</span><span class=\"p\">)</span>\n<span class=\"go\">0.16567527689031739</span>\n</code></pre>\n</div>\n\n<p>This function satisfies \\( B(1, b) = 1/b \\):</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">)</span>\n<span class=\"go\">0.25</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions,\nEq. 5.12.1. <a href=\"https://dlmf.nist.gov/5.12\">https://dlmf.nist.gov/5.12</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.betainc": {"fullname": "pyerrors.special.betainc", "modulename": "pyerrors.special", "qualname": "betainc", "kind": "function", "doc": "<p>betainc(x1, x2, x3, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>betainc(a, b, x, out=None)</p>\n\n<p>Regularized incomplete beta function.</p>\n\n<p>Computes the regularized incomplete beta function, defined as <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>:</p>\n\n<p>$$I_x(a, b) = \\frac{\\Gamma(a+b)}{\\Gamma(a)\\Gamma(b)} \\int_0^x\nt^{a-1}(1-t)^{b-1}dt,$$</p>\n\n<p>for \\( 0 \\leq x \\leq 1 \\).</p>\n\n<p>This function is the cumulative distribution function for the beta\ndistribution; its range is [0, 1].</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nPositive, real-valued parameters</li>\n<li><strong>x</strong> (array_like):\nReal-valued such that \\( 0 \\leq x \\leq 1 \\),\nthe upper limit of integration</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the regularized incomplete beta function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>beta</code>:  beta function<br />\n<code>betaincinv</code>:  inverse of the regularized incomplete beta function<br />\n<code>betaincc</code>:  complement of the regularized incomplete beta function<br />\n<code>scipy.stats.beta</code>:  beta distribution  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The term <em>regularized</em> in the name of this function refers to the\nscaling of the function by the gamma function terms shown in the\nformula.  When not qualified as <em>regularized</em>, the name <em>incomplete\nbeta function</em> often refers to just the integral expression,\nwithout the gamma terms.  One can use the function <code>beta</code> from\n<code>scipy.special</code> to get this \"nonregularized\" incomplete beta\nfunction by multiplying the result of <code>betainc(a, b, x)</code> by\n<code>beta(a, b)</code>.</p>\n\n<p>This function wraps the <code>ibeta</code> routine from the\nBoost Math C++ library <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">2</a></sup>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Let \\( B(a, b) \\) be the <code>beta</code> function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>The coefficient in terms of <code>gamma</code> is equal to\n\\( 1/B(a, b) \\). Also, when \\( x=1 \\)\nthe integral is equal to \\( B(a, b) \\).\nTherefore, \\( I_{x=1}(a, b) = 1 \\) for any \\( a, b \\).</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">0.2</span><span class=\"p\">,</span> <span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">1.0</span><span class=\"p\">)</span>\n<span class=\"go\">1.0</span>\n</code></pre>\n</div>\n\n<p>It satisfies\n\\( I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b)) \\),\nwhere \\( F \\) is the hypergeometric function <code>hyp2f1</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">1.4</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span><span class=\"o\">**</span><span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">hyp2f1</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">a</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"o\">*</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">))</span>\n<span class=\"go\">0.8148904036225295</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.8148904036225296</span>\n</code></pre>\n</div>\n\n<p>This functions satisfies the relationship\n\\( I_x(a, b) = 1 - I_{1-x}(b, a) \\):</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">2.2</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.49339638807619446</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">betainc</span><span class=\"p\">(</span><span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">2.2</span><span class=\"p\">,</span> <span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"mf\">0.4</span><span class=\"p\">)</span>\n<span class=\"go\">0.49339638807619446</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/8.17\">https://dlmf.nist.gov/8.17</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>The Boost Developers. \"Boost C++ Libraries\". <a href=\"https://www.boost.org/\">https://www.boost.org/</a>.&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.betaln": {"fullname": "pyerrors.special.betaln", "modulename": "pyerrors.special", "qualname": "betaln", "kind": "function", "doc": "<p>betaln(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>betaln(a, b, out=None)</p>\n\n<p>Natural logarithm of absolute value of beta function.</p>\n\n<p>Computes <code>ln(abs(beta(a, b)))</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a, b</strong> (array_like):\nPositive, real-valued parameters</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Value of the betaln function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>betainc</code>:   the regularized incomplete beta function<br />\n<code>beta</code>:  the beta function  </p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">betaln</span><span class=\"p\">,</span> <span class=\"n\">beta</span>\n</code></pre>\n</div>\n\n<p>Verify that, for moderate values of <code>a</code> and <code>b</code>, <code>betaln(a, b)</code>\nis the same as <code>log(beta(a, b))</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">betaln</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">)</span>\n<span class=\"go\">-4.0943445622221</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">))</span>\n<span class=\"go\">-4.0943445622221</span>\n</code></pre>\n</div>\n\n<p>In the following <code>beta(a, b)</code> underflows to 0, so we can't compute\nthe logarithm of the actual value.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"mi\">400</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"mi\">900</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">beta</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">0.0</span>\n</code></pre>\n</div>\n\n<p>We can compute the logarithm of <code>beta(a, b)</code> by using <code>betaln</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">betaln</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">-804.3069951764146</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.polygamma": {"fullname": "pyerrors.special.polygamma", "modulename": "pyerrors.special", "qualname": "polygamma", "kind": "function", "doc": "<p>Polygamma functions.</p>\n\n<p>Defined as \\( \\psi^{(n)}(x) \\) where \\( \\psi \\) is the\n<code>digamma</code> function. See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>n</strong> (array_like):\nThe order of the derivative of the digamma function; must be\nintegral</li>\n<li><strong>x</strong> (array_like):\nReal valued input</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>ndarray</strong>: Function results</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>digamma</code>  </p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST, Digital Library of Mathematical Functions,\n    <a href=\"https://dlmf.nist.gov/5.15\">https://dlmf.nist.gov/5.15</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">25.5</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">polygamma</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.64493407,  0.39493407,  0.03999467])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">polygamma</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span> <span class=\"o\">==</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ True,  True,  True], dtype=bool)</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.psi": {"fullname": "pyerrors.special.psi", "modulename": "pyerrors.special", "qualname": "psi", "kind": "function", "doc": "<p>psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>psi(z, out=None)</p>\n\n<p>The digamma function.</p>\n\n<p>The logarithmic derivative of the gamma function evaluated at <code>z</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex argument.</li>\n<li><strong>out</strong> (ndarray, optional):\nArray for the computed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>digamma</strong> (scalar or ndarray):\nComputed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For large values not close to the negative real axis, <code>psi</code> is\ncomputed using the asymptotic series (5.11.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">2</a></sup> is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">3</a></sup> is\nused first. Note that <code>psi</code> has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">4</a></sup>, so the\nfunction should maintain full accuracy around the origin.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">psi</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mi\">3</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<p>Verify psi(z) = psi(z + 1) - 1/z:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"o\">/</span><span class=\"n\">z</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 3 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) <a href=\"http://mpmath.org/\">http://mpmath.org/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 4 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.digamma": {"fullname": "pyerrors.special.digamma", "modulename": "pyerrors.special", "qualname": "digamma", "kind": "function", "doc": "<p>psi(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>psi(z, out=None)</p>\n\n<p>The digamma function.