From 7b6f7f64e6dffc77ec7a6c8886542087d729e921 Mon Sep 17 00:00:00 2001
From: fjosw <fjosw@users.noreply.github.com>
Date: Fri, 30 Sep 2022 15:27:14 +0000
Subject: [PATCH] Documentation updated

---
 docs/pyerrors.html | 906 +++++++++++++++++++++++----------------------
 docs/search.js     |   2 +-
 2 files changed, 455 insertions(+), 453 deletions(-)

diff --git a/docs/pyerrors.html b/docs/pyerrors.html
index 96c6644f..e6004137 100644
--- a/docs/pyerrors.html
+++ b/docs/pyerrors.html
@@ -111,7 +111,8 @@ It is based on the gamma method <a href="https://arxiv.org/abs/hep-lat/0306017">
 
 <p>More detailed examples can found in the <a href="https://github.com/fjosw/pyerrors/tree/develop/examples">GitHub repository</a> <a href="https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples"><img src="https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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" alt="badge" /></a>.</p>
 
-<p>If you use <code><a href="">pyerrors</a></code> for research that leads to a publication please consider citing:</p>
+<p>If you use <code><a href="">pyerrors</a></code> for research that leads to a publication please consider citing:
+Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, <em>pyerrors: a python framework for error analysis of Monte Carlo data</em>. [arXiv:2209.14371 [hep-lat]].</p>
 
 <ul>
 <li>Ulli Wolff, <em>Monte Carlo errors with less errors</em>. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</li>
@@ -642,458 +643,459 @@ The following entries are optional:</li>
 </span><span id="L-11"><a href="#L-11"><span class="linenos"> 11</span></a><span class="sd">More detailed examples can found in the [GitHub repository](https://github.com/fjosw/pyerrors/tree/develop/examples) [![badge](https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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)](https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples).</span>
 </span><span id="L-12"><a href="#L-12"><span class="linenos"> 12</span></a>
 </span><span id="L-13"><a href="#L-13"><span class="linenos"> 13</span></a><span class="sd">If you use `pyerrors` for research that leads to a publication please consider citing:</span>
-</span><span id="L-14"><a href="#L-14"><span class="linenos"> 14</span></a><span class="sd">- Ulli Wolff, *Monte Carlo errors with less errors*. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</span>
-</span><span id="L-15"><a href="#L-15"><span class="linenos"> 15</span></a><span class="sd">- Alberto Ramos, *Automatic differentiation for error analysis of Monte Carlo data*. Comput.Phys.Commun. 238 (2019) 19-35.</span>
-</span><span id="L-16"><a href="#L-16"><span class="linenos"> 16</span></a>
-</span><span id="L-17"><a href="#L-17"><span class="linenos"> 17</span></a><span class="sd">and</span>
-</span><span id="L-18"><a href="#L-18"><span class="linenos"> 18</span></a>
-</span><span id="L-19"><a href="#L-19"><span class="linenos"> 19</span></a><span class="sd">- Stefan Schaefer, Rainer Sommer, Francesco Virotta, *Critical slowing down and error analysis in lattice QCD simulations*. Nucl.Phys.B 845 (2011) 93-119.</span>
-</span><span id="L-20"><a href="#L-20"><span class="linenos"> 20</span></a>
-</span><span id="L-21"><a href="#L-21"><span class="linenos"> 21</span></a><span class="sd">where applicable.</span>
-</span><span id="L-22"><a href="#L-22"><span class="linenos"> 22</span></a>
-</span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a><span class="sd">There exist similar publicly available implementations of gamma method error analysis suites in [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors), [Julia](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl) and [Python](https://github.com/mbruno46/pyobs).</span>
-</span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a>
-</span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a><span class="sd">## Basic example</span>
-</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a>
-</span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a><span class="sd">```python</span>
-</span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a><span class="sd">import numpy as np</span>
-</span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a><span class="sd">import pyerrors as pe</span>
-</span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a>
-</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a><span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;]) # Initialize an Obs object</span>
