From 0353836815a541974f17cff0f6d98b50f06ae8d1 Mon Sep 17 00:00:00 2001
From: fjosw <fjosw@users.noreply.github.com>
Date: Tue, 7 Dec 2021 08:16:21 +0000
Subject: [PATCH] Documentation updated

---
 docs/pyerrors/linalg.html | 276 ++------------------------------------
 docs/pyerrors/obs.html    | 114 +++++++++++++---
 docs/search.js            |   2 +-
 3 files changed, 103 insertions(+), 289 deletions(-)

diff --git a/docs/pyerrors/linalg.html b/docs/pyerrors/linalg.html
index 570e34c9..5e92a4a9 100644
--- a/docs/pyerrors/linalg.html
+++ b/docs/pyerrors/linalg.html
@@ -47,9 +47,6 @@
 
                     <h2>API Documentation</h2>
                         <ul class="memberlist">
-            <li>
-                    <a class="function" href="#derived_array">derived_array</a>
-            </li>
             <li>
                     <a class="function" href="#matmul">matmul</a>
             </li>
@@ -106,125 +103,13 @@
                         <details>
             <summary>View Source</summary>
             <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="p">,</span> <span class="n">import_jackknife</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">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>
 
 
-<span class="k">def</span> <span class="nf">derived_array</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Construct a derived Obs for a matrix valued function according to func(data, **kwargs) using automatic differentiation.</span>
-
-<span class="sd">    Parameters</span>
-<span class="sd">    ----------</span>
-<span class="sd">    func : object</span>
-<span class="sd">        arbitrary function of the form func(data, **kwargs). For the</span>
-<span class="sd">        automatic differentiation to work, all numpy functions have to have</span>
-<span class="sd">        the autograd wrapper (use &#39;import autograd.numpy as anp&#39;).</span>
-<span class="sd">    data : list</span>
-<span class="sd">        list of Obs, e.g. [obs1, obs2, obs3].</span>
-<span class="sd">    man_grad : list</span>
-<span class="sd">        manually supply a list or an array which contains the jacobian</span>
-<span class="sd">        of func. Use cautiously, supplying the wrong derivative will</span>
-<span class="sd">        not be intercepted.</span>
-<span class="sd">    &quot;&quot;&quot;</span>
-
-    <span class="n">data</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">data</span><span class="p">)</span>
-    <span class="n">raveled_data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
-
-    <span class="c1"># Workaround for matrix operations containing non Obs data</span>
-    <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_data</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
-            <span class="n">first_name</span> <span class="o">=</span> <span class="n">i_data</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="n">first_shape</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">first_name</span><span class="p">]</span>
-            <span class="n">first_idl</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">first_name</span><span class="p">]</span>
-            <span class="k">break</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="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)):</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">)):</span>
-            <span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">Obs</span><span class="p">([</span><span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">]</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">first_shape</span><span class="p">)],</span> <span class="p">[</span><span class="n">first_name</span><span class="p">],</span> <span class="n">idl</span><span class="o">=</span><span class="p">[</span><span class="n">first_idl</span><span class="p">])</span>
-
-    <span class="n">n_obs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)</span>
-    <span class="n">new_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
-
-    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">}</span>
-    <span class="n">reweighted</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">reweighted</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span>
-    <span class="n">new_idl_d</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">idl</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
-            <span class="n">tmp</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">tmp</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-                <span class="n">idl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
-        <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_merge_idx</span><span class="p">(</span><span class="n">idl</span><span class="p">)</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]:</span>
-            <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span> <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="p">[</span><span class="o">*</span><span class="n">idl</span><span class="p">,</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]]])))</span>
-
-    <span class="k">if</span> <span class="n">data</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-        <span class="n">values</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="n">o</span><span class="o">.</span><span class="n">value</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>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">data</span><span class="p">)</span>
-
-    <span class="n">new_values</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="n">new_r_values</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">tmp_values</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_obs</span><span class="p">)</span>
-        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">):</span>
-            <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">r_values</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">tmp</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-                <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">value</span>
-            <span class="n">tmp_values</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
-        <span class="n">tmp_values</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="n">tmp_values</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
-        <span class="n">new_r_values</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">tmp_values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="k">if</span> <span class="s1">&#39;man_grad&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
-        <span class="n">deriv</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">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;man_grad&#39;</span><span class="p">))</span>
-        <span class="k">if</span> <span class="n">new_values</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">data</span><span class="o">.</span><span class="n">shape</span> <span class="o">!=</span> <span class="n">deriv</span><span class="o">.</span><span class="n">shape</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Manual derivative does not have correct shape.&#39;</span><span class="p">)</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">deriv</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="n">final_result</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">new_values</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
-
-    <span class="n">d_extracted</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
-            <span class="n">ens_length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
-            <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">o</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">o</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">ens_length</span><span class="p">,</span> <span class="p">)))</span>
-
-    <span class="k">for</span> <span class="n">i_val</span><span class="p">,</span> <span class="n">new_val</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">new_values</span><span class="p">):</span>
-        <span class="n">new_deltas</span> <span class="o">=</span> <span class="p">{}</span>
-        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-            <span class="n">ens_length</span> <span class="o">=</span> <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-            <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</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">ens_length</span><span class="p">)</span>
-            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
-                <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
-
-        <span class="n">new_samples</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="n">new_means</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="n">new_idl</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-            <span class="k">if</span> <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]:</span>
-                <span class="n">filtered_deltas</span><span class="p">,</span> <span class="n">filtered_idl_d</span> <span class="o">=</span> <span class="n">_filter_zeroes</span><span class="p">(</span><span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
-            <span class="k">else</span><span class="p">:</span>
-                <span class="n">filtered_deltas</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>
-                <span class="n">filtered_idl_d</span> <span class="o">=</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>
-
-            <span class="n">new_samples</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">filtered_deltas</span><span class="p">)</span>
-            <span class="n">new_idl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">filtered_idl_d</span><span class="p">)</span>
-            <span class="n">new_means</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_r_values</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="n">i_val</span><span class="p">])</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span> <span class="o">=</span> <span class="n">Obs</span><span class="p">(</span><span class="n">new_samples</span><span class="p">,</span> <span class="n">new_names</span><span class="p">,</span> <span class="n">means</span><span class="o">=</span><span class="n">new_means</span><span class="p">,</span> <span class="n">idl</span><span class="o">=</span><span class="n">new_idl</span><span class="p">)</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">_value</span> <span class="o">=</span> <span class="n">new_val</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">is_merged</span> <span class="o">=</span> <span class="n">is_merged</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">reweighted</span> <span class="o">=</span> <span class="n">reweighted</span>
-
-    <span class="k">return</span> <span class="n">final_result</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>
 
@@ -264,8 +149,8 @@
         <span class="k">def</span> <span class="nf">multi_dot_i</span><span class="p">(</span><span class="n">operands</span><span class="p">):</span>
             <span class="k">return</span> <span class="n">multi_dot</span><span class="p">(</span><span class="n">operands</span><span class="p">,</span> <span class="s1">&#39;Imag&#39;</span><span class="p">)</span>
 
-        <span class="n">Nr</span> <span class="o">=</span> <span class="n">derived_array</span><span class="p">(</span><span class="n">multi_dot_r</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">)</span>
-        <span class="n">Ni</span> <span class="o">=</span> <span class="n">derived_array</span><span class="p">(</span><span class="n">multi_dot_i</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">)</span>
+        <span class="n">Nr</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="n">multi_dot_r</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">Ni</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="n">multi_dot_i</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 
         <span class="n">res</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">Nr</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">Nr</span><span class="p">):</span>
@@ -278,7 +163,7 @@
             <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">:]:</span>
                 <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span> <span class="o">@</span> <span class="n">op</span>
             <span class="k">return</span> <span class="n">stack</span>
-        <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">return</span> <span class="n">derived_observable</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="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 
 
 <span class="k">def</span> <span class="nf">jack_matmul</span><span class="p">(</span><span class="o">*</span><span class="n">operands</span><span class="p">):</span>
@@ -467,7 +352,7 @@
         <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;num_grad&#39;</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
             <span class="n">op_big_matrix</span> <span class="o">=</span> <span class="n">_num_diff_mat_mat_op</span><span class="p">(</span><span class="n">op</span><span class="p">,</span> <span class="n">big_matrix</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
         <span class="k">else</span><span class="p">:</span>
-            <span class="n">op_big_matrix</span> <span class="o">=</span> <span class="n">derived_array</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">big_matrix</span><span class="p">])[</span><span class="mi">0</span><span class="p">]</span>
+            <span class="n">op_big_matrix</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">big_matrix</span><span class="p">],</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">dim</span> <span class="o">=</span> <span class="n">op_big_matrix</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
         <span class="n">op_A</span> <span class="o">=</span> <span class="n">op_big_matrix</span><span class="p">[</span><span class="mi">0</span><span class="p">:</span> <span class="n">dim</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="n">dim</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span>
         <span class="n">op_B</span> <span class="o">=</span> <span class="n">op_big_matrix</span><span class="p">[</span><span class="n">dim</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="n">dim</span> <span class="o">//</span> <span class="mi">2</span><span class="p">]</span>
@@ -478,7 +363,7 @@
     <span class="k">else</span><span class="p">:</span>
         <span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;num_grad&#39;</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
             <span class="k">return</span> <span class="n">_num_diff_mat_mat_op</span><span class="p">(</span><span class="n">op</span><span class="p">,</span> <span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-        <span class="k">return</span> <span class="n">derived_array</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">obs</span><span class="p">])[</span><span class="mi">0</span><span class="p">]</span>
+        <span class="k">return</span> <span class="n">derived_observable</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">:</span> <span class="n">op</span><span class="p">(</span><span class="n">x</span><span class="p">),</span> <span class="p">[</span><span class="n">obs</span><span class="p">],</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
 
 
 <span class="k">def</span> <span class="nf">eigh</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
@@ -799,149 +684,6 @@
         </details>
 
