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<ul>
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<li><a href="#exponential-tails">Exponential tails</a></li>
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</ul></li>
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<li><a href="#multiple-ensemblesreplica">Multiple ensembles/replica</a></li>
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<li><a href="#multiple-ensemblesreplica">Multiple ensembles/replica</a>
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<ul>
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<li><a href="#error-estimation-for-multiple-ensembles">Error estimation for multiple ensembles</a></li>
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</ul></li>
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<li><a href="#irregular-monte-carlo-chains">Irregular Monte Carlo chains</a></li>
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</ul></li>
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<li><a href="#correlators">Correlators</a></li>
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@ -164,10 +167,42 @@ as introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0
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<p>The error propagation is based on the gamma method introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0306017</a>.</p>
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<p>For the full API see <code><a href="pyerrors/obs.html#Obs.gamma_method">pyerrors.obs.Obs.gamma_method</a></code></p>
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<p>After having arrived at</p>
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<p>Example:</p>
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<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>
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<span class="n">my_sum</span><span class="o">.</span><span class="n">details</span><span class="p">()</span>
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</code></pre></div>
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<p>The standard value for the automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the <code>gamma_method</code> as parameter.</p>
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<p>Example:</p>
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<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>
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<span class="n">my_sum</span><span class="o">.</span><span class="n">details</span><span class="p">()</span>
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</code></pre></div>
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<p>The integrated autocorrelation time $\tau_\mathrm{int}$ and the autocorrelation function $\rho(W)$ can be monitored via the methods ´<a href="pyerrors/obs.html#Obs.plot_tauint">pyerrors.obs.Obs.plot_tauint</a><code>and ´<a href="pyerrors/obs.html#Obs.plot_tauint">pyerrors.obs.Obs.plot_tauint</a></code>.</p>
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<p>Example:</p>
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<div class="codehilite"><pre><span></span><code><span class="n">my_sum</span><span class="o">.</span><span class="n">plot_tauint</span><span class="p">()</span>
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<span class="n">my_sum</span><span class="o">.</span><span class="n">plot_rho</span><span class="p">()</span>
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</code></pre></div>
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<h3 id="exponential-tails">Exponential tails</h3>
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<p>Slow modes in the Monte Carlo history can be accounted for by attaching and exponntial 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>
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<p>Example:</p>
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<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">4.2</span><span class="p">)</span>
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<span class="n">my_sum</span><span class="o">.</span><span class="n">details</span><span class="p">()</span>
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</code></pre></div>
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<p>For the full API see <code><a href="pyerrors/obs.html#Obs.gamma_method">pyerrors.obs.Obs.gamma_method</a></code></p>
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<h2 id="multiple-ensemblesreplica">Multiple ensembles/replica</h2>
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<p>Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handeled automatically. Ensembles are uniquely identified by their <code>name</code>.</p>
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@ -201,6 +236,17 @@ as introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0
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<span class="o">></span> <span class="err">·</span> <span class="n">Replicum</span> <span class="s1">'r02'</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>
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</code></pre></div>
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<h3 id="error-estimation-for-multiple-ensembles">Error estimation for multiple ensembles</h3>
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<p>In order to keep track of different error analyis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.</p>
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<p>Example:</p>
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<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">'ensemble1'</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.5</span>
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<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">'ensemble2'</span><span class="p">]</span> <span class="o">=</span> <span class="mf">8.0</span>
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<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">'ensemble3'</span><span class="p">]</span> <span class="o">=</span> <span class="mf">2.0</span>
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</code></pre></div>
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<h2 id="irregular-monte-carlo-chains">Irregular Monte Carlo chains</h2>
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<p>Irregular Monte Carlo chains can be initilized with the parameter <code>idl</code>.</p>
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@ -309,9 +355,41 @@ Make sure to check the with e.g. <code><a href="pyerrors/obs.html#Obs.plot_rho">
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<span class="sd">The error propagation is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
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<span class="sd">After having arrived at</span>
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<span class="sd">Example:</span>
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<span class="sd">```python</span>
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<span class="sd">my_sum.gamma_method()</span>
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<span class="sd">my_sum.details()</span>
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<span class="sd">```</span>
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<span class="sd">The standard value for the automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter.</span>
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<span class="sd">Example:</span>
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<span class="sd">```python</span>
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<span class="sd">my_sum.gamma_method(S=3.0)</span>
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<span class="sd">my_sum.details()</span>
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<span class="sd">```</span>
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<span class="sd">The integrated autocorrelation time $\tau_\mathrm{int}$ and the autocorrelation function $\rho(W)$ can be monitored via the methods ´pyerrors.obs.Obs.plot_tauint` and ´pyerrors.obs.Obs.plot_tauint`.</span>
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<span class="sd">Example:</span>
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<span class="sd">```python</span>
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<span class="sd">my_sum.plot_tauint()</span>
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<span class="sd">my_sum.plot_rho()</span>
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<span class="sd">```</span>
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<span class="sd">### Exponential tails</span>
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<span class="sd">Slow modes in the Monte Carlo history can be accounted for by attaching and exponntial tail to the autocorrelation function $\rho$ as suggested in [arXiv:1009.5228](https://arxiv.org/abs/1009.5228). The longest autocorrelation time in the history, $\tau_\mathrm{exp}$, can be passed to the `gamma_method` as parameter. In this case the automatic windowing procedure is vacated and the parameter $S$ does not affect the error estimate.</span>
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<span class="sd">Example:</span>
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<span class="sd">```python</span>
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<span class="sd">my_sum.gamma_method(tau_exp=4.2)</span>
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<span class="sd">my_sum.details()</span>
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<span class="sd">```</span>
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<span class="sd">For the full API see `pyerrors.obs.Obs.gamma_method`</span>
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<span class="sd">### Exponential tails</span>
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<span class="sd">## Multiple ensembles/replica</span>
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@ -345,6 +423,18 @@ Make sure to check the with e.g. <code><a href="pyerrors/obs.html#Obs.plot_rho">
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<span class="sd">> · Replicum 'r01' : 1000 configurations (from 1 to 1000)</span>
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<span class="sd">> · Replicum 'r02' : 500 configurations (from 1 to 500)</span>
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<span class="sd">```</span>
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<span class="sd">### Error estimation for multiple ensembles</span>
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<span class="sd">In order to keep track of different error analyis parameters for different ensembles one can make use of global dictionaries as detailed in the following example.</span>
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<span class="sd">Example:</span>
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<span class="sd">```python</span>
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<span class="sd">pe.Obs.S_dict['ensemble1'] = 2.5</span>
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<span class="sd">pe.Obs.tau_exp_dict['ensemble2'] = 8.0</span>
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<span class="sd">pe.Obs.tau_exp_dict['ensemble3'] = 2.0</span>
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<span class="sd">```</span>
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<span class="sd">## Irregular Monte Carlo chains</span>
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<span class="sd">Irregular Monte Carlo chains can be initilized with the parameter `idl`.</span>
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