</p>\n\n<p>The logarithmic derivative of the gamma function evaluated at <code>z</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex argument.</li>\n<li><strong>out</strong> (ndarray, optional):\nArray for the computed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>digamma</strong> (scalar or ndarray):\nComputed values of <code>psi</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For large values not close to the negative real axis, <code>psi</code> is\ncomputed using the asymptotic series (5.11.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>. For small\narguments not close to the negative real axis, the recurrence\nrelation (5.5.2) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">2</a></sup> is used until the argument is large\nenough to use the asymptotic series. For values close to the\nnegative real axis, the reflection formula (5.5.4) from <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">3</a></sup> is\nused first. Note that <code>psi</code> has a family of zeros on the\nnegative real axis which occur between the poles at nonpositive\nintegers. Around the zeros the reflection formula suffers from\ncancellation and the implementation loses precision. The sole\npositive zero and the first negative zero, however, are handled\nseparately by precomputing series expansions using <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">4</a></sup>, so the\nfunction should maintain full accuracy around the origin.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">psi</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mi\">3</span> <span class=\"o\">+</span> <span class=\"mi\">4</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<p>Verify psi(z) = psi(z + 1) - 1/z:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">psi</span><span class=\"p\">(</span><span class=\"n\">z</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"mi\">1</span><span class=\"o\">/</span><span class=\"n\">z</span>\n<span class=\"go\">(1.55035981733341+1.0105022091860445j)</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-1\">\n<p>NIST Digital Library of Mathematical Functions\n<a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 3 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Fredrik Johansson and others.\n\"mpmath: a Python library for arbitrary-precision floating-point arithmetic\"\n(Version 0.19) <a href=\"http://mpmath.org/\">http://mpmath.org/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 4 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gamma": {"fullname": "pyerrors.special.gamma", "modulename": "pyerrors.special", "qualname": "gamma", "kind": "function", "doc": "<p>gamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gamma(z, out=None)</p>\n\n<p>gamma function.</p>\n\n<p>The gamma function is defined as</p>\n\n<p>$$\\Gamma(z) = \\int_0^\\infty t^{z-1} e^{-t} dt$$</p>\n\n<p>for \\( \\Re(z) &gt; 0 \\) and is extended to the rest of the complex\nplane by analytic continuation. See [dlmf]_ for more details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex valued argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the gamma function</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function is often referred to as the generalized\nfactorial since \\( \\Gamma(n + 1) = n! \\) for natural numbers\n\\( n \\). More generally it satisfies the recurrence relation\n\\( \\Gamma(z + 1) = z \\cdot \\Gamma(z) \\) for complex \\( z \\),\nwhich, combined with the fact that \\( \\Gamma(1) = 1 \\), implies\nthe above identity for \\( z = n \\).</p>\n\n<p>The gamma function has poles at non-negative integers and the sign\nof infinity as z approaches each pole depends upon the direction in\nwhich the pole is approached. For this reason, the consistent thing\nis for gamma(z) to return NaN at negative integers, and to return\n-inf when x = -0.0 and +inf when x = 0.0, using the signbit of zero\nto signify the direction in which the origin is being approached. This\nis for instance what is recommended for the gamma function in annex F\nentry 9.5.4 of the Iso C 99 standard [isoc99]_.</p>\n\n<p>Prior to SciPy version 1.15, <code>scipy.special.gamma(z)</code> returned <code>+inf</code>\nat each pole. This was fixed in version 1.15, but with the following\nconsequence. Expressions where gamma appears in the denominator\nsuch as</p>\n\n<p><code>gamma(u) * gamma(v) / (gamma(w) * gamma(x))</code></p>\n\n<p>no longer evaluate to 0 if the numerator is well defined but there is a\npole in the denominator. Instead such expressions evaluate to NaN. We\nrecommend instead using the function <code>rgamma</code> for the reciprocal gamma\nfunction in such cases. The above expression could for instance be written\nas</p>\n\n<p><code>gamma(u) * gamma(v) * (rgamma(w) * rgamma(x))</code></p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5.2#E1\">https://dlmf.nist.gov/5.2#E1</a>\n.. [isoc99] <a href=\"https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf\">https://www.open-std.org/jtc1/sc22/wg14/www/docs/n1256.pdf</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">gamma</span><span class=\"p\">,</span> <span class=\"n\">factorial</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">5</span><span class=\"p\">])</span>\n<span class=\"go\">array([         inf,   1.77245385,   1.        ,  24.        ])</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">z</span> <span class=\"o\">=</span> <span class=\"mf\">2.5</span> <span class=\"o\">+</span> <span class=\"mi\">1</span><span class=\"n\">j</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>\n<span class=\"go\">(0.77476210455108352+0.70763120437959293j)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"o\">+</span><span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"n\">z</span><span class=\"o\">*</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">z</span><span class=\"p\">)</span>  <span class=\"c1\"># Recurrence property</span>\n<span class=\"go\">((1.2292740569981171+2.5438401155000685j),</span>\n<span class=\"go\"> (1.2292740569981158+2.5438401155000658j))</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span><span class=\"o\">**</span><span class=\"mi\">2</span>  <span class=\"c1\"># gamma(0.5) = sqrt(pi)</span>\n<span class=\"go\">3.1415926535897927</span>\n</code></pre>\n</div>\n\n<p>Plot gamma(x) for real x</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">5.5</span><span class=\"p\">,</span> <span class=\"mi\">2251</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"s1\">&#39;b&#39;</span><span class=\"p\">,</span> <span class=\"n\">alpha</span><span class=\"o\">=</span><span class=\"mf\">0.6</span><span class=\"p\">,</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"s1\">&#39;gamma(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">k</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">7</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">k</span><span class=\"p\">,</span> <span class=\"n\">factorial</span><span class=\"p\">(</span><span class=\"n\">k</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">),</span> <span class=\"s1\">&#39;k*&#39;</span><span class=\"p\">,</span> <span class=\"n\">alpha</span><span class=\"o\">=</span><span class=\"mf\">0.6</span><span class=\"p\">,</span>\n<span class=\"gp\">... </span>         <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"s1\">&#39;(x-1)!, x = 1, 2, ...&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">,</span> <span class=\"mf\">5.5</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">(</span><span class=\"n\">loc</span><span class=\"o\">=</span><span class=\"s1\">&#39;lower right&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammaln": {"fullname": "pyerrors.special.gammaln", "modulename": "pyerrors.special", "qualname": "gammaln", "kind": "function", "doc": "<p>gammaln(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammaln(x, out=None)</p>\n\n<p>Logarithm of the absolute value of the gamma function.</p>\n\n<p>Defined as</p>\n\n<p>$$\\ln(\\lvert\\Gamma(x)\\rvert)$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function. For more details on\nthe gamma function, see [dlmf]_.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the log of the absolute value of gamma</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammasgn</code>:  sign of the gamma function<br />\n<code>loggamma</code>:  principal branch of the logarithm of the gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is the same function as the Python standard library function\n<code>math.lgamma()</code>.</p>\n\n<p>When used in conjunction with <code>gammasgn</code>, this function is useful\nfor working in logspace on the real axis without having to deal\nwith complex numbers via the relation <code>exp(gammaln(x)) =\ngammasgn(x) * gamma(x)</code>.</p>\n\n<p>For complex-valued log-gamma, use <code>loggamma</code> instead of <code>gammaln</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5\">https://dlmf.nist.gov/5</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It has two positive zeros.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">])</span>\n<span class=\"go\">array([0., 0.])