             </section>
-                <section id="derived_array">
-                            <div class="attr function"><a class="headerlink" href="#derived_array">#&nbsp;&nbsp</a>
-
-        
-            <span class="def">def</span>
-            <span class="name">derived_array</span><span class="signature">(func, data, **kwargs)</span>:
-    </div>
-
-                <details>
-            <summary>View Source</summary>
-            <div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">derived_array</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
-    <span class="sd">&quot;&quot;&quot;Construct a derived Obs for a matrix valued function according to func(data, **kwargs) using automatic differentiation.</span>
-
-<span class="sd">    Parameters</span>
-<span class="sd">    ----------</span>
-<span class="sd">    func : object</span>
-<span class="sd">        arbitrary function of the form func(data, **kwargs). For the</span>
-<span class="sd">        automatic differentiation to work, all numpy functions have to have</span>
-<span class="sd">        the autograd wrapper (use &#39;import autograd.numpy as anp&#39;).</span>
-<span class="sd">    data : list</span>
-<span class="sd">        list of Obs, e.g. [obs1, obs2, obs3].</span>
-<span class="sd">    man_grad : list</span>
-<span class="sd">        manually supply a list or an array which contains the jacobian</span>
-<span class="sd">        of func. Use cautiously, supplying the wrong derivative will</span>
-<span class="sd">        not be intercepted.</span>
-<span class="sd">    &quot;&quot;&quot;</span>
-
-    <span class="n">data</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">data</span><span class="p">)</span>
-    <span class="n">raveled_data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
-
-    <span class="c1"># Workaround for matrix operations containing non Obs data</span>
-    <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_data</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
-            <span class="n">first_name</span> <span class="o">=</span> <span class="n">i_data</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="n">first_shape</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">first_name</span><span class="p">]</span>
-            <span class="n">first_idl</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">first_name</span><span class="p">]</span>
-            <span class="k">break</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="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)):</span>
-        <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="p">(</span><span class="nb">int</span><span class="p">,</span> <span class="nb">float</span><span class="p">)):</span>
-            <span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">Obs</span><span class="p">([</span><span class="n">raveled_data</span><span class="p">[</span><span class="n">i</span><span class="p">]</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">first_shape</span><span class="p">)],</span> <span class="p">[</span><span class="n">first_name</span><span class="p">],</span> <span class="n">idl</span><span class="o">=</span><span class="p">[</span><span class="n">first_idl</span><span class="p">])</span>
-
-    <span class="n">n_obs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)</span>
-    <span class="n">new_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
-
-    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">}</span>
-    <span class="n">reweighted</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">reweighted</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span>
-    <span class="n">new_idl_d</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">idl</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
-            <span class="n">tmp</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">tmp</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
-                <span class="n">idl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">tmp</span><span class="p">)</span>
-        <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_merge_idx</span><span class="p">(</span><span class="n">idl</span><span class="p">)</span>
-        <span class="k">if</span> <span class="ow">not</span> <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]:</span>
-            <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">!=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="nb">len</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span> <span class="k">for</span> <span class="n">idx</span> <span class="ow">in</span> <span class="p">[</span><span class="o">*</span><span class="n">idl</span><span class="p">,</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]]])))</span>
-
-    <span class="k">if</span> <span class="n">data</span><span class="o">.</span><span class="n">ndim</span> <span class="o">==</span> <span class="mi">1</span><span class="p">:</span>
-        <span class="n">values</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="n">o</span><span class="o">.</span><span class="n">value</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>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">values</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">vectorize</span><span class="p">(</span><span class="k">lambda</span> <span class="n">x</span><span class="p">:</span> <span class="n">x</span><span class="o">.</span><span class="n">value</span><span class="p">)(</span><span class="n">data</span><span class="p">)</span>
-
-    <span class="n">new_values</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="n">new_r_values</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">tmp_values</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_obs</span><span class="p">)</span>
-        <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">):</span>
-            <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">r_values</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
-            <span class="k">if</span> <span class="n">tmp</span> <span class="ow">is</span> <span class="kc">None</span><span class="p">:</span>
-                <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">value</span>
-            <span class="n">tmp_values</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">=</span> <span class="n">tmp</span>
-        <span class="n">tmp_values</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="n">tmp_values</span><span class="p">)</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">data</span><span class="o">.</span><span class="n">shape</span><span class="p">)</span>
-        <span class="n">new_r_values</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">func</span><span class="p">(</span><span class="n">tmp_values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="k">if</span> <span class="s1">&#39;man_grad&#39;</span> <span class="ow">in</span> <span class="n">kwargs</span><span class="p">:</span>
-        <span class="n">deriv</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">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">&#39;man_grad&#39;</span><span class="p">))</span>
-        <span class="k">if</span> <span class="n">new_values</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="n">data</span><span class="o">.</span><span class="n">shape</span> <span class="o">!=</span> <span class="n">deriv</span><span class="o">.</span><span class="n">shape</span><span class="p">:</span>
-            <span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">&#39;Manual derivative does not have correct shape.&#39;</span><span class="p">)</span>
-    <span class="k">else</span><span class="p">:</span>
-        <span class="n">deriv</span> <span class="o">=</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">values</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">)</span>
-
-    <span class="n">final_result</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">new_values</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
-
-    <span class="n">d_extracted</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-        <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
-            <span class="n">ens_length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
-            <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">o</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">o</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">ens_length</span><span class="p">,</span> <span class="p">)))</span>
-
-    <span class="k">for</span> <span class="n">i_val</span><span class="p">,</span> <span class="n">new_val</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">new_values</span><span class="p">):</span>
-        <span class="n">new_deltas</span> <span class="o">=</span> <span class="p">{}</span>
-        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-            <span class="n">ens_length</span> <span class="o">=</span> <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
-            <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</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">ens_length</span><span class="p">)</span>
-            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
-                <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
-
-        <span class="n">new_samples</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="n">new_means</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="n">new_idl</span> <span class="o">=</span> <span class="p">[]</span>
-        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
-            <span class="k">if</span> <span class="n">is_merged</span><span class="p">[</span><span class="n">name</span><span class="p">]:</span>
-                <span class="n">filtered_deltas</span><span class="p">,</span> <span class="n">filtered_idl_d</span> <span class="o">=</span> <span class="n">_filter_zeroes</span><span class="p">(</span><span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
-            <span class="k">else</span><span class="p">:</span>
-                <span class="n">filtered_deltas</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>
-                <span class="n">filtered_idl_d</span> <span class="o">=</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]</span>
-
-            <span class="n">new_samples</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">filtered_deltas</span><span class="p">)</span>
-            <span class="n">new_idl</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">filtered_idl_d</span><span class="p">)</span>
-            <span class="n">new_means</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">new_r_values</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="n">i_val</span><span class="p">])</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span> <span class="o">=</span> <span class="n">Obs</span><span class="p">(</span><span class="n">new_samples</span><span class="p">,</span> <span class="n">new_names</span><span class="p">,</span> <span class="n">means</span><span class="o">=</span><span class="n">new_means</span><span class="p">,</span> <span class="n">idl</span><span class="o">=</span><span class="n">new_idl</span><span class="p">)</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">_value</span> <span class="o">=</span> <span class="n">new_val</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">is_merged</span> <span class="o">=</span> <span class="n">is_merged</span>
-        <span class="n">final_result</span><span class="p">[</span><span class="n">i_val</span><span class="p">]</span><span class="o">.</span><span class="n">reweighted</span> <span class="o">=</span> <span class="n">reweighted</span>
-
-    <span class="k">return</span> <span class="n">final_result</span>
-</pre></div>
-
-        </details>
-
-            <div class="docstring"><p>Construct a derived Obs for a matrix valued function according to func(data, **kwargs) using automatic differentiation.</p>
-
-<h6 id="parameters">Parameters</h6>
-
-<ul>
-<li><strong>func</strong> (object):
-arbitrary function of the form func(data, **kwargs). For the
-automatic differentiation to work, all numpy functions have to have
-the autograd wrapper (use 'import autograd.numpy as anp').</li>
-<li><strong>data</strong> (list):
-list of Obs, e.g. [obs1, obs2, obs3].</li>
-<li><strong>man_grad</strong> (list):
-manually supply a list or an array which contains the jacobian
-of func. Use cautiously, supplying the wrong derivative will
-not be intercepted.</li>
-</ul>
-</div>
-
-
-                </section>
                 <section id="matmul">
                             <div class="attr function"><a class="headerlink" href="#matmul">#&nbsp;&nbsp</a>
 
@@ -991,8 +733,8 @@ not be intercepted.</li>
         <span class="k">def</span> <span class="nf">multi_dot_i</span><span class="p">(</span><span class="n">operands</span><span class="p">):</span>
             <span class="k">return</span> <span class="n">multi_dot</span><span class="p">(</span><span class="n">operands</span><span class="p">,</span> <span class="s1">&#39;Imag&#39;</span><span class="p">)</span>
 
-        <span class="n">Nr</span> <span class="o">=</span> <span class="n">derived_array</span><span class="p">(</span><span class="n">multi_dot_r</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">)</span>
-        <span class="n">Ni</span> <span class="o">=</span> <span class="n">derived_array</span><span class="p">(</span><span class="n">multi_dot_i</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">)</span>
+        <span class="n">Nr</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="n">multi_dot_r</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
+        <span class="n">Ni</span> <span class="o">=</span> <span class="n">derived_observable</span><span class="p">(</span><span class="n">multi_dot_i</span><span class="p">,</span> <span class="n">extended_operands</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 
         <span class="n">res</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">Nr</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">Nr</span><span class="p">):</span>
@@ -1005,7 +747,7 @@ not be intercepted.</li>
             <span class="k">for</span> <span class="n">op</span> <span class="ow">in</span> <span class="n">operands</span><span class="p">[</span><span class="mi">1</span><span class="p">:]:</span>
                 <span class="n">stack</span> <span class="o">=</span> <span class="n">stack</span> <span class="o">@</span> <span class="n">op</span>
             <span class="k">return</span> <span class="n">stack</span>
-        <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">return</span> <span class="n">derived_observable</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="n">array_mode</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
 </pre></div>
 
         </details>
diff --git a/docs/pyerrors/obs.html b/docs/pyerrors/obs.html
index 9468f8a1..95050f29 100644
--- a/docs/pyerrors/obs.html
+++ b/docs/pyerrors/obs.html
@@ -1346,7 +1346,7 @@
         <span class="k">return</span> <span class="n">deltas</span><span class="p">,</span> <span class="n">idx</span>
 
 
-<span class="k">def</span> <span class="nf">derived_observable</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+<span class="k">def</span> <span class="nf">derived_observable</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.</span>
 
 <span class="sd">    Parameters</span>
@@ -1379,6 +1379,7 @@
     <span class="n">raveled_data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
 
     <span class="c1"># Workaround for matrix operations containing non Obs data</span>
+    <span class="c1"># TODO: Find more elegant solution here.</span>
     <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
         <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_data</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
             <span class="n">first_name</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
@@ -1401,11 +1402,13 @@
 
     <span class="n">n_obs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)</span>
     <span class="n">new_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+    <span class="n">new_cov_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">cov_names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+    <span class="n">new_sample_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">new_names</span><span class="p">)</span> <span class="o">-</span> <span class="nb">set</span><span class="p">(</span><span class="n">new_cov_names</span><span class="p">))</span>
 
-    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">}</span>
+    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">}</span>
     <span class="n">reweighted</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">reweighted</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span>
     <span class="n">new_idl_d</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
+    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
         <span class="n">idl</span> <span class="o">=</span> <span class="p">[]</span>
         <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
@@ -1427,7 +1430,7 @@
         <span class="n">multi</span> <span class="o">=</span> <span class="mi">1</span>
 
     <span class="n">new_r_values</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
+    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
         <span class="n">tmp_values</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_obs</span><span class="p">)</span>
         <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">):</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">r_values</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
@@ -1469,15 +1472,48 @@
 
     <span class="n">final_result</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">new_values</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
 
+    <span class="k">if</span> <span class="n">array_mode</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+
+        <span class="n">new_covobs_lengths</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[[(</span><span class="n">n</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">.</span><span class="n">N</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">o</span><span class="o">.</span><span class="n">cov_names</span><span class="p">]</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+
+        <span class="k">class</span> <span class="nc">_Zero_grad</span><span class="p">():</span>
+            <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
+                <span class="c1"># self.grad = np.zeros(N)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">grad</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="mi">1</span><span class="p">))</span>
+
+        <span class="n">d_extracted</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="n">g_extracted</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
+            <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="n">ens_length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
+                <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">ens_length</span><span class="p">)),</span> <span class="n">o</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]),</span> <span class="n">o</span><span class="o">.</span><span class="n">shape</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">ens_length</span><span class="p">),</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">ens_length</span><span class="p">,</span> <span class="p">)))</span>
+        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_cov_names</span><span class="p">:</span>
+            <span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="n">zero_grad</span> <span class="o">=</span> <span class="n">_Zero_grad</span><span class="p">(</span><span class="n">new_covobs_lengths</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
+                <span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">o</span><span class="o">.</span><span class="n">covobs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">zero_grad</span><span class="p">)</span><span class="o">.</span><span class="n">grad</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">new_covobs_lengths</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="mi">1</span><span class="p">)))</span>
+
     <span class="k">for</span> <span class="n">i_val</span><span class="p">,</span> <span class="n">new_val</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">new_values</span><span class="p">):</span>
         <span class="n">new_deltas</span> <span class="o">=</span> <span class="p">{}</span>
         <span class="n">new_grad</span> <span class="o">=</span> <span class="p">{}</span>
-        <span class="k">for</span> <span class="n">j_obs</span><span class="p">,</span> <span class="n">obs</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">data</span><span class="p">):</span>
-            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">names</span><span class="p">:</span>
-                <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
-                    <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_grad</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">obs</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span>
-                <span class="k">else</span><span class="p">:</span>
-                    <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+        <span class="k">if</span> <span class="n">array_mode</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
+                <span class="n">ens_length</span> <span class="o">=</span> <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+                <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</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">ens_length</span><span class="p">)</span>
+                <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
+                    <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
+            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_cov_names</span><span class="p">:</span>
+                <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+                <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
+                    <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">j_obs</span><span class="p">,</span> <span class="n">obs</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">data</span><span class="p">):</span>
+                <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">names</span><span class="p">:</span>
+                    <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
+                        <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_grad</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">obs</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
 
         <span class="n">new_covobs</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="n">Covobs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">allcov</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">name</span><span class="p">,</span> <span class="n">grad</span><span class="o">=</span><span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_grad</span><span class="p">}</span>
 
@@ -4587,12 +4623,12 @@ should agree with samples from a full jackknife analysis up to O(1/N).</li>
 
