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@ -123,9 +123,9 @@ It is based on the <strong>gamma method</strong> <a href="https://arxiv.org/abs/
<div class="codehilite"><pre><span></span><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span> <div class="codehilite"><pre><span></span><code><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">pyerrors</span> <span class="k">as</span> <span class="nn">pe</span> <span class="kn">import</span> <span class="nn">pyerrors</span> <span class="k">as</span> <span class="nn">pe</span>
<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 with Monte Carlo samples</span> <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>
<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> <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>
<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 error with the gamma_method</span> <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>
<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> <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>
<span class="o">&gt;</span> <span class="mf">0.31498</span><span class="p">(</span><span class="mi">72</span><span class="p">)</span> <span class="o">&gt;</span> <span class="mf">0.31498</span><span class="p">(</span><span class="mi">72</span><span class="p">)</span>
</code></pre></div> </code></pre></div>
@ -148,9 +148,8 @@ The second argument is a list containing the names of the respective Monte Carlo
<p>When performing mathematical operations on <code>Obs</code> objects the correct error propagation is intrinsically taken care using a first order Taylor expansion <p>When performing mathematical operations on <code>Obs</code> objects the correct error propagation is intrinsically taken care using a first order Taylor expansion
$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$ $$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$
as introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0306017</a>.</p> as introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0306017</a>.
The 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>
<p>The 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>
<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> <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>
@ -359,9 +358,9 @@ See <code><a href="pyerrors/obs.html#Obs.export_jackknife">pyerrors.obs.Obs.expo
<span class="sd">import numpy as np</span> <span class="sd">import numpy as np</span>
<span class="sd">import pyerrors as pe</span> <span class="sd">import pyerrors as pe</span>
<span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;]) # Initialize an Obs object with Monte Carlo samples</span> <span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;]) # Initialize an Obs object</span>
<span class="sd">my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object</span> <span class="sd">my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object</span>
<span class="sd">my_new_obs.gamma_method() # Estimate the error with the gamma_method</span> <span class="sd">my_new_obs.gamma_method() # Estimate the statistical error</span>
<span class="sd">print(my_new_obs) # Print the result to stdout</span> <span class="sd">print(my_new_obs) # Print the result to stdout</span>
<span class="sd">&gt; 0.31498(72)</span> <span class="sd">&gt; 0.31498(72)</span>
<span class="sd">```</span> <span class="sd">```</span>
@ -385,7 +384,6 @@ See <code><a href="pyerrors/obs.html#Obs.export_jackknife">pyerrors.obs.Obs.expo
<span class="sd">When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care using a first order Taylor expansion</span> <span class="sd">When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care using a first order Taylor expansion</span>
<span class="sd">$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$</span> <span class="sd">$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$</span>
<span class="sd">as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span> <span class="sd">as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
<span class="sd">The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span> <span class="sd">The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span>
<span class="sd">The `Obs` class is designed such that mathematical numpy functions can be used on `Obs` just as for regular floats.</span> <span class="sd">The `Obs` class is designed such that mathematical numpy functions can be used on `Obs` just as for regular floats.</span>

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