</span>\n</code></pre>\n</div>\n\n<p>It has poles at nonpositive integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([inf, inf, inf, inf, inf])</span>\n</code></pre>\n</div>\n\n<p>It asymptotically approaches <code>x * log(x)</code> (Stirling's formula).</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">1e10</span><span class=\"p\">,</span> <span class=\"mf\">1e20</span><span class=\"p\">,</span> <span class=\"mf\">1e40</span><span class=\"p\">,</span> <span class=\"mf\">1e80</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammainc": {"fullname": "pyerrors.special.gammainc", "modulename": "pyerrors.special", "qualname": "gammainc", "kind": "function", "doc": "<p>gammainc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammainc(a, x, out=None)</p>\n\n<p>Regularized lower incomplete gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$P(a, x) = \\frac{1}{\\Gamma(a)} \\int_0^x t^{a - 1}e^{-t} dt$$</p>\n\n<p>for \\( a &gt; 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nPositive parameter</li>\n<li><strong>x</strong> (array_like):\nNonnegative argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the lower incomplete gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammaincc</code>:  regularized upper incomplete gamma function<br />\n<code>gammaincinv</code>:  inverse of the regularized lower incomplete gamma function<br />\n<code>gammainccinv</code>:  inverse of the regularized upper incomplete gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The function satisfies the relation <code>gammainc(a, x) +\ngammaincc(a, x) = 1</code> where <code>gammaincc</code> is the regularized upper\nincomplete gamma function.</p>\n\n<p>The implementation largely follows that of [boost]_.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical functions\n          <a href=\"https://dlmf.nist.gov/8.2#E4\">https://dlmf.nist.gov/8.2#E4</a>\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   <a href=\"https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html\">https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the CDF of the gamma distribution, so it starts at 0 and\nmonotonically increases to 1.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">])</span>\n<span class=\"go\">array([0.        , 0.84270079, 0.99999226, 1.        ])</span>\n</code></pre>\n</div>\n\n<p>It is equal to one minus the upper incomplete gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.6289066304773024</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.6289066304773024</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammaincc": {"fullname": "pyerrors.special.gammaincc", "modulename": "pyerrors.special", "qualname": "gammaincc", "kind": "function", "doc": "<p>gammaincc(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammaincc(a, x, out=None)</p>\n\n<p>Regularized upper incomplete gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$Q(a, x) = \\frac{1}{\\Gamma(a)} \\int_x^\\infty t^{a - 1}e^{-t} dt$$</p>\n\n<p>for \\( a &gt; 0 \\) and \\( x \\geq 0 \\). See [dlmf]_ for details.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nPositive parameter</li>\n<li><strong>x</strong> (array_like):\nNonnegative argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the upper incomplete gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gammainc</code>:  regularized lower incomplete gamma function<br />\n<code>gammaincinv</code>:  inverse of the regularized lower incomplete gamma function<br />\n<code>gammainccinv</code>:  inverse of the regularized upper incomplete gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The function satisfies the relation <code>gammainc(a, x) +\ngammaincc(a, x) = 1</code> where <code>gammainc</code> is the regularized lower\nincomplete gamma function.</p>\n\n<p>The implementation largely follows that of [boost]_.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical functions\n          <a href=\"https://dlmf.nist.gov/8.2#E4\">https://dlmf.nist.gov/8.2#E4</a>\n.. [boost] Maddock et. al., \"Incomplete Gamma Functions\",\n   <a href=\"https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html\">https://www.boost.org/doc/libs/1_61_0/libs/math/doc/html/math_toolkit/sf_gamma/igamma.html</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the survival function of the gamma distribution, so it\nstarts at 1 and monotonically decreases to 0.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.00000000e+00, 1.57299207e-01, 7.74421643e-06, 2.08848758e-45,</span>\n<span class=\"go\">       0.00000000e+00])</span>\n</code></pre>\n</div>\n\n<p>It is equal to one minus the lower incomplete gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.4</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaincc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.37109336952269756</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">-</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammainc</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">0.37109336952269756</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.gammasgn": {"fullname": "pyerrors.special.gammasgn", "modulename": "pyerrors.special", "qualname": "gammasgn", "kind": "function", "doc": "<p>gammasgn(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>gammasgn(x, out=None)</p>\n\n<p>Sign of the gamma function.</p>\n\n<p>It is defined as</p>\n\n<p>$$\\text{gammasgn}(x) =\n\\begin{cases}\n  +1 &amp; \\Gamma(x) &gt; 0 \\\n  -1 &amp; \\Gamma(x) &lt; 0\n\\end{cases}$$</p>\n\n<p>where \\( \\Gamma \\) is the gamma function; see <code>gamma</code>. This\ndefinition is complete since the gamma function is never zero;\nsee the discussion after [dlmf]_.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Sign of the gamma function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma</code>:  the gamma function<br />\n<code>gammaln</code>:  log of the absolute value of the gamma function<br />\n<code>loggamma</code>:  analytic continuation of the log of the gamma function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function can be computed as <code>gammasgn(x) *\nnp.exp(gammaln(x))</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] NIST Digital Library of Mathematical Functions\n          <a href=\"https://dlmf.nist.gov/5.2#E1\">https://dlmf.nist.gov/5.2#E1</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is 1 for <code>x &gt; 0</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1., 1., 1., 1.])</span>\n</code></pre>\n</div>\n\n<p>It alternates between -1 and 1 for negative integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">3.5</span><span class=\"p\">])</span>\n<span class=\"go\">array([-1.,  1., -1.,  1.])</span>\n</code></pre>\n</div>\n\n<p>It can be used to compute the gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"p\">[</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">]</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammasgn</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span> <span class=\"o\">*</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"go\">array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.88622693,  1.77245385, -3.5449077 ,  2.3632718 ])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.rgamma": {"fullname": "pyerrors.special.rgamma", "modulename": "pyerrors.special", "qualname": "rgamma", "kind": "function", "doc": "<p>rgamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>rgamma(z, out=None)</p>\n\n<p>Reciprocal of the gamma function.</p>\n\n<p>Defined as \\( 1 / \\Gamma(z) \\), where \\( \\Gamma \\) is the\ngamma function. For more on the gamma function see <code>gamma</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>z</strong> (array_like):\nReal or complex valued input</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Function results</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>gamma,</code>, <code>gammaln,</code>, <code>loggamma</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The gamma function has no zeros and has simple poles at\nnonpositive integers, so <code>rgamma</code> is an entire function with zeros\nat the nonpositive integers. See the discussion in [dlmf]_ for\nmore details.</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>.. [dlmf] Nist, Digital Library of Mathematical functions,\n    <a href=\"https://dlmf.nist.gov/5.2#i\">https://dlmf.nist.gov/5.2#i</a></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">sc</span>\n</code></pre>\n</div>\n\n<p>It is the reciprocal of the gamma function.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.        , 1.        , 0.5       , 0.16666667])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"mi\">1</span> <span class=\"o\">/</span> <span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">gamma</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">4</span><span class=\"p\">])</span>\n<span class=\"go\">array([1.        , 1.        , 0.5       , 0.16666667])</span>\n</code></pre>\n</div>\n\n<p>It is zero at nonpositive integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"go\">array([0., 0., 0., 0.])</span>\n</code></pre>\n</div>\n\n<p>It rapidly underflows to zero along the positive real axis.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">sc</span><span class=\"o\">.