         
             <span class="def">def</span>
-            <span class="name">derived_observable</span><span class="signature">(func, data, **kwargs)</span>:
+            <span class="name">derived_observable</span><span class="signature">(func, data, array_mode=False, **kwargs)</span>:
     </div>
 
                 <details>
             <summary>View Source</summary>
-            <div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">derived_observable</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
+            <div class="codehilite"><pre><span></span><span class="k">def</span> <span class="nf">derived_observable</span><span class="p">(</span><span class="n">func</span><span class="p">,</span> <span class="n">data</span><span class="p">,</span> <span class="n">array_mode</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
     <span class="sd">&quot;&quot;&quot;Construct a derived Obs according to func(data, **kwargs) using automatic differentiation.</span>
 
 <span class="sd">    Parameters</span>
@@ -4625,6 +4661,7 @@ should agree with samples from a full jackknife analysis up to O(1/N).</li>
     <span class="n">raveled_data</span> <span class="o">=</span> <span class="n">data</span><span class="o">.</span><span class="n">ravel</span><span class="p">()</span>
 
     <span class="c1"># Workaround for matrix operations containing non Obs data</span>
+    <span class="c1"># TODO: Find more elegant solution here.</span>
     <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
         <span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">i_data</span><span class="p">,</span> <span class="n">Obs</span><span class="p">):</span>
             <span class="n">first_name</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">names</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span>
@@ -4647,11 +4684,13 @@ should agree with samples from a full jackknife analysis up to O(1/N).</li>
 
     <span class="n">n_obs</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">)</span>
     <span class="n">new_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+    <span class="n">new_cov_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">cov_names</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+    <span class="n">new_sample_names</span> <span class="o">=</span> <span class="nb">sorted</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">new_names</span><span class="p">)</span> <span class="o">-</span> <span class="nb">set</span><span class="p">(</span><span class="n">new_cov_names</span><span class="p">))</span>
 
-    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">}</span>
+    <span class="n">is_merged</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">is_merged</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="kc">False</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span><span class="p">)</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">}</span>
     <span class="n">reweighted</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="nb">list</span><span class="p">(</span><span class="nb">filter</span><span class="p">(</span><span class="k">lambda</span> <span class="n">o</span><span class="p">:</span> <span class="n">o</span><span class="o">.</span><span class="n">reweighted</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">,</span> <span class="n">raveled_data</span><span class="p">)))</span> <span class="o">&gt;</span> <span class="mi">0</span>
     <span class="n">new_idl_d</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
+    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
         <span class="n">idl</span> <span class="o">=</span> <span class="p">[]</span>
         <span class="k">for</span> <span class="n">i_data</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">:</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">i_data</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
@@ -4673,7 +4712,7 @@ should agree with samples from a full jackknife analysis up to O(1/N).</li>
         <span class="n">multi</span> <span class="o">=</span> <span class="mi">1</span>
 
     <span class="n">new_r_values</span> <span class="o">=</span> <span class="p">{}</span>
-    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_names</span><span class="p">:</span>
+    <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
         <span class="n">tmp_values</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_obs</span><span class="p">)</span>
         <span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">raveled_data</span><span class="p">):</span>
             <span class="n">tmp</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">r_values</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">)</span>
@@ -4715,15 +4754,48 @@ should agree with samples from a full jackknife analysis up to O(1/N).</li>
 
     <span class="n">final_result</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">new_values</span><span class="o">.</span><span class="n">shape</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="nb">object</span><span class="p">)</span>
 
+    <span class="k">if</span> <span class="n">array_mode</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+
+        <span class="n">new_covobs_lengths</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span><span class="nb">set</span><span class="p">([</span><span class="n">y</span> <span class="k">for</span> <span class="n">x</span> <span class="ow">in</span> <span class="p">[[(</span><span class="n">n</span><span class="p">,</span> <span class="n">o</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">n</span><span class="p">]</span><span class="o">.</span><span class="n">N</span><span class="p">)</span> <span class="k">for</span> <span class="n">n</span> <span class="ow">in</span> <span class="n">o</span><span class="o">.</span><span class="n">cov_names</span><span class="p">]</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">raveled_data</span><span class="p">]</span> <span class="k">for</span> <span class="n">y</span> <span class="ow">in</span> <span class="n">x</span><span class="p">]))</span>
+
+        <span class="k">class</span> <span class="nc">_Zero_grad</span><span class="p">():</span>
+            <span class="k">def</span> <span class="fm">__init__</span><span class="p">(</span><span class="bp">self</span><span class="p">,</span> <span class="n">N</span><span class="p">):</span>
+                <span class="c1"># self.grad = np.zeros(N)</span>
+                <span class="bp">self</span><span class="o">.</span><span class="n">grad</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="mi">1</span><span class="p">))</span>
+
+        <span class="n">d_extracted</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="n">g_extracted</span> <span class="o">=</span> <span class="p">{}</span>
+        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
+            <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="n">ens_length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
+                <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">o</span><span class="o">.</span><span class="n">deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">ens_length</span><span class="p">)),</span> <span class="n">o</span><span class="o">.</span><span class="n">idl</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">]),</span> <span class="n">o</span><span class="o">.</span><span class="n">shape</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">ens_length</span><span class="p">),</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">ens_length</span><span class="p">,</span> <span class="p">)))</span>
+        <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_cov_names</span><span class="p">:</span>
+            <span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="p">[]</span>
+            <span class="n">zero_grad</span> <span class="o">=</span> <span class="n">_Zero_grad</span><span class="p">(</span><span class="n">new_covobs_lengths</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+            <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">data</span><span class="p">):</span>
+                <span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">append</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">o</span><span class="o">.</span><span class="n">covobs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="n">zero_grad</span><span class="p">)</span><span class="o">.</span><span class="n">grad</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">dat</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">prod</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span><span class="p">))])</span><span class="o">.</span><span class="n">reshape</span><span class="p">(</span><span class="n">dat</span><span class="o">.</span><span class="n">shape</span> <span class="o">+</span> <span class="p">(</span><span class="n">new_covobs_lengths</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="mi">1</span><span class="p">)))</span>
+
     <span class="k">for</span> <span class="n">i_val</span><span class="p">,</span> <span class="n">new_val</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">new_values</span><span class="p">):</span>
         <span class="n">new_deltas</span> <span class="o">=</span> <span class="p">{}</span>
         <span class="n">new_grad</span> <span class="o">=</span> <span class="p">{}</span>
-        <span class="k">for</span> <span class="n">j_obs</span><span class="p">,</span> <span class="n">obs</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">data</span><span class="p">):</span>
-            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">names</span><span class="p">:</span>
-                <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
-                    <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_grad</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">obs</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span>
-                <span class="k">else</span><span class="p">:</span>
-                    <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
+        <span class="k">if</span> <span class="n">array_mode</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_sample_names</span><span class="p">:</span>
+                <span class="n">ens_length</span> <span class="o">=</span> <span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span>
+                <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</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">ens_length</span><span class="p">)</span>
+                <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">d_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
+                    <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
+            <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_cov_names</span><span class="p">:</span>
+                <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="mi">0</span>
+                <span class="k">for</span> <span class="n">i_dat</span><span class="p">,</span> <span class="n">dat</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">g_extracted</span><span class="p">[</span><span class="n">name</span><span class="p">]):</span>
+                    <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">tensordot</span><span class="p">(</span><span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="p">(</span><span class="n">i_dat</span><span class="p">,</span> <span class="p">)],</span> <span class="n">dat</span><span class="p">)</span>
+        <span class="k">else</span><span class="p">:</span>
+            <span class="k">for</span> <span class="n">j_obs</span><span class="p">,</span> <span class="n">obs</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">data</span><span class="p">):</span>
+                <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">names</span><span class="p">:</span>
+                    <span class="k">if</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">obs</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
+                        <span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_grad</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">obs</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span>
+                    <span class="k">else</span><span class="p">:</span>
+                        <span class="n">new_deltas</span><span class="p">[</span><span class="n">name</span><span class="p">]</span> <span class="o">=</span> <span class="n">new_deltas</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="n">name</span><span class="p">,</span> <span class="mi">0</span><span class="p">)</span> <span class="o">+</span> <span class="n">deriv</span><span class="p">[</span><span class="n">i_val</span> <span class="o">+</span> <span class="n">j_obs</span><span class="p">]</span> <span class="o">*</span> <span class="n">_expand_deltas_for_merge</span><span class="p">(</span><span class="n">obs</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">obs</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">new_idl_d</span><span class="p">[</span><span class="n">name</span><span class="p">])</span>
 
         <span class="n">new_covobs</span> <span class="o">=</span> <span class="p">{</span><span class="n">name</span><span class="p">:</span> <span class="n">Covobs</span><span class="p">(</span><span class="mi">0</span><span class="p">,</span> <span class="n">allcov</span><span class="p">[</span><span class="n">name</span><span class="p">],</span> <span class="n">name</span><span class="p">,</span> <span class="n">grad</span><span class="o">=</span><span class="n">new_grad</span><span class="p">[</span><span class="n">name</span><span class="p">])</span> <span class="k">for</span> <span class="n">name</span> <span class="ow">in</span> <span class="n">new_grad</span><span class="p">}</span>
 