-</span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a><span class="sd">my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object</span>
-</span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a><span class="sd">my_new_obs.gamma_method()                     # Estimate the statistical error</span>
-</span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a><span class="sd">print(my_new_obs)                             # Print the result to stdout</span>
-</span><span id="L-35"><a href="#L-35"><span class="linenos"> 35</span></a><span class="sd">&gt; 0.31498(72)</span>
-</span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a><span class="sd">```</span>
-</span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a>
-</span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a><span class="sd"># The `Obs` class</span>
-</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a>
-</span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a><span class="sd">`pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.</span>
-</span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a><span class="sd">An `Obs` object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.</span>
-</span><span id="L-42"><a href="#L-42"><span class="linenos"> 42</span></a><span class="sd">The samples can either be provided as python list or as numpy array.</span>
-</span><span id="L-43"><a href="#L-43"><span class="linenos"> 43</span></a><span class="sd">The 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.</span>
-</span><span id="L-44"><a href="#L-44"><span class="linenos"> 44</span></a>
-</span><span id="L-45"><a href="#L-45"><span class="linenos"> 45</span></a><span class="sd">```python</span>
-</span><span id="L-46"><a href="#L-46"><span class="linenos"> 46</span></a><span class="sd">import pyerrors as pe</span>
-</span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a>
-</span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a><span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;])</span>
-</span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a><span class="sd">```</span>
-</span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a>
-</span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a><span class="sd">## Error propagation</span>
-</span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a>
-</span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a><span class="sd">When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion</span>
-</span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a><span class="sd">$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$</span>
-</span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a><span class="sd">as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
-</span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a><span class="sd">The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span>
-</span><span id="L-57"><a href="#L-57"><span class="linenos"> 57</span></a>
-</span><span id="L-58"><a href="#L-58"><span class="linenos"> 58</span></a><span class="sd">The `Obs` class is designed such that mathematical numpy functions can be used on `Obs` just as for regular floats.</span>
-</span><span id="L-59"><a href="#L-59"><span class="linenos"> 59</span></a>
-</span><span id="L-60"><a href="#L-60"><span class="linenos"> 60</span></a><span class="sd">```python</span>
-</span><span id="L-61"><a href="#L-61"><span class="linenos"> 61</span></a><span class="sd">import numpy as np</span>
-</span><span id="L-62"><a href="#L-62"><span class="linenos"> 62</span></a><span class="sd">import pyerrors as pe</span>
-</span><span id="L-63"><a href="#L-63"><span class="linenos"> 63</span></a>
-</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a><span class="sd">my_obs1 = pe.Obs([samples1], [&#39;ensemble_name&#39;])</span>
-</span><span id="L-65"><a href="#L-65"><span class="linenos"> 65</span></a><span class="sd">my_obs2 = pe.Obs([samples2], [&#39;ensemble_name&#39;])</span>
-</span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a>
-</span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a><span class="sd">my_sum = my_obs1 + my_obs2</span>
-</span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a>
-</span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a><span class="sd">my_m_eff = np.log(my_obs1 / my_obs2)</span>
-</span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a>