</span><span class=\"n\">rgamma</span><span class=\"p\">([</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">100</span><span class=\"p\">,</span> <span class=\"mi\">179</span><span class=\"p\">])</span>\n<span class=\"go\">array([2.75573192e-006, 1.07151029e-156, 0.00000000e+000])</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.multigammaln": {"fullname": "pyerrors.special.multigammaln", "modulename": "pyerrors.special", "qualname": "multigammaln", "kind": "function", "doc": "<p>Returns the log of multivariate gamma, also sometimes called the\ngeneralized gamma.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (ndarray):\nThe multivariate gamma is computed for each item of <code>a</code>.</li>\n<li><strong>d</strong> (int):\nThe dimension of the space of integration.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (ndarray):\nThe values of the log multivariate gamma at the given points <code>a</code>.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The formal definition of the multivariate gamma of dimension d for a real\n<code>a</code> is</p>\n\n<p>$$\\Gamma_d(a) = \\int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA$$</p>\n\n<p>with the condition \\( a &gt; (d-1)/2 \\), and \\( A &gt; 0 \\) being the set of\nall the positive definite matrices of dimension <code>d</code>.  Note that <code>a</code> is a\nscalar: the integrand only is multivariate, the argument is not (the\nfunction is defined over a subset of the real set).</p>\n\n<p>This can be proven to be equal to the much friendlier equation</p>\n\n<p>$$\\Gamma_d(a) = \\pi^{d(d-1)/4} \\prod_{i=1}^{d} \\Gamma(a - (i-1)/2).$$</p>\n\n<h6 id=\"references\">References</h6>\n\n<p>R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in\nprobability and mathematical statistics).</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">multigammaln</span><span class=\"p\">,</span> <span class=\"n\">gammaln</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"mf\">23.5</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">d</span> <span class=\"o\">=</span> <span class=\"mi\">10</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">multigammaln</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">)</span>\n<span class=\"go\">454.1488605074416</span>\n</code></pre>\n</div>\n\n<p>Verify that the result agrees with the logarithm of the equation\nshown above:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">d</span><span class=\"o\">*</span><span class=\"p\">(</span><span class=\"n\">d</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span><span class=\"o\">/</span><span class=\"mi\">4</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">pi</span><span class=\"p\">)</span> <span class=\"o\">+</span> <span class=\"n\">gammaln</span><span class=\"p\">(</span><span class=\"n\">a</span> <span class=\"o\">-</span> <span class=\"mf\">0.5</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">))</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">()</span>\n<span class=\"go\">454.1488605074416</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.kn": {"fullname": "pyerrors.special.kn", "modulename": "pyerrors.special", "qualname": "kn", "kind": "function", "doc": "<p>Modified Bessel function of the second kind of integer order n</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.j0": {"fullname": "pyerrors.special.j0", "modulename": "pyerrors.special", "qualname": "j0", "kind": "function", "doc": "<p>j0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>j0(x, out=None)</p>\n\n<p>Bessel function of the first kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function of the first kind of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jv</code>:  Bessel function of real order and complex argument.<br />\n<code>spherical_jn</code>:  spherical Bessel functions.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval the following rational approximation is used:</p>\n\n<p>$$J_0(x) \\approx (w - r_1^2)(w - r_2^2) \\frac{P_3(w)}{Q_8(w)},$$</p>\n\n<p>where \\( w = x^2 \\) and \\( r_1 \\), \\( r_2 \\) are the zeros of\n\\( J_0 \\), and \\( P_3 \\) and \\( Q_8 \\) are polynomials of degrees 3\nand 8, respectively.</p>\n\n<p>In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>j0</code>.\nIt should not be confused with the spherical Bessel functions (see\n<code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">j0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.7651976865579665</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">4.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([ 0.22389078,  1.        , -0.39714981])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -20 to 20.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">j0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.y0": {"fullname": "pyerrors.special.y0", "modulename": "pyerrors.special", "qualname": "y0", "kind": "function", "doc": "<p>y0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>y0(x, out=None)</p>\n\n<p>Bessel function of the second kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function of the second kind of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>j0</code>:  Bessel function of the first kind of order 0<br />\n<code>yv</code>:  Bessel function of the first kind  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 5] and (5, infinity). In the\nfirst interval a rational approximation \\( R(x) \\) is employed to\ncompute,</p>\n\n<p>$$Y_0(x) = R(x) + \\frac{2 \\log(x) J_0(x)}{\\pi},$$</p>\n\n<p>where \\( J_0 \\) is the Bessel function of the first kind of order 0.</p>\n\n<p>In the second interval, the Hankel asymptotic expansion is employed with\ntwo rational functions of degree 6/6 and 7/7.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>y0</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">y0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.08825696421567697</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-0.44451873,  0.51037567,  0.37685001])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.j1": {"fullname": "pyerrors.special.j1", "modulename": "pyerrors.special", "qualname": "j1", "kind": "function", "doc": "<p>j1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>j1(x, out=None)</p>\n\n<p>Bessel function of the first kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function of the first kind of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jv</code>:  Bessel function of the first kind<br />\n<code>spherical_jn</code>:  spherical Bessel functions.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 24 term Chebyshev expansion is used. In the second, the\nasymptotic trigonometric representation is employed using two rational\nfunctions of degree 5/5.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>j1</code>.\nIt should not be confused with the spherical Bessel functions (see\n<code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">j1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.44005058574493355</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">4.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-0.57672481,  0.        , -0.06604333])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -20 to 20.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mf\">20.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">j1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.y1": {"fullname": "pyerrors.special.y1", "modulename": "pyerrors.special", "qualname": "y1", "kind": "function", "doc": "<p>y1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>y1(x, out=None)</p>\n\n<p>Bessel function of the second kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function of the second kind of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>j1</code>:  Bessel function of the first kind of order 1<br />\n<code>yn</code>:  Bessel function of the second kind<br />\n<code>yv</code>:  Bessel function of the second kind  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The domain is divided into the intervals [0, 8] and (8, infinity). In the\nfirst interval a 25 term Chebyshev expansion is used, and computing\n\\( J_1 \\) (the Bessel function of the first kind) is required. In the\nsecond, the asymptotic trigonometric representation is employed using two\nrational functions of degree 5/5.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>y1</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">y1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">-0.7812128213002888</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-1.47147239, -0.10703243,  0.32467442])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">y1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.jn": {"fullname": "pyerrors.special.jn", "modulename": "pyerrors.special", "qualname": "jn", "kind": "function", "doc": "<p>jv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>jv(v, z, out=None)</p>\n\n<p>Bessel function of the first kind of real order and complex argument.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like):\nOrder (float).</li>\n<li><strong>z</strong> (array_like):\nArgument (float or complex).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>J</strong> (scalar or ndarray):\nValue of the Bessel function, \\( J_v(z) \\).</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>jve</code>:  \\( J_v \\) with leading exponential behavior stripped off.<br />\n<code>spherical_jn</code>:  spherical Bessel functions.<br />\n<code>j0</code>:  faster version of this function for order 0.<br />\n<code>j1</code>:  faster version of this function for order 1.