diff --git a/docs/search.js b/docs/search.js
index 259ed25e..292ea271 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 i=this.index[t].getDocFreq(e),o=1+Math.log(this.documentStore.length/(i+1));return this._idfCache[n]=o,o},t.Index.prototype.getFields=function(){return this._fields.slice()},t.Index.prototype.search=function(e,n){if(!e)return[];e="string"==typeof e?{any:e}:JSON.parse(JSON.stringify(e));var i=null;null!=n&&(i=JSON.stringify(n));for(var o=new t.Configuration(i,this.getFields()).get(),r={},s=Object.keys(e),u=0;u<s.length;u++){var a=s[u];r[a]=this.pipeline.run(t.tokenizer(e[a]))}var l={};for(var c in o){var d=r[c]||r.any;if(d){var f=this.fieldSearch(d,c,o),h=o[c].boost;for(var p in f)f[p]=f[p]*h;for(var p in f)p in l?l[p]+=f[p]:l[p]=f[p]}}var v,g=[];for(var p in l)v={ref:p,score:l[p]},this.documentStore.hasDoc(p)&&(v.doc=this.documentStore.getDoc(p)),g.push(v);return g.sort(function(e,t){return t.score-e.score}),g},t.Index.prototype.fieldSearch=function(e,t,n){var i=n[t].bool,o=n[t].expand,r=n[t].boost,s=null,u={};return 0!==r?(e.forEach(function(e){var 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 RegExp("^"+o+i+"[^aeiouwxy]$"),I=/^(.+?[^aeiou])y$/,b=/^(.+?)(ational|tional|enci|anci|izer|bli|alli|entli|eli|ousli|ization|ation|ator|alism|iveness|fulness|ousness|aliti|iviti|biliti|logi)$/,E=/^(.+?)(icate|ative|alize|iciti|ical|ful|ness)$/,D=/^(.+?)(al|ance|ence|er|ic|able|ible|ant|ement|ment|ent|ou|ism|ate|iti|ous|ive|ize)$/,F=/^(.+?)(s|t)(ion)$/,_=/^(.+?)e$/,P=/ll$/,k=new RegExp("^"+o+i+"[^aeiouwxy]$"),z=function(n){var i,o,r,s,u,a,l;if(n.length<3)return n;if(r=n.substr(0,1),"y"==r&&(n=r.toUpperCase()+n.substr(1)),s=p,u=v,s.test(n)?n=n.replace(s,"$1$2"):u.test(n)&&(n=n.replace(u,"$1$2")),s=g,u=m,s.test(n)){var z=s.exec(n);s=c,s.test(z[1])&&(s=y,n=n.replace(s,""))}else if(u.test(n)){var z=u.exec(n);i=z[1],u=h,u.test(i)&&(n=i,u=S,a=x,l=w,u.test(n)?n+="e":a.test(n)?(s=y,n=n.replace(s,"")):l.test(n)&&(n+="e"))}if(s=I,s.test(n)){var z=s.exec(n);i=z[1],n=i+"i"}if(s=b,s.test(n)){var z=s.exec(n);i=z[1],o=z[2],s=c,s.test(i)&&(n=i+e[o])}if(s=E,s.test(n)){var z=s.exec(n);i=z[1],o=z[2],s=c,s.test(i)&&(n=i+t[o])}if(s=D,u=F,s.test(n)){var z=s.exec(n);i=z[1],s=d,s.test(i)&&(n=i)}else if(u.test(n)){var z=u.exec(n);i=z[1]+z[2],u=d,u.test(i)&&(n=i)}if(s=_,s.test(n)){var z=s.exec(n);i=z[1],s=d,u=f,a=k,(s.test(i)||u.test(i)&&!a.test(i))&&(n=i)}return s=P,u=d,s.test(n)&&u.test(n)&&(s=y,n=n.replace(s,"")),"y"==r&&(n=r.toLowerCase()+n.substr(1)),n};return z}(),t.Pipeline.registerFunction(t.stemmer,"stemmer"),t.stopWordFilter=function(e){return e&&t.stopWordFilter.stopWords[e]!==!0?e:void 0},t.clearStopWords=function(){t.stopWordFilter.stopWords={}},t.addStopWords=function(e){null!=e&&Array.isArray(e)!==!1&&e.forEach(function(e){t.stopWordFilter.stopWords[e]=!0},this)},t.resetStopWords=function(){t.stopWordFilter.stopWords=t.defaultStopWords},t.defaultStopWords={"":!0,a:!0,able:!0,about:!0,across:!0,after:!0,all:!0,almost:!0,also:!0,am:!0,among:!0,an:!0,and:!0,any:!0,are:!0,as:!0,at:!0,be:!0,because:!0,been:!0,but:!0,by:!0,can:!0,cannot:!0,could:!0,dear:!0,did:!0,"do":!0,does:!0,either:!0,"else":!0,ever:!0,every:!0,"for":!0,from:!0,get:!0,got:!0,had:!0,has:!0,have:!0,he:!0,her:!0,hers:!0,him:!0,his:!0,how:!0,however:!0,i:!0,"if":!0,"in":!0,into:!0,is:!0,it:!0,its:!0,just:!0,least:!0,let:!0,like:!0,likely:!0,may:!0,me:!0,might:!0,most:!0,must:!0,my:!0,neither:!0,no:!0,nor:!0,not:!0,of:!0,off:!0,often:!0,on:!0,only:!0,or:!0,other:!0,our:!0,own:!0,rather:!0,said:!0,say:!0,says:!0,she:!0,should:!0,since:!0,so:!0,some:!0,than:!0,that:!0,the:!0,their:!0,them:!0,then:!0,there:!0,these:!0,they:!0,"this":!0,tis:!0,to:!0,too:!0,twas:!0,us:!0,wants:!0,was:!0,we:!0,were:!0,what:!0,when:!0,where:!0,which:!0,"while":!0,who:!0,whom:!0,why:!0,will:!0,"with":!0,would:!0,yet:!0,you:!0,your:!0},t.stopWordFilter.stopWords=t.defaultStopWords,t.Pipeline.registerFunction(t.stopWordFilter,"stopWordFilter"),t.trimmer=function(e){if(null===e||void 0===e)throw new Error("token should not be undefined");return e.replace(/^\W+/,"").replace(/\W+$/,"")},t.Pipeline.registerFunction(t.trimmer,"trimmer"),t.InvertedIndex=function(){this.root={docs:{},df:0}},t.InvertedIndex.load=function(e){var t=new this;return t.root=e.root,t},t.InvertedIndex.prototype.addToken=function(e,t,n){for(var n=n||this.root,i=0;i<=e.length-1;){var o=e[i];o in n||(n[o]={docs:{},df:0}),i+=1,n=n[o]}var r=t.ref;n.docs[r]?n.docs[r]={tf:t.tf}:(n.docs[r]={tf:t.tf},n.df+=1)},t.InvertedIndex.prototype.hasToken=function(e){if(!e)return!1;for(var t=this.root,n=0;n<e.length;n++){if(!t[e[n]])return!1;t=t[e[n]]}return!0},t.InvertedIndex.prototype.getNode=function(e){if(!e)return null;for(var t=this.root,n=0;n<e.length;n++){if(!t[e[n]])return null;t=t[e[n]]}return t},t.InvertedIndex.prototype.getDocs=function(e){var t=this.getNode(e);return null==t?{}:t.docs},t.InvertedIndex.prototype.getTermFrequency=function(e,t){var n=this.getNode(e);return null==n?0:t in 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-    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "qualname": "", "type": "module", "doc": "<h1 id=\"what-is-pyerrors\">What is pyerrors?</h1>\n\n<p><code>pyerrors</code> is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the <strong>gamma method</strong> <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>. Some of its features are:</p>\n\n<ul>\n<li><strong>automatic differentiation</strong> 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><strong>treatment of slow modes</strong> in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a></li>\n<li>coherent <strong>error propagation</strong> for data from <strong>different Markov chains</strong></li>\n<li><strong>non-linear fits with x- and y-errors</strong> 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><strong>real and complex matrix operations</strong> and their error propagation based on automatic differentiation (Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)</li>\n</ul>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in</p>\n\n<ul>\n<li><a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a></li>\n<li><a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a></li>\n<li><a href=\"https://github.com/mbruno46/pyobs\">Python</a></li>\n</ul>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<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>\n<span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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.</p>\n\n<p>Example:</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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 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<p>Example:</p>\n\n<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>\n<span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></div>\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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></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_tauint</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that dataset does not exhibit any autocorrelation and the windowsize 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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre></div>\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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre></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<p>Example:</p>\n\n<div class=\"codehilite\"><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></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>Irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"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></div>\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>For the full API see <code>pyerrors.correlators.Corr</code></p>\n\n<h1 id=\"complex-observables\">Complex 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<p>Example:</p>\n\n<div class=\"codehilite\"><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></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=\"codehilite\"><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></div>\n\n<h1 id=\"optimization-fits-roots\">Optimization / fits / roots</h1>\n\n<p><code>pyerrors.fits</code>\n<code>pyerrors.roots</code></p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors.linalg</code></p>\n\n<h1 id=\"export-data\">Export data</h1>\n\n<p>The preferred exported file format within <code>pyerrors</code> is</p>\n\n<h2 id=\"jackknife-samples\">Jackknife samples</h2>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can generate jackknife samples from an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> for details.</p>\n\n<h1 id=\"input\">Input</h1>\n\n<p><code>pyerrors.input</code></p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "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 smearing matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nsmearing matrix at every timeslice. Other dependency (eg. spacial) are not supported.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "data_input", "padding_front", "padding_back", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "vector_l", "vector_r"], "funcdef": "def"}, "pyerrors.correlators.Corr.sum": {"fullname": "pyerrors.correlators.Corr.sum", "modulename": "pyerrors.correlators", "qualname": "Corr.sum", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing": {"fullname": "pyerrors.correlators.Corr.smearing", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "i", "j"], "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "<p>Symmetrize the correlator around x0=0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "<p>Anti-symmetrize the correlator around x0=0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing_symmetric": {"fullname": "pyerrors.correlators.Corr.smearing_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing_symmetric", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "t0", "ts", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "t0", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "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", "parameters": ["self", "dt"], "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "<p>Reverse the time ordering of the Corr</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "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", "parameters": ["self", "partner"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "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", "parameters": ["self", "weight", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "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>partity</strong> (int):\nParity quantum number of the correlator, can be +1 or -1</li>\n</ul>\n", "parameters": ["self", "partner", "parity"], "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "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>symmetric</strong> (bool):\ndecides whether symmetric of simple finite differences are used. Default: True</li>\n</ul>\n", "parameters": ["self", "symmetric"], "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "<p>Return the second derivative of the correlator with respect to x0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "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 periodicitiy 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-periodicitiy 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)</li>\n<li><strong>guess</strong> (float):\nguess for the root finder, only relevant for the root variant</li>\n</ul>\n", "parameters": ["self", "variant", "guess"], "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "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):\nRange in which the function is to be fitted to the data.\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", "parameters": ["self", "function", "fitrange", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "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</ul>\n", "parameters": ["self", "plateau_range", "method"], "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "<p>Sets the attribute prange of the Corr object.</p>\n", "parameters": ["self", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "<p>Plots the correlator, uses tag 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.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale</li>\n<li><strong>plateau</strong> (Obs):\nplateau 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>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</ul>\n", "parameters": ["self", "x_range", "comp", "y_range", "logscale", "plateau", "fit_res", "ylabel", "save"], "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "<p>Dumps the Corr into a pickle file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file</li>\n</ul>\n", "parameters": ["self", "filename"], "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "range"], "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "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", "parameters": ["self", "mean", "cov", "name", "pos", "grad"], "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "<p>Return the variance (= square of the error) of the Covobs</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "<p>Returns gamma matrix in Grid labeling.</p>\n", "parameters": ["gamma_tag"], "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "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</ul>\n"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "<p>Performs a non-linear fit to y = func(x).</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\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=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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=\"n\">y</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\">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   <span class=\"k\">return</span> <span class=\"n\">y</span>\n</code></pre></div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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></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>priors</strong> (list, optional):\npriors has to be a 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\n            non-linear fits with many parameters.</li>\n<li><strong>method</strong> (str):\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>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>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>correlated_fit</strong> (bool):\nIf true, use the full correlation matrix in the definition of the chisquare\n(only works for prior==None and when no method is given, at the moment).</li>\n<li><strong>const_par</strong> (list, optional):\nList of N Obs that are used to constrain the last N fit parameters of func.</li>\n</ul>\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "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=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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=\"n\">y</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\">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   <span class=\"k\">return</span> <span class=\"n\">y</span>\n</code></pre></div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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></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>const_par</strong> (list, optional):\nList of N Obs that are used to constrain the last N fit parameters of func.</li>\n<li><strong>Based on the orthogonal distance regression module of scipy</strong></li>\n</ul>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.prior_fit": {"fullname": "pyerrors.fits.prior_fit", "modulename": "pyerrors.fits", "qualname": "prior_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.standard_fit": {"fullname": "pyerrors.fits.standard_fit", "modulename": "pyerrors.fits", "qualname": "standard_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.odr_fit": {"fullname": "pyerrors.fits.odr_fit", "modulename": "pyerrors.fits", "qualname": "odr_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "<p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>\n\n<p>y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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.</p>\n", "parameters": ["x", "y", "kwargs"], "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "<p>Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.</p>\n", "parameters": ["x", "o_y", "func", "p"], "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "<p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>\n", "parameters": ["x", "y", "func", "fit_res"], "funcdef": "def"}, "pyerrors.fits.covariance_matrix": {"fullname": "pyerrors.fits.covariance_matrix", "modulename": "pyerrors.fits", "qualname": "covariance_matrix", "type": "function", "doc": "<p>Returns the covariance matrix of y.