Documentation updated

docs/pyerrors/linalg.html

@@ -53,6 +53,9 @@
             <li>
                     <a class="function" href="#matmul">matmul</a>
             </li>
+            <li>
+                    <a class="function" href="#jack_matmul">jack_matmul</a>
+            </li>
             <li>
                     <a class="function" href="#inv">inv</a>
             </li>
@@ -102,7 +105,7 @@
             <div class="codehilite"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="k">as</span> <span class="nn">np</span>
 <span class="kn">from</span> <span class="nn">autograd</span> <span class="kn">import</span> <span class="n">jacobian</span>
 <span class="kn">import</span> <span class="nn">autograd.numpy</span> <span class="k">as</span> <span class="nn">anp</span>  <span class="c1"># Thinly-wrapped numpy</span>
-<span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="n">derived_observable</span><span class="p">,</span> <span class="n">CObs</span><span class="p">,</span> <span class="n">Obs</span><span class="p">,</span> <span class="n">_merge_idx</span><span class="p">,</span> <span class="n">_expand_deltas_for_merge</span><span class="p">,</span> <span class="n">_filter_zeroes</span>
+<span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="n">derived_observable</span><span class="p">,</span> <span class="n">CObs</span><span class="p">,</span> <span class="n">Obs</span><span class="p">,</span> <span class="n">_merge_idx</span><span class="p">,</span> <span class="n">_expand_deltas_for_merge</span><span class="p">,</span> <span class="n">_filter_zeroes</span><span class="p">,</span> <span class="n">import_jackknife</span>
 
 <span class="kn">from</span> <span class="nn">functools</span> <span class="kn">import</span> <span class="n">partial</span>
 <span class="kn">from</span> <span class="nn">autograd.extend</span> <span class="kn">import</span> <span class="n">defvjp</span>
@@ -222,8 +225,13 @@
 <span class="k">def</span> <span class="nf">matmul</span><span class="p">(</span><span class="o">*</span><span class="n">operands</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Matrix multiply all operands.</span>
 
-<span class="sd">       Supports real and complex valued matrices and is faster compared to</span>
+<span class="sd">    Parameters</span>
-<span class="sd">       standard multiplication via the @ operator.</span>
+<span class="sd">    ----------</span>
+<span class="sd">    operands : numpy.ndarray</span>
+<span class="sd">        Arbitrary number of 2d-numpy arrays which can be real or complex</span>
+<span class="sd">        Obs valued.</span>
+
+<span class="sd">    This implementation is faster compared to standard multiplication via the @ operator.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">if</span> <span class="nb">any</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="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">CObs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">operands</span><span class="p">):</span>
         <span class="n">extended_operands</span> <span class="o">=</span> <span class="p">[]</span>
@@ -270,6 +278,56 @@
         <span class="k">return</span> <span class="n">derived_array</span><span class="p">(</span><span class="n">multi_dot</span><span class="p">,</span> <span class="n">operands</span><span class="p">)</span>
 
 
+<span class="k">def</span> <span class="nf">jack_matmul</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="sd">&quot;&quot;&quot;Matrix multiply both operands making use of the jackknife approximation.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    a : numpy.ndarray</span>
+<span class="sd">        First matrix, can be real or complex Obs valued</span>
+<span class="sd">    b : numpy.ndarray</span>
+<span class="sd">        Second matrix, can be real or complex Obs valued</span>
+
+<span class="sd">    For large matrices this is considerably faster compared to matmul.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">any</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="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">CObs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</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="k">def</span> <span class="nf">_exp_to_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">entry</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">entry</span><span class="o">.</span><span class="n">imag</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="k">def</span> <span class="nf">_imp_from_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">CObs</span><span class="p">(</span><span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">name</span><span class="p">),</span>
+                                         <span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">name</span><span class="p">))</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="n">j_a</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+        <span class="n">j_b</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="n">j_a</span> <span class="o">@</span> <span class="n">j_b</span>
+        <span class="k">return</span> <span class="n">_imp_from_jack</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">def</span> <span class="nf">_exp_to_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">entry</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="k">def</span> <span class="nf">_imp_from_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="n">j_a</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+        <span class="n">j_b</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="n">j_a</span> <span class="o">@</span> <span class="n">j_b</span>
+        <span class="k">return</span> <span class="n">_imp_from_jack</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+
+
 <span class="k">def</span> <span class="nf">inv</span><span class="p">(</span><span class="n">x</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Inverse of Obs or CObs valued matrices.&quot;&quot;&quot;</span>
     <span class="k">return</span> <span class="n">_mat_mat_op</span><span class="p">(</span><span class="n">anp</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
@@ -810,8 +868,13 @@ not be intercepted.</li>
             <div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">matmul</span><span class="p">(</span><span class="o">*</span><span class="n">operands</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Matrix multiply all operands.</span>
 