-</span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a><span class="sd">iamzero = my_m_eff - my_m_eff</span>
-</span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a><span class="sd"># Check that value and fluctuations are zero within machine precision</span>
-</span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a><span class="sd">print(iamzero == 0.0)</span>
-</span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a><span class="sd">&gt; True</span>
-</span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a><span class="sd">```</span>
-</span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a>
-</span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a><span class="sd">## Error estimation</span>
-</span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a>
-</span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a><span class="sd">The error estimation within `pyerrors` is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
-</span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a><span class="sd">After having arrived at the derived quantity of interest the `gamma_method` can be called as detailed in the following example.</span>
-</span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a>
-</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a><span class="sd">```python</span>
-</span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a><span class="sd">my_sum.gamma_method()</span>
-</span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd">print(my_sum)</span>
-</span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="sd">&gt; 1.70(57)</span>
-</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a><span class="sd">my_sum.details()</span>
-</span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)</span>
-</span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a><span class="sd">&gt;  t_int	 2.71422900e+00 +/- 6.40320983e-01 S = 2.00</span>
-</span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
-</span><span id="L-90"><a href="#L-90"><span class="linenos"> 90</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
-</span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a>
-</span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a><span class="sd">```</span>
-</span><span id="L-93"><a href="#L-93"><span class="linenos"> 93</span></a>
-</span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a><span class="sd">We use the following definition of the integrated autocorrelation time established in [Madras &amp; Sokal 1988](https://link.springer.com/article/10.1007/BF01022990)</span>
-</span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a><span class="sd">$$\tau_\mathrm{int}=\frac{1}{2}+\sum_{t=1}^{W}\rho(t)\geq \frac{1}{2}\,.$$</span>
-</span><span id="L-96"><a href="#L-96"><span class="linenos"> 96</span></a><span class="sd">The window $W$ is determined via the automatic windowing procedure described in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
-</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a><span class="sd">The standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter.</span>
-</span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a>
-</span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a><span class="sd">```python</span>
-</span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a><span class="sd">my_sum.gamma_method(S=3.0)</span>
-</span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a><span class="sd">my_sum.details()</span>
-</span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)</span>
-</span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a><span class="sd">&gt;  t_int	 3.29909703e+00 +/- 9.77310102e-01 S = 3.00</span>
-</span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
-</span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
-</span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a>
-</span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a><span class="sd">```</span>
-</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a>
-</span><span id="L-109"><a href="#L-109"><span class="linenos">109</span></a><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_rho`.</span>
-</span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a>
-</span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a><span class="sd">If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.</span>