</p>\n", "parameters": ["y"], "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "<p>Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>\n", "parameters": ["x", "func", "beta"], "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "<p>Performs a Kolmogorov\u2013Smirnov test for the Q-values of all fit object.</p>\n\n<p>If no list is given all Obs in memory are used.</p>\n\n<p>Disclaimer: The determination of the individual Q-values as well as this function have not been tested yet.</p>\n", "parameters": ["obs"], "funcdef": "def"}, "pyerrors.fits.fit_general": {"fullname": "pyerrors.fits.fit_general", "modulename": "pyerrors.fits", "qualname": "fit_general", "type": "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<p>Plausibility of the results should be checked. To control the numerical differentiation\nthe kwargs of numdifftools.step_generators.MaxStepGenerator can be used.</p>\n\n<p>func has to be of the form</p>\n\n<p>def func(a, x):\n    y = a[0] + a[1] * x + a[2] * np.sinh(x)\n    return y</p>\n\n<p>y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>silent -- If true all output to the console is omitted (default False).\ninitial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits\n                 with many parameters.</p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "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", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "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", "parameters": ["obs_list", "file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "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 -- 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<li><strong>stop -- stops reading at given configuration number (default None)</strong></li>\n<li><strong>alternative_ensemble_name -- Manually overwrite ensemble name</strong></li>\n</ul>\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "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 -- 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<li><strong>stop -- stops reading at given configuration number (default None)</strong></li>\n</ul>\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "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>tree</strong> (str):\nLabel of the upmost directory in the hdf5 file, default 'meson'\nfor outputs of the Meson module. Can be altered to read input\nfrom other modules with similar structures.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "parameters": ["path", "filestem", "ens_id", "meson", "tree", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "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>:  A :term:<code>generic &lt;generic type&gt;</code> version\nof ndarray.  </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=\"codehilite\"><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=\"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></div>\n\n<p>Second mode:</p>\n\n<div class=\"codehilite\"><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></div>\n"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "<p></p>\n", "parameters": [], "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "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", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl", "vertices"], "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "qualname": "", "type": "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", "type": "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 moments, these objects can be\neither of: Obs, list, numpy.ndarray.\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", "parameters": ["ol", "description", "indent"], "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "<p>Export a list 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>ol</strong> (list):\nList of objects that will be exported. At the moments, these objects can be\neither of: Obs, list, numpy.ndarray.\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", "parameters": ["ol", "fname", "description", "indent", "gz"], "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "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\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", "parameters": ["fname", "verbose", "gz", "full_output"], "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "<p>Read pbp format from given folder structure. Returns a list of length nrw</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>r_start -- list which contains the first config to be read for each replicum\nr_stop -- list which contains the last config to be read for each replicum</p>\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "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>version</strong> (str):\nversion of openQCD, default 2.0</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>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n</ul>\n", "parameters": ["path", "prefix", "version", "names", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "<p>Extract t0 from given .ms.dat files. Returns t0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have sufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - 0.3 is fitted with a linear function\nfrom which the exact root is extracted.\nOnly works with openQCD v 1.2.</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 when 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 effects 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 crossing to be included in the linear fit. (Default: 5)</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>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n</ul>\n", "parameters": ["path", "prefix", "dtr_read", "xmin", "spatial_extent", "fit_range", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "<p>Read sfcf C format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>im -- if True, read imaginary instead of real part of the correlation function.</strong></li>\n<li><strong>single -- if True, read a boundary-to-boundary correlation function with a single value</strong></li>\n<li><strong>b2b -- if True, read a time-dependent boundary-to-boundary correlation function</strong></li>\n<li><strong>names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length</strong></li>\n</ul>\n", "parameters": ["path", "prefix", "name", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_c": {"fullname": "pyerrors.input.sfcf.read_sfcf_c", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_c", "type": "function", "doc": "<p>Read sfcf c format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>quarks -- Label of the quarks used in the sfcf input file</strong></li>\n<li><strong>noffset -- Offset of the source (only relevant when wavefunctions are used)</strong></li>\n<li><strong>wf -- ID of wave function</strong></li>\n<li><strong>wf2 -- ID of the second wavefunction (only relevant for boundary-to-boundary correlation functions)</strong></li>\n<li><strong>im -- if True, read imaginary instead of real part of the correlation function.</strong></li>\n<li><strong>b2b -- if True, read a time-dependent boundary-to-boundary correlation function</strong></li>\n<li><strong>names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length</strong></li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n</ul>\n", "parameters": ["path", "prefix", "name", "quarks", "noffset", "wf", "wf2", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_qtop": {"fullname": "pyerrors.input.sfcf.read_qtop", "modulename": "pyerrors.input.sfcf", "qualname": "read_qtop", "type": "function", "doc": "<p>Read qtop format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>target -- specifies the topological sector to be reweighted to (default 0)</strong></li>\n<li><strong>full -- if true read the charge instead of the reweighting factor.</strong></li>\n</ul>\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.linalg.derived_array": {"fullname": "pyerrors.linalg.derived_array", "modulename": "pyerrors.linalg", "qualname": "derived_array", "type": "function", "doc": "<p>Construct a derived Obs for a matrix valued function 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>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", "parameters": ["func", "data", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "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", "parameters": ["operands"], "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "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", "parameters": ["operands"], "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "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", "parameters": ["subscripts", "operands"], "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "<p>Inverse of Obs or CObs valued matrices.</p>\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "<p>Cholesky decomposition of Obs or CObs valued matrices.</p>\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.scalar_mat_op": {"fullname": "pyerrors.linalg.scalar_mat_op", "modulename": "pyerrors.linalg", "qualname": "scalar_mat_op", "type": "function", "doc": "<p>Computes the matrix to scalar operation op to a given matrix of Obs.</p>\n", "parameters": ["op", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "<p>Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "<p>Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "<p>Computes the Moore-Penrose pseudoinverse of a matrix of Obs.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "<p>Computes the singular value decomposition of a matrix of Obs.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.slogdet": {"fullname": "pyerrors.linalg.slogdet", "modulename": "pyerrors.linalg", "qualname": "slogdet", "type": "function", "doc": "<p>Computes the determinant of a matrix of Obs via np.linalg.slogdet.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.grad_eig": {"fullname": "pyerrors.linalg.grad_eig", "modulename": "pyerrors.linalg", "qualname": "grad_eig", "type": "function", "doc": "<p>Gradient of a general square (complex valued) matrix</p>\n", "parameters": ["ans", "x"], "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "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", "parameters": ["obj", "name", "kwargs"], "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "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", "parameters": ["path"], "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "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", "parameters": ["means", "cov", "name", "tau", "samples"], "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "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", "parameters": ["corrs", "k", "p", "kwargs"], "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "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__", "type": "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<li><strong>means</strong> (list, optional):\nlist of mean values for the case that the mean values were\nalready subtracted from the samples</li>\n</ul>\n", "parameters": ["self", "samples", "names", "idl", "means", "covobs", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "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", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "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", "parameters": ["self", "ens_content"], "funcdef": "def"}, "pyerrors.obs.Obs.print": {"fullname": "pyerrors.obs.Obs.print", "modulename": "pyerrors.obs", "qualname": "Obs.print", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "level"], "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", "type": "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", "parameters": ["self", "sigma"], "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "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>rtol</strong> (float):\nRelative tolerance (for details see numpy documentation).</li>\n<li><strong>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "parameters": ["self", "rtol", "atol"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "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", "parameters": ["self", "save"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "<p>Plot normalized autocorrelation function time for each ensemble.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "<p>Plot replica distribution for each ensemble with more than one replicum.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "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", "parameters": ["self", "expand"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "<p>Dump the Obs to a pickle file 'name'.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>name</strong> (str):\nname of the file to be saved.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "parameters": ["self", "name", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinc": {"fullname": "pyerrors.obs.Obs.sinc", "modulename": "pyerrors.obs", "qualname": "Obs.sinc", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "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", "type": "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", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "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__", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "real", "imag"], "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "<p>Executes the gamma_method for the real and the imaginary part.</p>\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "<p>Checks whether both real and imaginary part are zero within machine precision.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "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", "parameters": ["func", "data", "kwargs"], "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "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.</li>\n</ul>\n", "parameters": ["weight", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "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<li><strong>Keep in mind to only correlate primary observables which have not been reweighted</strong></li>\n<li><strong>yet. The reweighting has to be applied after correlating the observables.</strong></li>\n<li><strong>Currently only works if ensembles are identical. This is not really necessary.</strong></li>\n</ul>\n", "parameters": ["obs_a", "obs_b"], "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "<p>Calculates the covariance of two observables.</p>\n\n<p>covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs1</strong> (Obs):\nFirst Obs</li>\n<li><strong>obs2</strong> (Obs):\nSecond Obs</li>\n<li><strong>correlation</strong> (bool):\nif true the correlation instead of the covariance is\nreturned (default False)</li>\n</ul>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance2": {"fullname": "pyerrors.obs.covariance2", "modulename": "pyerrors.obs", "qualname": "covariance2", "type": "function", "doc": "<p>Alternative implementation of the covariance of two observables.</p>\n\n<p>covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>correlation -- if true the correlation instead of the covariance is\n               returned (default False)</p>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance3": {"fullname": "pyerrors.obs.covariance3", "modulename": "pyerrors.obs", "qualname": "covariance3", "type": "function", "doc": "<p>Another alternative implementation of the covariance of two observables.</p>\n\n<p>covariance2(obs, obs) is equal to obs.dvalue ** 2\nCurrently only works if ensembles are identical.\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance2(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>correlation -- if true the correlation instead of the covariance is\n               returned (default False)\nplot -- if true, the integrated autocorrelation time for each ensemble is\n        plotted.</p>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.pseudo_Obs": {"fullname": "pyerrors.obs.pseudo_Obs", "modulename": "pyerrors.obs", "qualname": "pseudo_Obs", "type": "function", "doc": "<p>Generate a pseudo Obs with given value, dvalue and name</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", "parameters": ["value", "dvalue", "name", "samples"], "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "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", "parameters": ["jacks", "name", "idl"], "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "<p>Combine all observables in list_of_obs into one new observable</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<li><strong>It is not possible to combine obs which are based on the same replicum</strong></li>\n</ul>\n", "parameters": ["list_of_obs"], "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "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", "parameters": ["means", "cov", "name", "grad"], "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "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><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\n<code>python\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n</code></li>\n<li><strong>guess</strong> (float):\nInitial guess for the minimization.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Obs</strong>: <code>Obs</code> valued root of the function.</li>\n</ul>\n", "parameters": ["d", "func", "guess", "kwargs"], "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "qualname": "", "type": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "doc": 1044}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "doc": 0}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "doc": 51}, "pyerrors.correlators.Corr.__init__": {"qualname": 2, "fullname": 4, "doc": 0}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "doc": 0}, 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1.7320508075688772}}, "df": 1}}}}}, "i": {"docs": {}, "df": 0, "n": {"docs": {}, "df": 0, "i": {"docs": {}, "df": 0, "t": {"docs": {}, "df": 0, "_": {"docs": {}, "df": 0, "_": {"docs": {"pyerrors.input.hadrons.Npr_matrix": {"tf": 1}}, "df": 1}}}}}}}}}}}, "pipeline": ["trimmer", "stopWordFilter", "stemmer"], "_isPrebuiltIndex": true};
