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@ -136,8 +136,49 @@ It is based on the <strong>gamma method</strong> <a href="https://arxiv.org/abs/
<h2 id="multiple-ensemblesreplica">Multiple ensembles/replica</h2>
<p>Error propagation for multiple ensemblesi (Markov chains with different simulation parameters) are automatically handled.</p>
<p><strong>Example:</strong></p>
<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>
<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">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">samples1</span><span class="p">],</span> <span class="p">[</span><span class="s1">&#39;ensemble2&#39;</span><span class="p">])</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>
<span class="n">my_sum</span><span class="o">.</span><span class="n">details</span><span class="p">()</span>
<span class="o">&gt;</span> <span class="n">Result</span> <span class="mf">2.00596631e+00</span> <span class="o">+/-</span> <span class="mf">0.00000000e+00</span> <span class="o">+/-</span> <span class="mf">0.00000000e+00</span> <span class="p">(</span><span class="mf">0.000</span><span class="o">%</span><span class="p">)</span>
<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>
<span class="o">&gt;</span> <span class="n">ensemble1</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;ensemble1&#39;</span><span class="p">]</span>
<span class="o">&gt;</span> <span class="n">ensemble2</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;ensemble2&#39;</span><span class="p">]</span>
</code></pre></div>
<p><code><a href="">pyerrors</a></code> identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar <code>|</code> in the name of the dataset.</p>
<p><strong>Example:</strong></p>
<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>
<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>
<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">samples1</span><span class="p">],</span> <span class="p">[</span><span class="s1">&#39;ensemble1|r02&#39;</span><span class="p">])</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>
<span class="n">my_sum</span><span class="o">.</span><span class="n">details</span><span class="p">()</span>
<span class="o">&gt;</span> <span class="n">Result</span> <span class="mf">2.00596631e+00</span> <span class="o">+/-</span> <span class="mf">0.00000000e+00</span> <span class="o">+/-</span> <span class="mf">0.00000000e+00</span> <span class="p">(</span><span class="mf">0.000</span><span class="o">%</span><span class="p">)</span>
<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>
<span class="o">&gt;</span> <span class="n">ensemble1</span><span class="p">:</span> <span class="p">[</span><span class="s1">&#39;ensemble1|r01&#39;</span><span class="p">,</span> <span class="s1">&#39;ensemble1|r02&#39;</span><span class="p">]</span>
</code></pre></div>
<h2 id="irregular-monte-carlo-chains">Irregular Monte Carlo chains</h2>
<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>
<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>
<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">samples1</span><span class="p">],</span> <span class="p">[</span><span class="s1">&#39;ensemble1|r02&#39;</span><span class="p">])</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>
</code></pre></div>
<h1 id="error-propagation">Error propagation</h1>
<p>Automatic differentiation, cite Alberto,</p>
@ -219,8 +260,49 @@ It is based on the <strong>gamma method</strong> <a href="https://arxiv.org/abs/
<span class="sd">## Multiple ensembles/replica</span>
<span class="sd">Error propagation for multiple ensemblesi (Markov chains with different simulation parameters) are automatically handled.</span>
<span class="sd">**Example:**</span>
<span class="sd">```python</span>
<span class="sd">import pyerrors as pe</span>
<span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1&#39;])</span>
<span class="sd">obs2 = pe.Obs([samples1], [&#39;ensemble2&#39;])</span>
<span class="sd">my_sum = obs1 + obs2</span>
<span class="sd">my_sum.details()</span>
<span class="sd">&gt; Result 2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)</span>
<span class="sd">&gt; 1500 samples in 2 ensembles:</span>
<span class="sd">&gt; ensemble1: [&#39;ensemble1&#39;]</span>
<span class="sd">&gt; ensemble2: [&#39;ensemble2&#39;]</span>
<span class="sd">```</span>
<span class="sd">`pyerrors` identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar `|` in the name of the dataset.</span>
<span class="sd">**Example:**</span>
<span class="sd">```python</span>
<span class="sd">import pyerrors as pe</span>
<span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1|r01&#39;])</span>
<span class="sd">obs2 = pe.Obs([samples1], [&#39;ensemble1|r02&#39;])</span>
<span class="sd">my_sum = obs1 + obs2</span>
<span class="sd">my_sum.details()</span>
<span class="sd">&gt; Result 2.00596631e+00 +/- 0.00000000e+00 +/- 0.00000000e+00 (0.000%)</span>
<span class="sd">&gt; 1500 samples in 1 ensemble:</span>
<span class="sd">&gt; ensemble1: [&#39;ensemble1|r01&#39;, &#39;ensemble1|r02&#39;]</span>
<span class="sd">```</span>
<span class="sd">## Irregular Monte Carlo chains</span>
<span class="sd">```python</span>
<span class="sd">import pyerrors as pe</span>
<span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1|r01&#39;])</span>
<span class="sd">obs2 = pe.Obs([samples1], [&#39;ensemble1|r02&#39;])</span>
<span class="sd">my_sum = obs1 + obs2</span>
<span class="sd">```</span>
<span class="sd"># Error propagation</span>
<span class="sd">Automatic differentiation, cite Alberto,</span>