-</span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a><span class="sd">In this case the error estimate is identical to the sample standard error.</span>
-</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a>
-</span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a><span class="sd">### Exponential tails</span>
-</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a>
-</span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a><span class="sd">Slow modes in the Monte Carlo history can be accounted for by attaching an exponential 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>
-</span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a>
-</span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a><span class="sd">```python</span>
-</span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a><span class="sd">my_sum.gamma_method(tau_exp=7.2)</span>
-</span><span id="L-120"><a href="#L-120"><span class="linenos">120</span></a><span class="sd">my_sum.details()</span>
-</span><span id="L-121"><a href="#L-121"><span class="linenos">121</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)</span>
-</span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a><span class="sd">&gt;  t_int	 3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1</span>
-</span><span id="L-123"><a href="#L-123"><span class="linenos">123</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
-</span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
-</span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a><span class="sd">```</span>
-</span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a>
-</span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a><span class="sd">For the full API see `pyerrors.obs.Obs.gamma_method`.</span>
-</span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a>
-</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a><span class="sd">## Multiple ensembles/replica</span>
-</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a>
-</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a><span class="sd">Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their `name`.</span>
-</span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a>
-</span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a><span class="sd">```python</span>
-</span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1&#39;])</span>
-</span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble2&#39;])</span>
-</span><span id="L-136"><a href="#L-136"><span class="linenos">136</span></a>
-</span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a><span class="sd">my_sum = obs1 + obs2</span>
-</span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a><span class="sd">my_sum.details()</span>
-</span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a><span class="sd">&gt; Result   2.00697958e+00</span>
-</span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a><span class="sd">&gt; 1500 samples in 2 ensembles:</span>
-</span><span id="L-141"><a href="#L-141"><span class="linenos">141</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 1000 configurations (from 1 to 1000)</span>
-</span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble2&#39; : 500 configurations (from 1 to 500)</span>
-</span><span id="L-143"><a href="#L-143"><span class="linenos">143</span></a><span class="sd">```</span>
-</span><span id="L-144"><a href="#L-144"><span class="linenos">144</span></a>
-</span><span id="L-145"><a href="#L-145"><span class="linenos">145</span></a><span class="sd">`pyerrors` identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar `|` in the name of the data set.</span>
-</span><span id="L-146"><a href="#L-146"><span class="linenos">146</span></a>
-</span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a><span class="sd">```python</span>
-</span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1|r01&#39;])</span>
-</span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble1|r02&#39;])</span>
-</span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a>
-</span><span id="L-151"><a href="#L-151"><span class="linenos">151</span></a><span class="sd">&gt; my_sum = obs1 + obs2</span>
-</span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a><span class="sd">&gt; my_sum.details()</span>
-</span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a><span class="sd">&gt; Result   2.00697958e+00</span>
-</span><span id="L-154"><a href="#L-154"><span class="linenos">154</span></a><span class="sd">&gt; 1500 samples in 1 ensemble:</span>