+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "qualname": "", "type": "module", "doc": "<h1 id=\"what-is-pyerrors\">What is pyerrors?</h1>\n\n<p><code>pyerrors</code> is a python package for error computation and propagation of Markov chain Monte Carlo data.\nIt is based on the <strong>gamma method</strong> <a href=\"https://arxiv.org/abs/hep-lat/0306017\">arXiv:hep-lat/0306017</a>. Some of its features are:</p>\n\n<ul>\n<li><strong>automatic differentiation</strong> 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><strong>treatment of slow modes</strong> in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a></li>\n<li>coherent <strong>error propagation</strong> for data from <strong>different Markov chains</strong></li>\n<li><strong>non-linear fits with x- and y-errors</strong> 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><strong>real and complex matrix operations</strong> and their error propagation based on automatic differentiation (Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...)</li>\n</ul>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in</p>\n\n<ul>\n<li><a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a></li>\n<li><a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a></li>\n<li><a href=\"https://github.com/mbruno46/pyobs\">Python</a></li>\n</ul>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<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>\n<span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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.</p>\n\n<p>Example:</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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 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<p>Example:</p>\n\n<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>\n<span class=\"kn\">import</span> <span class=\"nn\">pyerrors</span> <span class=\"k\">as</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></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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></div>\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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></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_tauint</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that dataset does not exhibit any autocorrelation and the windowsize 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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">1000</span><span class=\"p\">)</span>\n</code></pre></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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre></div>\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<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"mi\">1</span> <span class=\"n\">to</span> <span class=\"mi\">500</span><span class=\"p\">)</span>\n</code></pre></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<p>Example:</p>\n\n<div class=\"codehilite\"><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></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>Irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<p>Example:</p>\n\n<div class=\"codehilite\"><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=\"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=\"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></div>\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>For the full API see <code>pyerrors.correlators.Corr</code></p>\n\n<h1 id=\"complex-observables\">Complex 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<p>Example:</p>\n\n<div class=\"codehilite\"><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></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=\"codehilite\"><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></div>\n\n<h1 id=\"optimization-fits-roots\">Optimization / fits / roots</h1>\n\n<p><code>pyerrors.fits</code>\n<code>pyerrors.roots</code></p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors.linalg</code></p>\n\n<h1 id=\"export-data\">Export data</h1>\n\n<p>The preferred exported file format within <code>pyerrors</code> is</p>\n\n<h2 id=\"jackknife-samples\">Jackknife samples</h2>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can generate jackknife samples from an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> for details.</p>\n\n<h1 id=\"input\">Input</h1>\n\n<p><code>pyerrors.input</code></p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr": {"fullname": "pyerrors.correlators.Corr", "modulename": "pyerrors.correlators", "qualname": "Corr", "type": "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 smearing matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nsmearing matrix at every timeslice. Other dependency (eg. spacial) are not supported.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "data_input", "padding_front", "padding_back", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweighted": {"fullname": "pyerrors.correlators.Corr.reweighted", "modulename": "pyerrors.correlators", "qualname": "Corr.reweighted", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.correlators.Corr.gamma_method": {"fullname": "pyerrors.correlators.Corr.gamma_method", "modulename": "pyerrors.correlators", "qualname": "Corr.gamma_method", "type": "function", "doc": "<p>Apply the gamma method to the content of the Corr.</p>\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "vector_l", "vector_r"], "funcdef": "def"}, "pyerrors.correlators.Corr.sum": {"fullname": "pyerrors.correlators.Corr.sum", "modulename": "pyerrors.correlators", "qualname": "Corr.sum", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing": {"fullname": "pyerrors.correlators.Corr.smearing", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "i", "j"], "funcdef": "def"}, "pyerrors.correlators.Corr.plottable": {"fullname": "pyerrors.correlators.Corr.plottable", "modulename": "pyerrors.correlators", "qualname": "Corr.plottable", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.symmetric": {"fullname": "pyerrors.correlators.Corr.symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.symmetric", "type": "function", "doc": "<p>Symmetrize the correlator around x0=0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.anti_symmetric": {"fullname": "pyerrors.correlators.Corr.anti_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.anti_symmetric", "type": "function", "doc": "<p>Anti-symmetrize the correlator around x0=0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.smearing_symmetric": {"fullname": "pyerrors.correlators.Corr.smearing_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.smearing_symmetric", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "t0", "ts", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "t0", "state"], "funcdef": "def"}, "pyerrors.correlators.Corr.roll": {"fullname": "pyerrors.correlators.Corr.roll", "modulename": "pyerrors.correlators", "qualname": "Corr.roll", "type": "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", "parameters": ["self", "dt"], "funcdef": "def"}, "pyerrors.correlators.Corr.reverse": {"fullname": "pyerrors.correlators.Corr.reverse", "modulename": "pyerrors.correlators", "qualname": "Corr.reverse", "type": "function", "doc": "<p>Reverse the time ordering of the Corr</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.correlate": {"fullname": "pyerrors.correlators.Corr.correlate", "modulename": "pyerrors.correlators", "qualname": "Corr.correlate", "type": "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", "parameters": ["self", "partner"], "funcdef": "def"}, "pyerrors.correlators.Corr.reweight": {"fullname": "pyerrors.correlators.Corr.reweight", "modulename": "pyerrors.correlators", "qualname": "Corr.reweight", "type": "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", "parameters": ["self", "weight", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.T_symmetry": {"fullname": "pyerrors.correlators.Corr.T_symmetry", "modulename": "pyerrors.correlators", "qualname": "Corr.T_symmetry", "type": "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>partity</strong> (int):\nParity quantum number of the correlator, can be +1 or -1</li>\n</ul>\n", "parameters": ["self", "partner", "parity"], "funcdef": "def"}, "pyerrors.correlators.Corr.deriv": {"fullname": "pyerrors.correlators.Corr.deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.deriv", "type": "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>symmetric</strong> (bool):\ndecides whether symmetric of simple finite differences are used. Default: True</li>\n</ul>\n", "parameters": ["self", "symmetric"], "funcdef": "def"}, "pyerrors.correlators.Corr.second_deriv": {"fullname": "pyerrors.correlators.Corr.second_deriv", "modulename": "pyerrors.correlators", "qualname": "Corr.second_deriv", "type": "function", "doc": "<p>Return the second derivative of the correlator with respect to x0.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.m_eff": {"fullname": "pyerrors.correlators.Corr.m_eff", "modulename": "pyerrors.correlators", "qualname": "Corr.m_eff", "type": "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 periodicitiy 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-periodicitiy 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)</li>\n<li><strong>guess</strong> (float):\nguess for the root finder, only relevant for the root variant</li>\n</ul>\n", "parameters": ["self", "variant", "guess"], "funcdef": "def"}, "pyerrors.correlators.Corr.fit": {"fullname": "pyerrors.correlators.Corr.fit", "modulename": "pyerrors.correlators", "qualname": "Corr.fit", "type": "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):\nRange in which the function is to be fitted to the data.\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", "parameters": ["self", "function", "fitrange", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.correlators.Corr.plateau": {"fullname": "pyerrors.correlators.Corr.plateau", "modulename": "pyerrors.correlators", "qualname": "Corr.plateau", "type": "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</ul>\n", "parameters": ["self", "plateau_range", "method"], "funcdef": "def"}, "pyerrors.correlators.Corr.set_prange": {"fullname": "pyerrors.correlators.Corr.set_prange", "modulename": "pyerrors.correlators", "qualname": "Corr.set_prange", "type": "function", "doc": "<p>Sets the attribute prange of the Corr object.</p>\n", "parameters": ["self", "prange"], "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "<p>Plots the correlator, uses tag 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.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale</li>\n<li><strong>plateau</strong> (Obs):\nplateau 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>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</ul>\n", "parameters": ["self", "x_range", "comp", "y_range", "logscale", "plateau", "fit_res", "ylabel", "save"], "funcdef": "def"}, "pyerrors.correlators.Corr.dump": {"fullname": "pyerrors.correlators.Corr.dump", "modulename": "pyerrors.correlators", "qualname": "Corr.dump", "type": "function", "doc": "<p>Dumps the Corr into a pickle file</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file</li>\n</ul>\n", "parameters": ["self", "filename"], "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "range"], "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs": {"fullname": "pyerrors.covobs.Covobs", "modulename": "pyerrors.covobs", "qualname": "Covobs", "type": "class", "doc": "<p></p>\n"}, "pyerrors.covobs.Covobs.__init__": {"fullname": "pyerrors.covobs.Covobs.__init__", "modulename": "pyerrors.covobs", "qualname": "Covobs.__init__", "type": "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", "parameters": ["self", "mean", "cov", "name", "pos", "grad"], "funcdef": "def"}, "pyerrors.covobs.Covobs.errsq": {"fullname": "pyerrors.covobs.Covobs.errsq", "modulename": "pyerrors.covobs", "qualname": "Covobs.errsq", "type": "function", "doc": "<p>Return the variance (= square of the error) of the Covobs</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.Grid_gamma": {"fullname": "pyerrors.dirac.Grid_gamma", "modulename": "pyerrors.dirac", "qualname": "Grid_gamma", "type": "function", "doc": "<p>Returns gamma matrix in Grid labeling.</p>\n", "parameters": ["gamma_tag"], "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.fits.Fit_result": {"fullname": "pyerrors.fits.Fit_result", "modulename": "pyerrors.fits", "qualname": "Fit_result", "type": "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</ul>\n"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.Fit_result.gamma_method": {"fullname": "pyerrors.fits.Fit_result.gamma_method", "modulename": "pyerrors.fits", "qualname": "Fit_result.gamma_method", "type": "function", "doc": "<p>Apply the gamma method to all fit parameters</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.fits.least_squares": {"fullname": "pyerrors.fits.least_squares", "modulename": "pyerrors.fits", "qualname": "least_squares", "type": "function", "doc": "<p>Performs a non-linear fit to y = func(x).</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\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=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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=\"n\">y</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\">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   <span class=\"k\">return</span> <span class=\"n\">y</span>\n</code></pre></div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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></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>priors</strong> (list, optional):\npriors has to be a 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\n            non-linear fits with many parameters.</li>\n<li><strong>method</strong> (str):\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>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>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>correlated_fit</strong> (bool):\nIf true, use the full correlation matrix in the definition of the chisquare\n(only works for prior==None and when no method is given, at the moment).</li>\n<li><strong>const_par</strong> (list, optional):\nList of N Obs that are used to constrain the last N fit parameters of func.</li>\n</ul>\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.total_least_squares": {"fullname": "pyerrors.fits.total_least_squares", "modulename": "pyerrors.fits", "qualname": "total_least_squares", "type": "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=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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=\"n\">y</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\">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   <span class=\"k\">return</span> <span class=\"n\">y</span>\n</code></pre></div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"codehilite\"><pre><span></span><code><span class=\"k\">def</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></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>const_par</strong> (list, optional):\nList of N Obs that are used to constrain the last N fit parameters of func.