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For positive <code>v</code> values, the computation is carried out using the AMOS\n<sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> <code>zbesj</code> routine, which exploits the connection to the modified\nBessel function \\( I_v \\),</p>\n\n<p>$$J_v(z) = \\exp(v\\pi\\imath/2) I_v(-\\imath z)\\qquad (\\Im z &gt; 0)</p>\n\n<p>J_v(z) = \\exp(-v\\pi\\imath/2) I_v(\\imath z)\\qquad (\\Im z &lt; 0)$$</p>\n\n<p>For negative <code>v</code> values the formula,</p>\n\n<p>$$J_{-v}(z) = J_v(z) \\cos(\\pi v) - Y_v(z) \\sin(\\pi v)$$</p>\n\n<p>is used, where \\( Y_v(z) \\) is the Bessel function of the second\nkind, computed using the AMOS routine <code>zbesy</code>.  Note that the second\nterm is exactly zero for integer <code>v</code>; to improve accuracy the second\nterm is explicitly omitted for <code>v</code> values such that <code>v = floor(v)</code>.</p>\n\n<p>Not to be confused with the spherical Bessel functions (see <code>spherical_jn</code>).</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">jv</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.7651976865579666</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(0.7651976865579666, 0.44005058574493355, 0.24029783912342725)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.76519769, 0.44005059, 0.24029784])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.22389078,  1.        , -0.26005195])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 0.22389078,  1.        , -0.26005195],</span>\n<span class=\"go\">       [-0.57672481,  0.        ,  0.33905896]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -10 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">jv</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$J_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.yn": {"fullname": "pyerrors.special.yn", "modulename": "pyerrors.special", "qualname": "yn", "kind": "function", "doc": "<p>yn(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>yn(n, x, out=None)</p>\n\n<p>Bessel function of the second kind of integer order and real argument.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>n</strong> (array_like):\nOrder (integer).</li>\n<li><strong>x</strong> (array_like):\nArgument (float).</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Y</strong> (scalar or ndarray):\nValue of the Bessel function, \\( Y_n(x) \\).</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>yv</code>:  For real order and real or complex argument.<br />\n<code>y0</code>:  faster implementation of this function for order 0<br />\n<code>y1</code>:  faster implementation of this function for order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>yn</code>.</p>\n\n<p>The function is evaluated by forward recurrence on <code>n</code>, starting with\nvalues computed by the Cephes routines <code>y0</code> and <code>y1</code>. If <code>n = 0</code> or 1,\nthe routine for <code>y0</code> or <code>y1</code> is called directly.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">yn</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.08825696421567697</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(0.08825696421567697, -0.7812128213002888, -1.6506826068162546)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([ 0.08825696, -0.78121282, -1.65068261])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">,</span> <span class=\"mf\">8.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([-0.44451873,  0.37685001,  0.22352149])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[-0.44451873,  0.37685001,  0.22352149],</span>\n<span class=\"go\">       [-1.47147239,  0.32467442, -0.15806046]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from 0 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">yn</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$Y_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.i0": {"fullname": "pyerrors.special.i0", "modulename": "pyerrors.special", "qualname": "i0", "kind": "function", "doc": "<p>i0(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>i0(x, out=None)</p>\n\n<p>Modified Bessel function of order 0.</p>\n\n<p>Defined as,</p>\n\n<p>$$I_0(x) = \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{(k!)^2} = J_0(\\imath x),$$</p>\n\n<p>where \\( J_0 \\) is the Bessel function of the first kind of order 0.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float)</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>I</strong> (scalar or ndarray):\nValue of the modified Bessel function of order 0 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of any order<br />\n<code>i0e</code>:  Exponentially scaled modified Bessel function of order 0  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>i0</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">i0</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">1.2660658777520082</span>\n</code></pre>\n</div>\n\n<p>Calculate at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.5</span><span class=\"p\">]))</span>\n<span class=\"go\">array([2.2795853 , 1.        , 7.37820343])</span>\n</code></pre>\n</div>\n\n<p>Plot the function from -10 to 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">i0</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.i1": {"fullname": "pyerrors.special.i1", "modulename": "pyerrors.special", "qualname": "i1", "kind": "function", "doc": "<p>i1(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>i1(x, out=None)</p>\n\n<p>Modified Bessel function of order 1.</p>\n\n<p>Defined as,</p>\n\n<p>$$I_1(x) = \\frac{1}{2}x \\sum_{k=0}^\\infty \\frac{(x^2/4)^k}{k! (k + 1)!}\n       = -\\imath J_1(\\imath x),$$</p>\n\n<p>where \\( J_1 \\) is the Bessel function of the first kind of order 1.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nArgument (float)</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>I</strong> (scalar or ndarray):\nValue of the modified Bessel function of order 1 at <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of the first kind<br />\n<code>i1e</code>:  Exponentially scaled modified Bessel function of order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The range is partitioned into the two intervals [0, 8] and (8, infinity).\nChebyshev polynomial expansions are employed in each interval.</p>\n\n<p>This function is a wrapper for the Cephes <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> routine <code>i1</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Calculate the function at one point:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">i1</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">0.5651591039924851</span>\n</code></pre>\n</div>\n\n<p>Calculate the function at several points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">6.</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-1.59063685,  0.        , 61.34193678])</span>\n</code></pre>\n</div>\n\n<p>Plot the function between -10 and 10.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mf\">10.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">i1</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Cephes Mathematical Functions Library,\n<a href=\"http://www.netlib.org/cephes/\">http://www.netlib.org/cephes/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.iv": {"fullname": "pyerrors.special.iv", "modulename": "pyerrors.special", "qualname": "iv", "kind": "function", "doc": "<p>iv(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>iv(v, z, out=None)</p>\n\n<p>Modified Bessel function of the first kind of real order.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like):\nOrder. If <code>z</code> is of real type and negative, <code>v</code> must be integer\nvalued.</li>\n<li><strong>z</strong> (array_like of float or complex):\nArgument.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the modified Bessel function.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>ive</code>:  This function with leading exponential behavior stripped off.<br />\n<code>i0</code>:  Faster version of this function for order 0.<br />\n<code>i1</code>:  Faster version of this function for order 1.  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For real <code>z</code> and \\( v \\in [-50, 50] \\), the evaluation is carried out\nusing Temme's method <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>.  For larger orders, uniform asymptotic\nexpansions are applied.</p>\n\n<p>For complex <code>z</code> and positive <code>v</code>, the AMOS <sup class=\"footnote-ref\" id=\"fnref-2\"><a href=\"#fn-2\">2</a></sup> <code>zbesi</code> routine is\ncalled. It uses a power series for small <code>z</code>, the asymptotic expansion\nfor large <code>abs(z)</code>, the Miller algorithm normalized by the Wronskian\nand a Neumann series for intermediate magnitudes, and the uniform\nasymptotic expansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large\norders. Backward recurrence is used to generate sequences or reduce\norders when necessary.</p>\n\n<p>The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,</p>\n\n<p>$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$</p>\n\n<p>(valid when the real part of <code>z</code> is positive).  For negative <code>v</code>, the\nformula</p>\n\n<p>$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$</p>\n\n<p>is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine <code>zbesk</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>Evaluate the function of order 0 at one point.