-</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39;</span>
-</span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a><span class="sd">&gt;     · Replicum &#39;r01&#39; : 1000 configurations (from 1 to 1000)</span>
-</span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="sd">&gt;     · Replicum &#39;r02&#39; : 500 configurations (from 1 to 500)</span>
-</span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="sd">```</span>
-</span><span id="L-159"><a href="#L-159"><span class="linenos">159</span></a>
-</span><span id="L-160"><a href="#L-160"><span class="linenos">160</span></a><span class="sd">### Error estimation for multiple ensembles</span>
-</span><span id="L-161"><a href="#L-161"><span class="linenos">161</span></a>
-</span><span id="L-162"><a href="#L-162"><span class="linenos">162</span></a><span class="sd">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.</span>
-</span><span id="L-163"><a href="#L-163"><span class="linenos">163</span></a>
-</span><span id="L-164"><a href="#L-164"><span class="linenos">164</span></a><span class="sd">```python</span>
-</span><span id="L-165"><a href="#L-165"><span class="linenos">165</span></a><span class="sd">pe.Obs.S_dict[&#39;ensemble1&#39;] = 2.5</span>
-</span><span id="L-166"><a href="#L-166"><span class="linenos">166</span></a><span class="sd">pe.Obs.tau_exp_dict[&#39;ensemble2&#39;] = 8.0</span>
-</span><span id="L-167"><a href="#L-167"><span class="linenos">167</span></a><span class="sd">pe.Obs.tau_exp_dict[&#39;ensemble3&#39;] = 2.0</span>
-</span><span id="L-168"><a href="#L-168"><span class="linenos">168</span></a><span class="sd">```</span>
-</span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a>
-</span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a><span class="sd">In case the `gamma_method` is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.</span>
-</span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a><span class="sd">Passing arguments to the `gamma_method` still dominates over the dictionaries.</span>
-</span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a>
+</span><span id="L-14"><a href="#L-14"><span class="linenos"> 14</span></a><span class="sd">Fabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, *pyerrors: a python framework for error analysis of Monte Carlo data*. [arXiv:2209.14371 [hep-lat]].</span>
+</span><span id="L-15"><a href="#L-15"><span class="linenos"> 15</span></a><span class="sd">- Ulli Wolff, *Monte Carlo errors with less errors*. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</span>
+</span><span id="L-16"><a href="#L-16"><span class="linenos"> 16</span></a><span class="sd">- Alberto Ramos, *Automatic differentiation for error analysis of Monte Carlo data*. Comput.Phys.Commun. 238 (2019) 19-35.</span>
+</span><span id="L-17"><a href="#L-17"><span class="linenos"> 17</span></a>
+</span><span id="L-18"><a href="#L-18"><span class="linenos"> 18</span></a><span class="sd">and</span>
+</span><span id="L-19"><a href="#L-19"><span class="linenos"> 19</span></a>
+</span><span id="L-20"><a href="#L-20"><span class="linenos"> 20</span></a><span class="sd">- Stefan Schaefer, Rainer Sommer, Francesco Virotta, *Critical slowing down and error analysis in lattice QCD simulations*. Nucl.Phys.B 845 (2011) 93-119.</span>
+</span><span id="L-21"><a href="#L-21"><span class="linenos"> 21</span></a>
+</span><span id="L-22"><a href="#L-22"><span class="linenos"> 22</span></a><span class="sd">where applicable.</span>
+</span><span id="L-23"><a href="#L-23"><span class="linenos"> 23</span></a>
+</span><span id="L-24"><a href="#L-24"><span class="linenos"> 24</span></a><span class="sd">There exist similar publicly available implementations of gamma method error analysis suites in [Fortran](https://gitlab.ift.uam-csic.es/alberto/aderrors), [Julia](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl) and [Python](https://github.com/mbruno46/pyobs).</span>
+</span><span id="L-25"><a href="#L-25"><span class="linenos"> 25</span></a>
+</span><span id="L-26"><a href="#L-26"><span class="linenos"> 26</span></a><span class="sd">## Basic example</span>
+</span><span id="L-27"><a href="#L-27"><span class="linenos"> 27</span></a>
+</span><span id="L-28"><a href="#L-28"><span class="linenos"> 28</span></a><span class="sd">```python</span>
+</span><span id="L-29"><a href="#L-29"><span class="linenos"> 29</span></a><span class="sd">import numpy as np</span>