</li>\n<li><strong>Based on the orthogonal distance regression module of scipy</strong></li>\n</ul>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.prior_fit": {"fullname": "pyerrors.fits.prior_fit", "modulename": "pyerrors.fits", "qualname": "prior_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "priors", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.standard_fit": {"fullname": "pyerrors.fits.standard_fit", "modulename": "pyerrors.fits", "qualname": "standard_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.odr_fit": {"fullname": "pyerrors.fits.odr_fit", "modulename": "pyerrors.fits", "qualname": "odr_fit", "type": "function", "doc": "<p></p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.fits.fit_lin": {"fullname": "pyerrors.fits.fit_lin", "modulename": "pyerrors.fits", "qualname": "fit_lin", "type": "function", "doc": "<p>Performs a linear fit to y = n + m * x and returns two Obs n, m.</p>\n\n<p>y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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.</p>\n", "parameters": ["x", "y", "kwargs"], "funcdef": "def"}, "pyerrors.fits.qqplot": {"fullname": "pyerrors.fits.qqplot", "modulename": "pyerrors.fits", "qualname": "qqplot", "type": "function", "doc": "<p>Generates a quantile-quantile plot of the fit result which can be used to\ncheck if the residuals of the fit are gaussian distributed.</p>\n", "parameters": ["x", "o_y", "func", "p"], "funcdef": "def"}, "pyerrors.fits.residual_plot": {"fullname": "pyerrors.fits.residual_plot", "modulename": "pyerrors.fits", "qualname": "residual_plot", "type": "function", "doc": "<p>Generates a plot which compares the fit to the data and displays the corresponding residuals</p>\n", "parameters": ["x", "y", "func", "fit_res"], "funcdef": "def"}, "pyerrors.fits.covariance_matrix": {"fullname": "pyerrors.fits.covariance_matrix", "modulename": "pyerrors.fits", "qualname": "covariance_matrix", "type": "function", "doc": "<p>Returns the covariance matrix of y.</p>\n", "parameters": ["y"], "funcdef": "def"}, "pyerrors.fits.error_band": {"fullname": "pyerrors.fits.error_band", "modulename": "pyerrors.fits", "qualname": "error_band", "type": "function", "doc": "<p>Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta.</p>\n", "parameters": ["x", "func", "beta"], "funcdef": "def"}, "pyerrors.fits.ks_test": {"fullname": "pyerrors.fits.ks_test", "modulename": "pyerrors.fits", "qualname": "ks_test", "type": "function", "doc": "<p>Performs a Kolmogorov\u2013Smirnov test for the Q-values of all fit object.</p>\n\n<p>If no list is given all Obs in memory are used.</p>\n\n<p>Disclaimer: The determination of the individual Q-values as well as this function have not been tested yet.</p>\n", "parameters": ["obs"], "funcdef": "def"}, "pyerrors.fits.fit_general": {"fullname": "pyerrors.fits.fit_general", "modulename": "pyerrors.fits", "qualname": "fit_general", "type": "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<p>Plausibility of the results should be checked. To control the numerical differentiation\nthe kwargs of numdifftools.step_generators.MaxStepGenerator can be used.</p>\n\n<p>func has to be of the form</p>\n\n<p>def func(a, x):\n    y = a[0] + a[1] * x + a[2] * np.sinh(x)\n    return y</p>\n\n<p>y has to be a list of Obs, the dvalues of the Obs are used as yerror for the fit.\nx can 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.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>silent -- If true all output to the console is omitted (default False).\ninitial_guess -- can provide an initial guess for the input parameters. Relevant for non-linear fits\n                 with many parameters.</p>\n", "parameters": ["x", "y", "func", "silent", "kwargs"], "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.bdio.read_ADerrors": {"fullname": "pyerrors.input.bdio.read_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "read_ADerrors", "type": "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", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.write_ADerrors": {"fullname": "pyerrors.input.bdio.write_ADerrors", "modulename": "pyerrors.input.bdio", "qualname": "write_ADerrors", "type": "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", "parameters": ["obs_list", "file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_mesons": {"fullname": "pyerrors.input.bdio.read_mesons", "modulename": "pyerrors.input.bdio", "qualname": "read_mesons", "type": "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 -- 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<li><strong>stop -- stops reading at given configuration number (default None)</strong></li>\n<li><strong>alternative_ensemble_name -- Manually overwrite ensemble name</strong></li>\n</ul>\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.bdio.read_dSdm": {"fullname": "pyerrors.input.bdio.read_dSdm", "modulename": "pyerrors.input.bdio", "qualname": "read_dSdm", "type": "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 -- 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<li><strong>stop -- stops reading at given configuration number (default None)</strong></li>\n</ul>\n", "parameters": ["file_path", "bdio_path", "kwargs"], "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.hadrons.read_meson_hd5": {"fullname": "pyerrors.input.hadrons.read_meson_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_meson_hd5", "type": "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>tree</strong> (str):\nLabel of the upmost directory in the hdf5 file, default 'meson'\nfor outputs of the Meson module. Can be altered to read input\nfrom other modules with similar structures.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "parameters": ["path", "filestem", "ens_id", "meson", "tree", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix": {"fullname": "pyerrors.input.hadrons.Npr_matrix", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix", "type": "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>:  A :term:<code>generic &lt;generic type&gt;</code> version\nof ndarray.  </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=\"codehilite\"><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=\"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></div>\n\n<p>Second mode:</p>\n\n<div class=\"codehilite\"><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></div>\n"}, "pyerrors.input.hadrons.Npr_matrix.__init__": {"fullname": "pyerrors.input.hadrons.Npr_matrix.__init__", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.__init__", "type": "function", "doc": "<p></p>\n", "parameters": [], "funcdef": "def"}, "pyerrors.input.hadrons.Npr_matrix.g5H": {"fullname": "pyerrors.input.hadrons.Npr_matrix.g5H", "modulename": "pyerrors.input.hadrons", "qualname": "Npr_matrix.g5H", "type": "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", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.read_Bilinear_hd5": {"fullname": "pyerrors.input.hadrons.read_Bilinear_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Bilinear_hd5", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl"], "funcdef": "def"}, "pyerrors.input.hadrons.read_Fourquark_hd5": {"fullname": "pyerrors.input.hadrons.read_Fourquark_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_Fourquark_hd5", "type": "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", "parameters": ["path", "filestem", "ens_id", "idl", "vertices"], "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "qualname": "", "type": "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", "type": "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 moments, these objects can be\neither of: Obs, list, numpy.ndarray.\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", "parameters": ["ol", "description", "indent"], "funcdef": "def"}, "pyerrors.input.json.dump_to_json": {"fullname": "pyerrors.input.json.dump_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_to_json", "type": "function", "doc": "<p>Export a list 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>ol</strong> (list):\nList of objects that will be exported. At the moments, these objects can be\neither of: Obs, list, numpy.ndarray.\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", "parameters": ["ol", "fname", "description", "indent", "gz"], "funcdef": "def"}, "pyerrors.input.json.load_json": {"fullname": "pyerrors.input.json.load_json", "modulename": "pyerrors.input.json", "qualname": "load_json", "type": "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\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", "parameters": ["fname", "verbose", "gz", "full_output"], "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.misc.read_pbp": {"fullname": "pyerrors.input.misc.read_pbp", "modulename": "pyerrors.input.misc", "qualname": "read_pbp", "type": "function", "doc": "<p>Read pbp format from given folder structure. Returns a list of length nrw</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>r_start -- list which contains the first config to be read for each replicum\nr_stop -- list which contains the last config to be read for each replicum</p>\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.openQCD.read_rwms": {"fullname": "pyerrors.input.openQCD.read_rwms", "modulename": "pyerrors.input.openQCD", "qualname": "read_rwms", "type": "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>version</strong> (str):\nversion of openQCD, default 2.0</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>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n</ul>\n", "parameters": ["path", "prefix", "version", "names", "kwargs"], "funcdef": "def"}, "pyerrors.input.openQCD.extract_t0": {"fullname": "pyerrors.input.openQCD.extract_t0", "modulename": "pyerrors.input.openQCD", "qualname": "extract_t0", "type": "function", "doc": "<p>Extract t0 from given .ms.dat files. Returns t0 as Obs.</p>\n\n<p>It is assumed that all boundary effects have sufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - 0.3 is fitted with a linear function\nfrom which the exact root is extracted.\nOnly works with openQCD v 1.2.</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 when 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 effects 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 crossing to be included in the linear fit. (Default: 5)</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>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n</ul>\n", "parameters": ["path", "prefix", "dtr_read", "xmin", "spatial_extent", "fit_range", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.sfcf.read_sfcf": {"fullname": "pyerrors.input.sfcf.read_sfcf", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf", "type": "function", "doc": "<p>Read sfcf C format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>im -- if True, read imaginary instead of real part of the correlation function.</strong></li>\n<li><strong>single -- if True, read a boundary-to-boundary correlation function with a single value</strong></li>\n<li><strong>b2b -- if True, read a time-dependent boundary-to-boundary correlation function</strong></li>\n<li><strong>names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length</strong></li>\n</ul>\n", "parameters": ["path", "prefix", "name", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_sfcf_c": {"fullname": "pyerrors.input.sfcf.read_sfcf_c", "modulename": "pyerrors.input.sfcf", "qualname": "read_sfcf_c", "type": "function", "doc": "<p>Read sfcf c format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>quarks -- Label of the quarks used in the sfcf input file</strong></li>\n<li><strong>noffset -- Offset of the source (only relevant when wavefunctions are used)</strong></li>\n<li><strong>wf -- ID of wave function</strong></li>\n<li><strong>wf2 -- ID of the second wavefunction (only relevant for boundary-to-boundary correlation functions)</strong></li>\n<li><strong>im -- if True, read imaginary instead of real part of the correlation function.</strong></li>\n<li><strong>b2b -- if True, read a time-dependent boundary-to-boundary correlation function</strong></li>\n<li><strong>names -- Alternative labeling for replicas/ensembles. Has to have the appropriate length</strong></li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n</ul>\n", "parameters": ["path", "prefix", "name", "quarks", "noffset", "wf", "wf2", "kwargs"], "funcdef": "def"}, "pyerrors.input.sfcf.read_qtop": {"fullname": "pyerrors.input.sfcf.read_qtop", "modulename": "pyerrors.input.sfcf", "qualname": "read_qtop", "type": "function", "doc": "<p>Read qtop format from given folder structure.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>target -- specifies the topological sector to be reweighted to (default 0)</strong></li>\n<li><strong>full -- if true read the charge instead of the reweighting factor.</strong></li>\n</ul>\n", "parameters": ["path", "prefix", "kwargs"], "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.linalg.matmul": {"fullname": "pyerrors.linalg.matmul", "modulename": "pyerrors.linalg", "qualname": "matmul", "type": "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", "parameters": ["operands"], "funcdef": "def"}, "pyerrors.linalg.jack_matmul": {"fullname": "pyerrors.linalg.jack_matmul", "modulename": "pyerrors.linalg", "qualname": "jack_matmul", "type": "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", "parameters": ["operands"], "funcdef": "def"}, "pyerrors.linalg.einsum": {"fullname": "pyerrors.linalg.einsum", "modulename": "pyerrors.linalg", "qualname": "einsum", "type": "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", "parameters": ["subscripts", "operands"], "funcdef": "def"}, "pyerrors.linalg.inv": {"fullname": "pyerrors.linalg.inv", "modulename": "pyerrors.linalg", "qualname": "inv", "type": "function", "doc": "<p>Inverse of Obs or CObs valued matrices.</p>\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "<p>Cholesky decomposition of Obs or CObs valued matrices.</p>\n", "parameters": ["x"], "funcdef": "def"}, "pyerrors.linalg.scalar_mat_op": {"fullname": "pyerrors.linalg.scalar_mat_op", "modulename": "pyerrors.linalg", "qualname": "scalar_mat_op", "type": "function", "doc": "<p>Computes the matrix to scalar operation op to a given matrix of Obs.</p>\n", "parameters": ["op", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eigh": {"fullname": "pyerrors.linalg.eigh", "modulename": "pyerrors.linalg", "qualname": "eigh", "type": "function", "doc": "<p>Computes the eigenvalues and eigenvectors of a given hermitian matrix of Obs according to np.linalg.eigh.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.eig": {"fullname": "pyerrors.linalg.eig", "modulename": "pyerrors.linalg", "qualname": "eig", "type": "function", "doc": "<p>Computes the eigenvalues of a given matrix of Obs according to np.linalg.eig.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.pinv": {"fullname": "pyerrors.linalg.pinv", "modulename": "pyerrors.linalg", "qualname": "pinv", "type": "function", "doc": "<p>Computes the Moore-Penrose pseudoinverse of a matrix of Obs.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.svd": {"fullname": "pyerrors.linalg.svd", "modulename": "pyerrors.linalg", "qualname": "svd", "type": "function", "doc": "<p>Computes the singular value decomposition of a matrix of Obs.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.slogdet": {"fullname": "pyerrors.linalg.slogdet", "modulename": "pyerrors.linalg", "qualname": "slogdet", "type": "function", "doc": "<p>Computes the determinant of a matrix of Obs via np.linalg.slogdet.