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">iv</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">1.2660658777520084</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">),</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">(1.2660658777520084, 0.565159103992485, 0.2935253263474798)</span>\n</code></pre>\n</div>\n\n<p>The evaluation for different orders can be carried out in one call by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([1.26606588, 0.5651591 , 0.29352533])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([2.2795853 , 1.        , 4.88079259])</span>\n</code></pre>\n</div>\n\n<p>If <code>z</code> is an array, the order parameter <code>v</code> must be broadcastable to\nthe correct shape if different orders shall be computed in one call.\nTo calculate the orders 0 and 1 for an 1D array:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">]])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">orders</span><span class=\"o\">.</span><span class=\"n\">shape</span>\n<span class=\"go\">(2, 1)</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"n\">orders</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 2.2795853 ,  1.        ,  4.88079259],</span>\n<span class=\"go\">       [-1.59063685,  0.        ,  3.95337022]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -5 to 5.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">f</span><span class=\"s1\">&#39;$I_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Temme, Journal of Computational Physics, vol 21, 343 (1976)&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n\n<li id=\"fn-2\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-2\" class=\"footnoteBackLink\" title=\"Jump back to footnote 2 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.ive": {"fullname": "pyerrors.special.ive", "modulename": "pyerrors.special", "qualname": "ive", "kind": "function", "doc": "<p>ive(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>ive(v, z, out=None)</p>\n\n<p>Exponentially scaled modified Bessel function of the first kind.</p>\n\n<p>Defined as::</p>\n\n<pre><code>ive(v, z) = iv(v, z) * exp(-abs(z.real))\n</code></pre>\n\n<p>For imaginary numbers without a real part, returns the unscaled\nBessel function of the first kind <code>iv</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>v</strong> (array_like of float):\nOrder.</li>\n<li><strong>z</strong> (array_like of float or complex):\nArgument.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the exponentially scaled modified Bessel function.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>iv</code>:  Modified Bessel function of the first kind<br />\n<code>i0e</code>:  Faster implementation of this function for order 0<br />\n<code>i1e</code>:  Faster implementation of this function for order 1  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>For positive <code>v</code>, the AMOS <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup> <code>zbesi</code> routine is called. It uses a\npower series for small <code>z</code>, the asymptotic expansion for large\n<code>abs(z)</code>, the Miller algorithm normalized by the Wronskian and a\nNeumann series for intermediate magnitudes, and the uniform asymptotic\nexpansions for \\( I_v(z) \\) and \\( J_v(z) \\) for large orders.\nBackward recurrence is used to generate sequences or reduce orders when\nnecessary.</p>\n\n<p>The calculations above are done in the right half plane and continued\ninto the left half plane by the formula,</p>\n\n<p>$$I_v(z \\exp(\\pm\\imath\\pi)) = \\exp(\\pm\\pi v) I_v(z)$$</p>\n\n<p>(valid when the real part of <code>z</code> is positive).  For negative <code>v</code>, the\nformula</p>\n\n<p>$$I_{-v}(z) = I_v(z) + \\frac{2}{\\pi} \\sin(\\pi v) K_v(z)$$</p>\n\n<p>is used, where \\( K_v(z) \\) is the modified Bessel function of the\nsecond kind, evaluated using the AMOS routine <code>zbesk</code>.</p>\n\n<p><code>ive</code> is useful for large arguments <code>z</code>: for these, <code>iv</code> easily overflows,\nwhile <code>ive</code> does not due to the exponential scaling.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<p>In the following example <code>iv</code> returns infinity whereas <code>ive</code> still returns\na finite number.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">iv</span><span class=\"p\">,</span> <span class=\"n\">ive</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">iv</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">1000.</span><span class=\"p\">),</span> <span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mf\">1000.</span><span class=\"p\">)</span>\n<span class=\"go\">(inf, 0.01256056218254712)</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at one point for different orders by\nproviding a list or NumPy array as argument for the <code>v</code> parameter:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">],</span> <span class=\"mf\">1.</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.46575961, 0.20791042, 0.10798193])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for order 0 by providing an\narray for <code>z</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">points</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.</span><span class=\"p\">,</span> <span class=\"mf\">0.</span><span class=\"p\">,</span> <span class=\"mf\">3.</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([0.30850832, 1.        , 0.24300035])</span>\n</code></pre>\n</div>\n\n<p>Evaluate the function at several points for different orders by\nproviding arrays for both <code>v</code> for <code>z</code>. Both arrays have to be\nbroadcastable to the correct shape. To calculate the orders 0, 1\nand 2 for a 1D array of points:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ive</span><span class=\"p\">([[</span><span class=\"mi\">0</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]],</span> <span class=\"n\">points</span><span class=\"p\">)</span>\n<span class=\"go\">array([[ 0.30850832,  1.        ,  0.24300035],</span>\n<span class=\"go\">       [-0.21526929,  0.        ,  0.19682671],</span>\n<span class=\"go\">       [ 0.09323903,  0.        ,  0.11178255]])</span>\n</code></pre>\n</div>\n\n<p>Plot the functions of order 0 to 3 from -5 to 5.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mf\">5.</span><span class=\"p\">,</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"k\">for</span> <span class=\"n\">i</span> <span class=\"ow\">in</span> <span class=\"nb\">range</span><span class=\"p\">(</span><span class=\"mi\">4</span><span class=\"p\">):</span>\n<span class=\"gp\">... </span>    <span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">ive</span><span class=\"p\">(</span><span class=\"n\">i</span><span class=\"p\">,</span> <span class=\"n\">x</span><span class=\"p\">),</span> <span class=\"n\">label</span><span class=\"o\">=</span><span class=\"sa\">fr</span><span class=\"s1\">&#39;$I_</span><span class=\"si\">{</span><span class=\"n\">i</span><span class=\"si\">!r}</span><span class=\"s1\">(z)\\cdot e^</span><span class=\"se\">{{</span><span class=\"s1\">-|z|</span><span class=\"se\">}}</span><span class=\"s1\">$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">legend</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"sa\">r</span><span class=\"s2\">&quot;$z$&quot;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>Donald E. Amos, \"AMOS, A Portable Package for Bessel Functions\nof a Complex Argument and Nonnegative Order\",\n<a href=\"http://netlib.org/amos/\">http://netlib.org/amos/</a>&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erf": {"fullname": "pyerrors.special.erf", "modulename": "pyerrors.special", "qualname": "erf", "kind": "function", "doc": "<p>erf(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erf(z, out=None)</p>\n\n<p>Returns the error function of complex argument.</p>\n\n<p>It is defined as <code>2/sqrt(pi)*integral(exp(-t**2), t=0..z)</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nInput array.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (scalar or ndarray):\nThe values of the error function at the given points <code>x</code>.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erfc,</code>, <code>erfinv,</code>, <code>erfcinv,</code>, <code>wofz,</code>, <code>erfcx,</code>, <code>erfi</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The cumulative of the unit normal distribution is given by\n<code>Phi(z) = 1/2[1 + erf(z/sqrt(2))]</code>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">erf</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$x$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$erf(x)$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfc": {"fullname": "pyerrors.special.erfc", "modulename": "pyerrors.special", "qualname": "erfc", "kind": "function", "doc": "<p>erfc(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfc(x, out=None)</p>\n\n<p>Complementary error function, <code>1 - erf(x)</code>.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (array_like):\nReal or complex valued argument</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: Values of the complementary error function</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf,</code>, <code>erfi,</code>, <code>erfcx,</code>, <code>dawsn,</code>, <code>wofz</code>  </p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">special</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">3</span><span class=\"p\">,</span> <span class=\"mi\">3</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">special</span><span class=\"o\">.