+</span><span id="L-30"><a href="#L-30"><span class="linenos"> 30</span></a><span class="sd">import pyerrors as pe</span>
+</span><span id="L-31"><a href="#L-31"><span class="linenos"> 31</span></a>
+</span><span id="L-32"><a href="#L-32"><span class="linenos"> 32</span></a><span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;]) # Initialize an Obs object</span>
+</span><span id="L-33"><a href="#L-33"><span class="linenos"> 33</span></a><span class="sd">my_new_obs = 2 * np.log(my_obs) / my_obs ** 2 # Construct derived Obs object</span>
+</span><span id="L-34"><a href="#L-34"><span class="linenos"> 34</span></a><span class="sd">my_new_obs.gamma_method()                     # Estimate the statistical error</span>
+</span><span id="L-35"><a href="#L-35"><span class="linenos"> 35</span></a><span class="sd">print(my_new_obs)                             # Print the result to stdout</span>
+</span><span id="L-36"><a href="#L-36"><span class="linenos"> 36</span></a><span class="sd">&gt; 0.31498(72)</span>
+</span><span id="L-37"><a href="#L-37"><span class="linenos"> 37</span></a><span class="sd">```</span>
+</span><span id="L-38"><a href="#L-38"><span class="linenos"> 38</span></a>
+</span><span id="L-39"><a href="#L-39"><span class="linenos"> 39</span></a><span class="sd"># The `Obs` class</span>
+</span><span id="L-40"><a href="#L-40"><span class="linenos"> 40</span></a>
+</span><span id="L-41"><a href="#L-41"><span class="linenos"> 41</span></a><span class="sd">`pyerrors` introduces a new datatype, `Obs`, which simplifies error propagation and estimation for auto- and cross-correlated data.</span>
+</span><span id="L-42"><a href="#L-42"><span class="linenos"> 42</span></a><span class="sd">An `Obs` object can be initialized with two arguments, the first is a list containing the samples for an observable from a Monte Carlo chain.</span>
+</span><span id="L-43"><a href="#L-43"><span class="linenos"> 43</span></a><span class="sd">The samples can either be provided as python list or as numpy array.</span>
+</span><span id="L-44"><a href="#L-44"><span class="linenos"> 44</span></a><span class="sd">The 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.</span>
+</span><span id="L-45"><a href="#L-45"><span class="linenos"> 45</span></a>
+</span><span id="L-46"><a href="#L-46"><span class="linenos"> 46</span></a><span class="sd">```python</span>
+</span><span id="L-47"><a href="#L-47"><span class="linenos"> 47</span></a><span class="sd">import pyerrors as pe</span>
+</span><span id="L-48"><a href="#L-48"><span class="linenos"> 48</span></a>
+</span><span id="L-49"><a href="#L-49"><span class="linenos"> 49</span></a><span class="sd">my_obs = pe.Obs([samples], [&#39;ensemble_name&#39;])</span>
+</span><span id="L-50"><a href="#L-50"><span class="linenos"> 50</span></a><span class="sd">```</span>
+</span><span id="L-51"><a href="#L-51"><span class="linenos"> 51</span></a>
+</span><span id="L-52"><a href="#L-52"><span class="linenos"> 52</span></a><span class="sd">## Error propagation</span>
+</span><span id="L-53"><a href="#L-53"><span class="linenos"> 53</span></a>
+</span><span id="L-54"><a href="#L-54"><span class="linenos"> 54</span></a><span class="sd">When performing mathematical operations on `Obs` objects the correct error propagation is intrinsically taken care of using a first order Taylor expansion</span>
+</span><span id="L-55"><a href="#L-55"><span class="linenos"> 55</span></a><span class="sd">$$\delta_f^i=\sum_\alpha \bar{f}_\alpha \delta_\alpha^i\,,\quad \delta_\alpha^i=a_\alpha^i-\bar{a}_\alpha\,,$$</span>
+</span><span id="L-56"><a href="#L-56"><span class="linenos"> 56</span></a><span class="sd">as introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
+</span><span id="L-57"><a href="#L-57"><span class="linenos"> 57</span></a><span class="sd">The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision via automatic differentiation as suggested in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span>
+</span><span id="L-58"><a href="#L-58"><span class="linenos"> 58</span></a>
+</span><span id="L-59"><a href="#L-59"><span class="linenos"> 59</span></a><span class="sd">The `Obs` class is designed such that mathematical numpy functions can be used on `Obs` just as for regular floats.</span>
+</span><span id="L-60"><a href="#L-60"><span class="linenos"> 60</span></a>
+</span><span id="L-61"><a href="#L-61"><span class="linenos"> 61</span></a><span class="sd">```python</span>