</p>\n", "parameters": ["obs", "kwargs"], "funcdef": "def"}, "pyerrors.linalg.grad_eig": {"fullname": "pyerrors.linalg.grad_eig", "modulename": "pyerrors.linalg", "qualname": "grad_eig", "type": "function", "doc": "<p>Gradient of a general square (complex valued) matrix</p>\n", "parameters": ["ans", "x"], "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.misc.dump_object": {"fullname": "pyerrors.misc.dump_object", "modulename": "pyerrors.misc", "qualname": "dump_object", "type": "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", "parameters": ["obj", "name", "kwargs"], "funcdef": "def"}, "pyerrors.misc.load_object": {"fullname": "pyerrors.misc.load_object", "modulename": "pyerrors.misc", "qualname": "load_object", "type": "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", "parameters": ["path"], "funcdef": "def"}, "pyerrors.misc.gen_correlated_data": {"fullname": "pyerrors.misc.gen_correlated_data", "modulename": "pyerrors.misc", "qualname": "gen_correlated_data", "type": "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", "parameters": ["means", "cov", "name", "tau", "samples"], "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.mpm.matrix_pencil_method": {"fullname": "pyerrors.mpm.matrix_pencil_method", "modulename": "pyerrors.mpm", "qualname": "matrix_pencil_method", "type": "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", "parameters": ["corrs", "k", "p", "kwargs"], "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.obs.Obs": {"fullname": "pyerrors.obs.Obs", "modulename": "pyerrors.obs", "qualname": "Obs", "type": "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__", "type": "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<li><strong>means</strong> (list, optional):\nlist of mean values for the case that the mean values were\nalready subtracted from the samples</li>\n</ul>\n", "parameters": ["self", "samples", "names", "idl", "means", "covobs", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.S_global": {"fullname": "pyerrors.obs.Obs.S_global", "modulename": "pyerrors.obs", "qualname": "Obs.S_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S_dict": {"fullname": "pyerrors.obs.Obs.S_dict", "modulename": "pyerrors.obs", "qualname": "Obs.S_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp_global": {"fullname": "pyerrors.obs.Obs.tau_exp_global", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp_dict": {"fullname": "pyerrors.obs.Obs.tau_exp_dict", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma_global": {"fullname": "pyerrors.obs.Obs.N_sigma_global", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_global", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma_dict": {"fullname": "pyerrors.obs.Obs.N_sigma_dict", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma_dict", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.filter_eps": {"fullname": "pyerrors.obs.Obs.filter_eps", "modulename": "pyerrors.obs", "qualname": "Obs.filter_eps", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.shape": {"fullname": "pyerrors.obs.Obs.shape", "modulename": "pyerrors.obs", "qualname": "Obs.shape", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.r_values": {"fullname": "pyerrors.obs.Obs.r_values", "modulename": "pyerrors.obs", "qualname": "Obs.r_values", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.deltas": {"fullname": "pyerrors.obs.Obs.deltas", "modulename": "pyerrors.obs", "qualname": "Obs.deltas", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.idl": {"fullname": "pyerrors.obs.Obs.idl", "modulename": "pyerrors.obs", "qualname": "Obs.idl", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.ddvalue": {"fullname": "pyerrors.obs.Obs.ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.ddvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.reweighted": {"fullname": "pyerrors.obs.Obs.reweighted", "modulename": "pyerrors.obs", "qualname": "Obs.reweighted", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tag": {"fullname": "pyerrors.obs.Obs.tag", "modulename": "pyerrors.obs", "qualname": "Obs.tag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.value": {"fullname": "pyerrors.obs.Obs.value", "modulename": "pyerrors.obs", "qualname": "Obs.value", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.dvalue": {"fullname": "pyerrors.obs.Obs.dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.dvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_names": {"fullname": "pyerrors.obs.Obs.e_names", "modulename": "pyerrors.obs", "qualname": "Obs.e_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.cov_names": {"fullname": "pyerrors.obs.Obs.cov_names", "modulename": "pyerrors.obs", "qualname": "Obs.cov_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.mc_names": {"fullname": "pyerrors.obs.Obs.mc_names", "modulename": "pyerrors.obs", "qualname": "Obs.mc_names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_content": {"fullname": "pyerrors.obs.Obs.e_content", "modulename": "pyerrors.obs", "qualname": "Obs.e_content", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.gamma_method": {"fullname": "pyerrors.obs.Obs.gamma_method", "modulename": "pyerrors.obs", "qualname": "Obs.gamma_method", "type": "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", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.details": {"fullname": "pyerrors.obs.Obs.details", "modulename": "pyerrors.obs", "qualname": "Obs.details", "type": "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", "parameters": ["self", "ens_content"], "funcdef": "def"}, "pyerrors.obs.Obs.print": {"fullname": "pyerrors.obs.Obs.print", "modulename": "pyerrors.obs", "qualname": "Obs.print", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "level"], "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", "type": "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", "parameters": ["self", "sigma"], "funcdef": "def"}, "pyerrors.obs.Obs.is_zero": {"fullname": "pyerrors.obs.Obs.is_zero", "modulename": "pyerrors.obs", "qualname": "Obs.is_zero", "type": "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>rtol</strong> (float):\nRelative tolerance (for details see numpy documentation).</li>\n<li><strong>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "parameters": ["self", "rtol", "atol"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_tauint": {"fullname": "pyerrors.obs.Obs.plot_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.plot_tauint", "type": "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", "parameters": ["self", "save"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rho": {"fullname": "pyerrors.obs.Obs.plot_rho", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rho", "type": "function", "doc": "<p>Plot normalized autocorrelation function time for each ensemble.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_rep_dist": {"fullname": "pyerrors.obs.Obs.plot_rep_dist", "modulename": "pyerrors.obs", "qualname": "Obs.plot_rep_dist", "type": "function", "doc": "<p>Plot replica distribution for each ensemble with more than one replicum.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_history": {"fullname": "pyerrors.obs.Obs.plot_history", "modulename": "pyerrors.obs", "qualname": "Obs.plot_history", "type": "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", "parameters": ["self", "expand"], "funcdef": "def"}, "pyerrors.obs.Obs.plot_piechart": {"fullname": "pyerrors.obs.Obs.plot_piechart", "modulename": "pyerrors.obs", "qualname": "Obs.plot_piechart", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.dump": {"fullname": "pyerrors.obs.Obs.dump", "modulename": "pyerrors.obs", "qualname": "Obs.dump", "type": "function", "doc": "<p>Dump the Obs to a pickle file 'name'.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>name</strong> (str):\nname of the file to be saved.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "parameters": ["self", "name", "kwargs"], "funcdef": "def"}, "pyerrors.obs.Obs.export_jackknife": {"fullname": "pyerrors.obs.Obs.export_jackknife", "modulename": "pyerrors.obs", "qualname": "Obs.export_jackknife", "type": "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", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.sinc": {"fullname": "pyerrors.obs.Obs.sinc", "modulename": "pyerrors.obs", "qualname": "Obs.sinc", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.Obs.N": {"fullname": "pyerrors.obs.Obs.N", "modulename": "pyerrors.obs", "qualname": "Obs.N", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.N_sigma": {"fullname": "pyerrors.obs.Obs.N_sigma", "modulename": "pyerrors.obs", "qualname": "Obs.N_sigma", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.S": {"fullname": "pyerrors.obs.Obs.S", "modulename": "pyerrors.obs", "qualname": "Obs.S", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.covobs": {"fullname": "pyerrors.obs.Obs.covobs", "modulename": "pyerrors.obs", "qualname": "Obs.covobs", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_ddvalue": {"fullname": "pyerrors.obs.Obs.e_ddvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_ddvalue", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_drho": {"fullname": "pyerrors.obs.Obs.e_drho", "modulename": "pyerrors.obs", "qualname": "Obs.e_drho", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dtauint": {"fullname": "pyerrors.obs.Obs.e_dtauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_dtauint", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_dvalue": {"fullname": "pyerrors.obs.Obs.e_dvalue", "modulename": "pyerrors.obs", "qualname": "Obs.e_dvalue", "type": "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", "type": "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", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_rho": {"fullname": "pyerrors.obs.Obs.e_rho", "modulename": "pyerrors.obs", "qualname": "Obs.e_rho", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_tauint": {"fullname": "pyerrors.obs.Obs.e_tauint", "modulename": "pyerrors.obs", "qualname": "Obs.e_tauint", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.e_windowsize": {"fullname": "pyerrors.obs.Obs.e_windowsize", "modulename": "pyerrors.obs", "qualname": "Obs.e_windowsize", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.is_merged": {"fullname": "pyerrors.obs.Obs.is_merged", "modulename": "pyerrors.obs", "qualname": "Obs.is_merged", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.names": {"fullname": "pyerrors.obs.Obs.names", "modulename": "pyerrors.obs", "qualname": "Obs.names", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.Obs.tau_exp": {"fullname": "pyerrors.obs.Obs.tau_exp", "modulename": "pyerrors.obs", "qualname": "Obs.tau_exp", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs": {"fullname": "pyerrors.obs.CObs", "modulename": "pyerrors.obs", "qualname": "CObs", "type": "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__", "type": "function", "doc": "<p></p>\n", "parameters": ["self", "real", "imag"], "funcdef": "def"}, "pyerrors.obs.CObs.tag": {"fullname": "pyerrors.obs.CObs.tag", "modulename": "pyerrors.obs", "qualname": "CObs.tag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.real": {"fullname": "pyerrors.obs.CObs.real", "modulename": "pyerrors.obs", "qualname": "CObs.real", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.imag": {"fullname": "pyerrors.obs.CObs.imag", "modulename": "pyerrors.obs", "qualname": "CObs.imag", "type": "variable", "doc": "<p></p>\n"}, "pyerrors.obs.CObs.gamma_method": {"fullname": "pyerrors.obs.CObs.gamma_method", "modulename": "pyerrors.obs", "qualname": "CObs.gamma_method", "type": "function", "doc": "<p>Executes the gamma_method for the real and the imaginary part.</p>\n", "parameters": ["self", "kwargs"], "funcdef": "def"}, "pyerrors.obs.CObs.is_zero": {"fullname": "pyerrors.obs.CObs.is_zero", "modulename": "pyerrors.obs", "qualname": "CObs.is_zero", "type": "function", "doc": "<p>Checks whether both real and imaginary part are zero within machine precision.</p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "<p></p>\n", "parameters": ["self"], "funcdef": "def"}, "pyerrors.obs.derived_observable": {"fullname": "pyerrors.obs.derived_observable", "modulename": "pyerrors.obs", "qualname": "derived_observable", "type": "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", "parameters": ["func", "data", "array_mode", "kwargs"], "funcdef": "def"}, "pyerrors.obs.reweight": {"fullname": "pyerrors.obs.reweight", "modulename": "pyerrors.obs", "qualname": "reweight", "type": "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.</li>\n</ul>\n", "parameters": ["weight", "obs", "kwargs"], "funcdef": "def"}, "pyerrors.obs.correlate": {"fullname": "pyerrors.obs.correlate", "modulename": "pyerrors.obs", "qualname": "correlate", "type": "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<li><strong>Keep in mind to only correlate primary observables which have not been reweighted</strong></li>\n<li><strong>yet. The reweighting has to be applied after correlating the observables.</strong></li>\n<li><strong>Currently only works if ensembles are identical. This is not really necessary.</strong></li>\n</ul>\n", "parameters": ["obs_a", "obs_b"], "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "<p>Calculates the covariance of two observables.</p>\n\n<p>covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs1</strong> (Obs):\nFirst Obs</li>\n<li><strong>obs2</strong> (Obs):\nSecond Obs</li>\n<li><strong>correlation</strong> (bool):\nif true the correlation instead of the covariance is\nreturned (default False)</li>\n</ul>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance2": {"fullname": "pyerrors.obs.covariance2", "modulename": "pyerrors.obs", "qualname": "covariance2", "type": "function", "doc": "<p>Alternative implementation of the covariance of two observables.</p>\n\n<p>covariance(obs, obs) is equal to obs.dvalue ** 2\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>correlation -- if true the correlation instead of the covariance is\n               returned (default False)</p>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.covariance3": {"fullname": "pyerrors.obs.covariance3", "modulename": "pyerrors.obs", "qualname": "covariance3", "type": "function", "doc": "<p>Another alternative implementation of the covariance of two observables.</p>\n\n<p>covariance2(obs, obs) is equal to obs.dvalue ** 2\nCurrently only works if ensembles are identical.\nThe gamma method has to be applied first to both observables.</p>\n\n<p>If abs(covariance2(obs1, obs2)) &gt; obs1.dvalue * obs2.dvalue, the covariance\nis constrained to the maximum value in order to make sure that covariance\nmatrices are positive semidefinite.</p>\n\n<h6 id=\"keyword-arguments\">Keyword arguments</h6>\n\n<p>correlation -- if true the correlation instead of the covariance is\n               returned (default False)\nplot -- if true, the integrated autocorrelation time for each ensemble is\n        plotted.</p>\n", "parameters": ["obs1", "obs2", "correlation", "kwargs"], "funcdef": "def"}, "pyerrors.obs.pseudo_Obs": {"fullname": "pyerrors.obs.pseudo_Obs", "modulename": "pyerrors.obs", "qualname": "pseudo_Obs", "type": "function", "doc": "<p>Generate a pseudo Obs with given value, dvalue and name</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", "parameters": ["value", "dvalue", "name", "samples"], "funcdef": "def"}, "pyerrors.obs.import_jackknife": {"fullname": "pyerrors.obs.import_jackknife", "modulename": "pyerrors.obs", "qualname": "import_jackknife", "type": "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", "parameters": ["jacks", "name", "idl"], "funcdef": "def"}, "pyerrors.obs.merge_obs": {"fullname": "pyerrors.obs.merge_obs", "modulename": "pyerrors.obs", "qualname": "merge_obs", "type": "function", "doc": "<p>Combine all observables in list_of_obs into one new observable</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<li><strong>It is not possible to combine obs which are based on the same replicum</strong></li>\n</ul>\n", "parameters": ["list_of_obs"], "funcdef": "def"}, "pyerrors.obs.cov_Obs": {"fullname": "pyerrors.obs.cov_Obs", "modulename": "pyerrors.obs", "qualname": "cov_Obs", "type": "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", "parameters": ["means", "cov", "name", "grad"], "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "qualname": "", "type": "module", "doc": "<p></p>\n"}, "pyerrors.roots.find_root": {"fullname": "pyerrors.roots.find_root", "modulename": "pyerrors.roots", "qualname": "find_root", "type": "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><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:\n<code>python\nimport autograd.numpy as anp\ndef root_func(x, d):\n   return anp.exp(-x ** 2) - d\n</code></li>\n<li><strong>guess</strong> (float):\nInitial guess for the minimization.</li>\n</ul>\n\n<h6 id=\"returns\">Returns</h6>\n\n<ul>\n<li><strong>Obs</strong>: <code>Obs</code> valued root of the function.</li>\n</ul>\n", "parameters": ["d", "func", "guess", "kwargs"], "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "qualname": "", "type": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "doc": 1044}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "doc": 0}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "doc": 51}, "pyerrors.correlators.Corr.__init__": {"qualname": 2, "fullname": 4, "doc": 0}, "pyerrors.correlators.Corr.reweighted": {"qualname": 2, "fullname": 4, "doc": 0}, 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