</span><span class=\"n\">erfc</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$x$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;$erfc(x)$&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfinv": {"fullname": "pyerrors.special.erfinv", "modulename": "pyerrors.special", "qualname": "erfinv", "kind": "function", "doc": "<p>erfinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfinv(y, out=None)</p>\n\n<p>Inverse of the error function.</p>\n\n<p>Computes the inverse of the error function.</p>\n\n<p>In the complex domain, there is no unique complex number w satisfying\nerf(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, -1 &lt; x &lt; 1, there is a unique real\nnumber satisfying erf(erfinv(x)) = x.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>y</strong> (ndarray):\nArgument at which to evaluate. Domain: [-1, 1]</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>erfinv</strong> (scalar or ndarray):\nThe inverse of erf of y, element-wise</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf</code>:  Error function of a complex argument<br />\n<code>erfc</code>:  Complementary error function, <code>1 - erf(x)</code><br />\n<code>erfcinv</code>:  Inverse of the complementary error function  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>This function wraps the <code>erf_inv</code> routine from the\nBoost Math C++ library <sup class=\"footnote-ref\" id=\"fnref-1\"><a href=\"#fn-1\">1</a></sup>.</p>\n\n<h6 id=\"references\">References</h6>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">erfinv</span><span class=\"p\">,</span> <span class=\"n\">erf</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span>\n<span class=\"go\">0.4769362762044699</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mf\">1.0</span><span class=\"p\">,</span> <span class=\"mf\">1.0</span><span class=\"p\">,</span> <span class=\"n\">num</span><span class=\"o\">=</span><span class=\"mi\">9</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span>\n<span class=\"go\">array([       -inf, -0.81341985, -0.47693628, -0.22531206,  0.        ,</span>\n<span class=\"go\">        0.22531206,  0.47693628,  0.81341985,         inf])</span>\n</code></pre>\n</div>\n\n<p>Verify that <code>erf(erfinv(y))</code> is <code>y</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erf</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"go\">array([-1.  , -0.75, -0.5 , -0.25,  0.  ,  0.25,  0.5 ,  0.75,  1.  ])</span>\n</code></pre>\n</div>\n\n<p>Plot the function:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">200</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">erfinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">(</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;y&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_title</span><span class=\"p\">(</span><span class=\"s1\">&#39;erfinv(y)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n\n<div class=\"footnotes\">\n<hr />\n<ol>\n<li id=\"fn-1\">\n<p>The Boost Developers. \"Boost C++ Libraries\". <a href=\"https://www.boost.org/\">https://www.boost.org/</a>.&#160;<a href=\"#fnref-1\" class=\"footnoteBackLink\" title=\"Jump back to footnote 1 in the text.\">&#8617;</a></p>\n</li>\n</ol>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.erfcinv": {"fullname": "pyerrors.special.erfcinv", "modulename": "pyerrors.special", "qualname": "erfcinv", "kind": "function", "doc": "<p>erfcinv(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>erfcinv(y, out=None)</p>\n\n<p>Inverse of the complementary error function.</p>\n\n<p>Computes the inverse of the complementary error function.</p>\n\n<p>In the complex domain, there is no unique complex number w satisfying\nerfc(w)=z. This indicates a true inverse function would be multivalued.\nWhen the domain restricts to the real, 0 &lt; x &lt; 2, there is a unique real\nnumber satisfying erfc(erfcinv(x)) = erfcinv(erfc(x)).</p>\n\n<p>It is related to inverse of the error function by erfcinv(1-x) = erfinv(x)</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>y</strong> (ndarray):\nArgument at which to evaluate. Domain: [0, 2]</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>erfcinv</strong> (scalar or ndarray):\nThe inverse of erfc of y, element-wise</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>erf</code>:  Error function of a complex argument<br />\n<code>erfc</code>:  Complementary error function, <code>1 - erf(x)</code><br />\n<code>erfinv</code>:  Inverse of the error function  </p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">erfcinv</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"mf\">0.5</span><span class=\"p\">)</span>\n<span class=\"go\">0.4769362762044699</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mf\">0.0</span><span class=\"p\">,</span> <span class=\"mf\">2.0</span><span class=\"p\">,</span> <span class=\"n\">num</span><span class=\"o\">=</span><span class=\"mi\">11</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"go\">array([        inf,  0.9061938 ,  0.59511608,  0.37080716,  0.17914345,</span>\n<span class=\"go\">       -0.        , -0.17914345, -0.37080716, -0.59511608, -0.9061938 ,</span>\n<span class=\"go\">              -inf])</span>\n</code></pre>\n</div>\n\n<p>Plot the function:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"mi\">200</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">fig</span><span class=\"p\">,</span> <span class=\"n\">ax</span> <span class=\"o\">=</span> <span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">subplots</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">erfcinv</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">))</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">(</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;y&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">ax</span><span class=\"o\">.</span><span class=\"n\">set_title</span><span class=\"p\">(</span><span class=\"s1\">&#39;erfcinv(y)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.logit": {"fullname": "pyerrors.special.logit", "modulename": "pyerrors.special", "qualname": "logit", "kind": "function", "doc": "<p>logit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>logit(x, out=None)</p>\n\n<p>Logit ufunc for ndarrays.</p>\n\n<p>The logit function is defined as logit(p) = log(p/(1-p)).\nNote that logit(0) = -inf, logit(1) = inf, and logit(p)\nfor p&lt;0 or p>1 yields nan.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nThe ndarray to apply logit to element-wise.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function results</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: An ndarray of the same shape as x. Its entries\nare logit of the corresponding entry of x.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>expit</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>As a ufunc logit takes a number of optional\nkeyword arguments. For more information\nsee <a href=\"https://docs.scipy.org/doc/numpy/reference/ufuncs.html\">ufuncs </a></p>\n\n<p><em>New in version 0.10.0.</em></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">logit</span><span class=\"p\">,</span> <span class=\"n\">expit</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logit</span><span class=\"p\">([</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">0.25</span><span class=\"p\">,</span> <span class=\"mf\">0.5</span><span class=\"p\">,</span> <span class=\"mf\">0.75</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"go\">array([       -inf, -1.09861229,  0.        ,  1.09861229,         inf])</span>\n</code></pre>\n</div>\n\n<p><code>expit</code> is the inverse of <code>logit</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">expit</span><span class=\"p\">(</span><span class=\"n\">logit</span><span class=\"p\">([</span><span class=\"mf\">0.1</span><span class=\"p\">,</span> <span class=\"mf\">0.75</span><span class=\"p\">,</span> <span class=\"mf\">0.999</span><span class=\"p\">]))</span>\n<span class=\"go\">array([ 0.1  ,  0.75 ,  0.999])</span>\n</code></pre>\n</div>\n\n<p>Plot logit(x) for x in [0, 1]:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">501</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">logit</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">ylim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">title</span><span class=\"p\">(</span><span class=\"s1\">&#39;logit(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.expit": {"fullname": "pyerrors.special.expit", "modulename": "pyerrors.special", "qualname": "expit", "kind": "function", "doc": "<p>expit(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])</p>\n\n<p>expit(x, out=None)</p>\n\n<p>Expit (a.k.a. logistic sigmoid) ufunc for ndarrays.</p>\n\n<p>The expit function, also known as the logistic sigmoid function, is\ndefined as <code>expit(x) = 1/(1+exp(-x))</code>.  It is the inverse of the\nlogit function.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (ndarray):\nThe ndarray to apply expit to element-wise.</li>\n<li><strong>out</strong> (ndarray, optional):\nOptional output array for the function values</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>scalar or ndarray</strong>: An ndarray of the same shape as x. Its entries\nare <code>expit</code> of the corresponding entry of x.