+</span><span id="L-62"><a href="#L-62"><span class="linenos"> 62</span></a><span class="sd">import numpy as np</span>
+</span><span id="L-63"><a href="#L-63"><span class="linenos"> 63</span></a><span class="sd">import pyerrors as pe</span>
+</span><span id="L-64"><a href="#L-64"><span class="linenos"> 64</span></a>
+</span><span id="L-65"><a href="#L-65"><span class="linenos"> 65</span></a><span class="sd">my_obs1 = pe.Obs([samples1], [&#39;ensemble_name&#39;])</span>
+</span><span id="L-66"><a href="#L-66"><span class="linenos"> 66</span></a><span class="sd">my_obs2 = pe.Obs([samples2], [&#39;ensemble_name&#39;])</span>
+</span><span id="L-67"><a href="#L-67"><span class="linenos"> 67</span></a>
+</span><span id="L-68"><a href="#L-68"><span class="linenos"> 68</span></a><span class="sd">my_sum = my_obs1 + my_obs2</span>
+</span><span id="L-69"><a href="#L-69"><span class="linenos"> 69</span></a>
+</span><span id="L-70"><a href="#L-70"><span class="linenos"> 70</span></a><span class="sd">my_m_eff = np.log(my_obs1 / my_obs2)</span>
+</span><span id="L-71"><a href="#L-71"><span class="linenos"> 71</span></a>
+</span><span id="L-72"><a href="#L-72"><span class="linenos"> 72</span></a><span class="sd">iamzero = my_m_eff - my_m_eff</span>
+</span><span id="L-73"><a href="#L-73"><span class="linenos"> 73</span></a><span class="sd"># Check that value and fluctuations are zero within machine precision</span>
+</span><span id="L-74"><a href="#L-74"><span class="linenos"> 74</span></a><span class="sd">print(iamzero == 0.0)</span>
+</span><span id="L-75"><a href="#L-75"><span class="linenos"> 75</span></a><span class="sd">&gt; True</span>
+</span><span id="L-76"><a href="#L-76"><span class="linenos"> 76</span></a><span class="sd">```</span>
+</span><span id="L-77"><a href="#L-77"><span class="linenos"> 77</span></a>
+</span><span id="L-78"><a href="#L-78"><span class="linenos"> 78</span></a><span class="sd">## Error estimation</span>
+</span><span id="L-79"><a href="#L-79"><span class="linenos"> 79</span></a>
+</span><span id="L-80"><a href="#L-80"><span class="linenos"> 80</span></a><span class="sd">The error estimation within `pyerrors` is based on the gamma method introduced in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
+</span><span id="L-81"><a href="#L-81"><span class="linenos"> 81</span></a><span class="sd">After having arrived at the derived quantity of interest the `gamma_method` can be called as detailed in the following example.</span>
+</span><span id="L-82"><a href="#L-82"><span class="linenos"> 82</span></a>
+</span><span id="L-83"><a href="#L-83"><span class="linenos"> 83</span></a><span class="sd">```python</span>
+</span><span id="L-84"><a href="#L-84"><span class="linenos"> 84</span></a><span class="sd">my_sum.gamma_method()</span>
+</span><span id="L-85"><a href="#L-85"><span class="linenos"> 85</span></a><span class="sd">print(my_sum)</span>
+</span><span id="L-86"><a href="#L-86"><span class="linenos"> 86</span></a><span class="sd">&gt; 1.70(57)</span>
+</span><span id="L-87"><a href="#L-87"><span class="linenos"> 87</span></a><span class="sd">my_sum.details()</span>
+</span><span id="L-88"><a href="#L-88"><span class="linenos"> 88</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 5.72046658e-01 +/- 7.56746598e-02 (33.650%)</span>
+</span><span id="L-89"><a href="#L-89"><span class="linenos"> 89</span></a><span class="sd">&gt;  t_int	 2.71422900e+00 +/- 6.40320983e-01 S = 2.00</span>
+</span><span id="L-90"><a href="#L-90"><span class="linenos"> 90</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
+</span><span id="L-91"><a href="#L-91"><span class="linenos"> 91</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
+</span><span id="L-92"><a href="#L-92"><span class="linenos"> 92</span></a>
+</span><span id="L-93"><a href="#L-93"><span class="linenos"> 93</span></a><span class="sd">```</span>
+</span><span id="L-94"><a href="#L-94"><span class="linenos"> 94</span></a>
+</span><span id="L-95"><a href="#L-95"><span class="linenos"> 95</span></a><span class="sd">We use the following definition of the integrated autocorrelation time established in [Madras &amp; Sokal 1988](https://link.springer.com/article/10.1007/BF01022990)</span>
+</span><span id="L-96"><a href="#L-96"><span class="linenos"> 96</span></a><span class="sd">$$\tau_\mathrm{int}=\frac{1}{2}+\sum_{t=1}^{W}\rho(t)\geq \frac{1}{2}\,.$$</span>