-<span class="sd">       Supports real and complex valued matrices and is faster compared to</span>
+<span class="sd">    Parameters</span>
-<span class="sd">       standard multiplication via the @ operator.</span>
+<span class="sd">    ----------</span>
+<span class="sd">    operands : numpy.ndarray</span>
+<span class="sd">        Arbitrary number of 2d-numpy arrays which can be real or complex</span>
+<span class="sd">        Obs valued.</span>
+
+<span class="sd">    This implementation is faster compared to standard multiplication via the @ operator.</span>
 <span class="sd">    &quot;&quot;&quot;</span>
     <span class="k">if</span> <span class="nb">any</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="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">CObs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">operands</span><span class="p">):</span>
         <span class="n">extended_operands</span> <span class="o">=</span> <span class="p">[]</span>
@@ -862,8 +925,91 @@ not be intercepted.</li>
 
             <div class="docstring"><p>Matrix multiply all operands.</p>
 
-<p>Supports real and complex valued matrices and is faster compared to
+<h6 id="parameters">Parameters</h6>
-standard multiplication via the @ operator.</p>
+
+<ul>
+<li><strong>operands</strong> (numpy.ndarray):
+Arbitrary number of 2d-numpy arrays which can be real or complex
+Obs valued.</li>
+<li><strong>This implementation is faster compared to standard multiplication via the @ operator.</strong></li>
+</ul>
+</div>
+
+
+                </section>
+                <section id="jack_matmul">
+                            <div class="attr function"><a class="headerlink" href="#jack_matmul">#&nbsp;&nbsp</a>
+
+        
+            <span class="def">def</span>
+            <span class="name">jack_matmul</span><span class="signature">(a, b)</span>:
+    </div>
+
+                <details>
+            <summary>View Source</summary>
+            <div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">jack_matmul</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="sd">&quot;&quot;&quot;Matrix multiply both operands making use of the jackknife approximation.</span>
+
+<span class="sd">    Parameters</span>
+<span class="sd">    ----------</span>
+<span class="sd">    a : numpy.ndarray</span>
+<span class="sd">        First matrix, can be real or complex Obs valued</span>
+<span class="sd">    b : numpy.ndarray</span>
+<span class="sd">        Second matrix, can be real or complex Obs valued</span>
+
+<span class="sd">    For large matrices this is considerably faster compared to matmul.</span>
+<span class="sd">    &quot;&quot;&quot;</span>
+
+    <span class="k">if</span> <span class="nb">any</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="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="n">CObs</span><span class="p">)</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</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="k">def</span> <span class="nf">_exp_to_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">entry</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span> <span class="o">+</span> <span class="mi">1</span><span class="n">j</span> <span class="o">*</span> <span class="n">entry</span><span class="o">.</span><span class="n">imag</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="k">def</span> <span class="nf">_imp_from_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">CObs</span><span class="p">(</span><span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="o">.</span><span class="n">real</span><span class="p">,</span> <span class="n">name</span><span class="p">),</span>
+                                         <span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="o">.</span><span class="n">imag</span><span class="p">,</span> <span class="n">name</span><span class="p">))</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="n">j_a</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+        <span class="n">j_b</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="n">j_a</span> <span class="o">@</span> <span class="n">j_b</span>
+        <span class="k">return</span> <span class="n">_imp_from_jack</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">real</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+    <span class="k">else</span><span class="p">:</span>
+        <span class="k">def</span> <span class="nf">_exp_to_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">entry</span><span class="o">.</span><span class="n">export_jackknife</span><span class="p">()</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="k">def</span> <span class="nf">_imp_from_jack</span><span class="p">(</span><span class="n">matrix</span><span class="p">,</span> <span class="n">name</span><span class="p">):</span>
+            <span class="n">base_matrix</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">empty_like</span><span class="p">(</span><span class="n">matrix</span><span class="p">)</span>
+            <span class="k">for</span> <span class="p">(</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">),</span> <span class="n">entry</span> <span class="ow">in</span> <span class="n">np</span><span class="o">.</span><span class="n">ndenumerate</span><span class="p">(</span><span class="n">matrix</span><span class="p">):</span>
+                <span class="n">base_matrix</span><span class="p">[</span><span class="n">n</span><span class="p">,</span> <span class="n">m</span><span class="p">]</span> <span class="o">=</span> <span class="n">import_jackknife</span><span class="p">(</span><span class="n">entry</span><span class="p">,</span> <span class="n">name</span><span class="p">)</span>
+            <span class="k">return</span> <span class="n">base_matrix</span>
+
+        <span class="n">j_a</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">a</span><span class="p">)</span>
+        <span class="n">j_b</span> <span class="o">=</span> <span class="n">_exp_to_jack</span><span class="p">(</span><span class="n">b</span><span class="p">)</span>
+        <span class="n">r</span> <span class="o">=</span> <span class="n">j_a</span> <span class="o">@</span> <span class="n">j_b</span>
+        <span class="k">return</span> <span class="n">_imp_from_jack</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">a</span><span class="o">.</span><span class="n">ravel</span><span class="p">()[</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">])</span>
+</pre></div>
+
+        </details>
+
+            <div class="docstring"><p>Matrix multiply both operands making use of the jackknife approximation.</p>
+
+<h6 id="parameters">Parameters</h6>
+
+<ul>
+<li><strong>a</strong> (numpy.ndarray):
+First matrix, can be real or complex Obs valued</li>
+<li><strong>b</strong> (numpy.ndarray):
+Second matrix, can be real or complex Obs valued</li>
+<li><strong>For large matrices this is considerably faster compared to matmul.</strong></li>
+</ul>
 </div>