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>logit</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>As a ufunc expit takes a number of optional\nkeyword arguments. For more information\nsee <a href=\"https://docs.scipy.org/doc/numpy/reference/ufuncs.html\">ufuncs </a></p>\n\n<p><em>New in version 0.10.0.</em></p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">expit</span><span class=\"p\">,</span> <span class=\"n\">logit</span>\n</code></pre>\n</div>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">expit</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">inf</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">1.5</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">inf</span><span class=\"p\">])</span>\n<span class=\"go\">array([ 0.        ,  0.18242552,  0.5       ,  0.81757448,  1.        ])</span>\n</code></pre>\n</div>\n\n<p><code>logit</code> is the inverse of <code>expit</code>:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logit</span><span class=\"p\">(</span><span class=\"n\">expit</span><span class=\"p\">([</span><span class=\"o\">-</span><span class=\"mf\">2.5</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mf\">3.1</span><span class=\"p\">,</span> <span class=\"mf\">5.0</span><span class=\"p\">]))</span>\n<span class=\"go\">array([-2.5,  0. ,  3.1,  5. ])</span>\n</code></pre>\n</div>\n\n<p>Plot expit(x) for x in [-6, 6]:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">matplotlib.pyplot</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">plt</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">x</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">linspace</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">121</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">y</span> <span class=\"o\">=</span> <span class=\"n\">expit</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">plot</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">grid</span><span class=\"p\">()</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlim</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"mi\">6</span><span class=\"p\">,</span> <span class=\"mi\">6</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">xlabel</span><span class=\"p\">(</span><span class=\"s1\">&#39;x&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">title</span><span class=\"p\">(</span><span class=\"s1\">&#39;expit(x)&#39;</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">plt</span><span class=\"o\">.</span><span class=\"n\">show</span><span class=\"p\">()</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.special.logsumexp": {"fullname": "pyerrors.special.logsumexp", "modulename": "pyerrors.special", "qualname": "logsumexp", "kind": "function", "doc": "<p>Compute the log of the sum of exponentials of input elements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>a</strong> (array_like):\nInput array.</li>\n<li><p><strong>axis</strong> (None or int or tuple of ints, optional):\nAxis or axes over which the sum is taken. By default <code>axis</code> is None,\nand all elements are summed.</p>\n\n<p><em>New in version 0.11.0.</em></p></li>\n<li><p><strong>b</strong> (array-like, optional):\nScaling factor for exp(<code>a</code>) must be of the same shape as <code>a</code> or\nbroadcastable to <code>a</code>. These values may be negative in order to\nimplement subtraction.</p>\n\n<p><em>New in version 0.12.0.</em></p></li>\n<li><p><strong>keepdims</strong> (bool, optional):\nIf this is set to True, the axes which are reduced are left in the\nresult as dimensions with size one. With this option, the result\nwill broadcast correctly against the original array.</p>\n\n<p><em>New in version 0.15.0.</em></p></li>\n<li><p><strong>return_sign</strong> (bool, optional):\nIf this is set to True, the result will be a pair containing sign\ninformation; if False, results that are negative will be returned\nas NaN. Default is False (no sign information).</p>\n\n<p><em>New in version 0.16.0.</em></p></li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>res</strong> (ndarray):\nThe result, <code>np.log(np.sum(np.exp(a)))</code> calculated in a numerically\nmore stable way. If <code>b</code> is given then <code>np.log(np.sum(b*np.exp(a)))</code>\nis returned. If <code>return_sign</code> is True, <code>res</code> contains the log of\nthe absolute value of the argument.</li>\n<li><strong>sgn</strong> (ndarray):\nIf <code>return_sign</code> is True, this will be an array of floating-point\nnumbers matching res containing +1, 0, -1 (for real-valued inputs)\nor a complex phase (for complex inputs). This gives the sign of the\nargument of the logarithm in <code>res</code>.\nIf <code>return_sign</code> is False, only one result is returned.</li>\n</ul>\n\n<h6 id=\"see-also\">See Also</h6>\n\n<p><code>numpy.logaddexp,</code>, <code>numpy.logaddexp2</code>  </p>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>NumPy has a logaddexp function which is very similar to <code>logsumexp</code>, but\nonly handles two arguments. <code>logaddexp.reduce</code> is similar to this\nfunction, but may be less stable.</p>\n\n<p>The logarithm is a multivalued function: for each \\( x \\) there is an\ninfinite number of \\( z \\) such that \\( exp(z) = x \\). The convention\nis to return the \\( z \\) whose imaginary part lies in \\( (-pi, pi] \\).</p>\n\n<h6 id=\"examples\">Examples</h6>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">import</span><span class=\"w\"> </span><span class=\"nn\">numpy</span><span class=\"w\"> </span><span class=\"k\">as</span><span class=\"w\"> </span><span class=\"nn\">np</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"kn\">from</span><span class=\"w\"> </span><span class=\"nn\">scipy.special</span><span class=\"w\"> </span><span class=\"kn\">import</span> <span class=\"n\">logsumexp</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"go\">9.4586297444267107</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)))</span>\n<span class=\"go\">9.4586297444267107</span>\n</code></pre>\n</div>\n\n<p>With weights</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">arange</span><span class=\"p\">(</span><span class=\"mi\">10</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"o\">=</span><span class=\"n\">b</span><span class=\"p\">)</span>\n<span class=\"go\">9.9170178533034665</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">sum</span><span class=\"p\">(</span><span class=\"n\">b</span><span class=\"o\">*</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"p\">)))</span>\n<span class=\"go\">9.9170178533034647</span>\n</code></pre>\n</div>\n\n<p>Returning a sign flag</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">([</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"mi\">2</span><span class=\"p\">],</span><span class=\"n\">b</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span><span class=\"o\">-</span><span class=\"mi\">1</span><span class=\"p\">],</span><span class=\"n\">return_sign</span><span class=\"o\">=</span><span class=\"kc\">True</span><span class=\"p\">)</span>\n<span class=\"go\">(1.5413248546129181, -1.0)</span>\n</code></pre>\n</div>\n\n<p>Notice that <code>logsumexp</code> does not directly support masked arrays. To use it\non a masked array, convert the mask into zero weights:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">a</span> <span class=\"o\">=</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">ma</span><span class=\"o\">.</span><span class=\"n\">array</span><span class=\"p\">([</span><span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">2</span><span class=\"p\">),</span> <span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">3</span><span class=\"p\">)],</span>\n<span class=\"gp\">... </span>                 <span class=\"n\">mask</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"kc\">False</span><span class=\"p\">,</span> <span class=\"kc\">True</span><span class=\"p\">,</span> <span class=\"kc\">False</span><span class=\"p\">])</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">b</span> <span class=\"o\">=</span> <span class=\"p\">(</span><span class=\"o\">~</span><span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">mask</span><span class=\"p\">)</span><span class=\"o\">.</span><span class=\"n\">astype</span><span class=\"p\">(</span><span class=\"nb\">int</span><span class=\"p\">)</span>\n<span class=\"gp\">&gt;&gt;&gt; </span><span class=\"n\">logsumexp</span><span class=\"p\">(</span><span class=\"n\">a</span><span class=\"o\">.</span><span class=\"n\">data</span><span class=\"p\">,</span> <span class=\"n\">b</span><span class=\"o\">=</span><span class=\"n\">b</span><span class=\"p\">),</span> <span class=\"n\">np</span><span class=\"o\">.</span><span class=\"n\">log</span><span class=\"p\">(</span><span class=\"mi\">5</span><span class=\"p\">)</span>\n<span class=\"go\">1.6094379124341005, 1.6094379124341005</span>\n</code></pre>\n</div>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">args</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "kind": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8400}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 367}, "pyerrors.correlators.Corr.__init__": {"qualname": 3, "fullname": 5, "annotation": 0, "default_value": 0, 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