+</span><span id="L-97"><a href="#L-97"><span class="linenos"> 97</span></a><span class="sd">The window $W$ is determined via the automatic windowing procedure described in [arXiv:hep-lat/0306017](https://arxiv.org/abs/hep-lat/0306017).</span>
+</span><span id="L-98"><a href="#L-98"><span class="linenos"> 98</span></a><span class="sd">The standard value for the parameter $S$ of this automatic windowing procedure is $S=2$. Other values for $S$ can be passed to the `gamma_method` as parameter.</span>
+</span><span id="L-99"><a href="#L-99"><span class="linenos"> 99</span></a>
+</span><span id="L-100"><a href="#L-100"><span class="linenos">100</span></a><span class="sd">```python</span>
+</span><span id="L-101"><a href="#L-101"><span class="linenos">101</span></a><span class="sd">my_sum.gamma_method(S=3.0)</span>
+</span><span id="L-102"><a href="#L-102"><span class="linenos">102</span></a><span class="sd">my_sum.details()</span>
+</span><span id="L-103"><a href="#L-103"><span class="linenos">103</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 6.30675201e-01 +/- 1.04585650e-01 (37.099%)</span>
+</span><span id="L-104"><a href="#L-104"><span class="linenos">104</span></a><span class="sd">&gt;  t_int	 3.29909703e+00 +/- 9.77310102e-01 S = 3.00</span>
+</span><span id="L-105"><a href="#L-105"><span class="linenos">105</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
+</span><span id="L-106"><a href="#L-106"><span class="linenos">106</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
+</span><span id="L-107"><a href="#L-107"><span class="linenos">107</span></a>
+</span><span id="L-108"><a href="#L-108"><span class="linenos">108</span></a><span class="sd">```</span>
+</span><span id="L-109"><a href="#L-109"><span class="linenos">109</span></a>
+</span><span id="L-110"><a href="#L-110"><span class="linenos">110</span></a><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_rho`.</span>
+</span><span id="L-111"><a href="#L-111"><span class="linenos">111</span></a>
+</span><span id="L-112"><a href="#L-112"><span class="linenos">112</span></a><span class="sd">If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size is chosen to be zero.</span>
+</span><span id="L-113"><a href="#L-113"><span class="linenos">113</span></a><span class="sd">In this case the error estimate is identical to the sample standard error.</span>
+</span><span id="L-114"><a href="#L-114"><span class="linenos">114</span></a>
+</span><span id="L-115"><a href="#L-115"><span class="linenos">115</span></a><span class="sd">### Exponential tails</span>
+</span><span id="L-116"><a href="#L-116"><span class="linenos">116</span></a>
+</span><span id="L-117"><a href="#L-117"><span class="linenos">117</span></a><span class="sd">Slow modes in the Monte Carlo history can be accounted for by attaching an exponential 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>
+</span><span id="L-118"><a href="#L-118"><span class="linenos">118</span></a>
+</span><span id="L-119"><a href="#L-119"><span class="linenos">119</span></a><span class="sd">```python</span>
+</span><span id="L-120"><a href="#L-120"><span class="linenos">120</span></a><span class="sd">my_sum.gamma_method(tau_exp=7.2)</span>
+</span><span id="L-121"><a href="#L-121"><span class="linenos">121</span></a><span class="sd">my_sum.details()</span>
+</span><span id="L-122"><a href="#L-122"><span class="linenos">122</span></a><span class="sd">&gt; Result	 1.70000000e+00 +/- 6.28097762e-01 +/- 5.79077524e-02 (36.947%)</span>
+</span><span id="L-123"><a href="#L-123"><span class="linenos">123</span></a><span class="sd">&gt;  t_int	 3.27218667e+00 +/- 7.99583654e-01 tau_exp = 7.20,  N_sigma = 1</span>
+</span><span id="L-124"><a href="#L-124"><span class="linenos">124</span></a><span class="sd">&gt; 1000 samples in 1 ensemble:</span>
+</span><span id="L-125"><a href="#L-125"><span class="linenos">125</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble_name&#39; : 1000 configurations (from 1 to 1000)</span>
+</span><span id="L-126"><a href="#L-126"><span class="linenos">126</span></a><span class="sd">```</span>
+</span><span id="L-127"><a href="#L-127"><span class="linenos">127</span></a>
+</span><span id="L-128"><a href="#L-128"><span class="linenos">128</span></a><span class="sd">For the full API see `pyerrors.obs.Obs.gamma_method`.</span>
+</span><span id="L-129"><a href="#L-129"><span class="linenos">129</span></a>
+</span><span id="L-130"><a href="#L-130"><span class="linenos">130</span></a><span class="sd">## Multiple ensembles/replica</span>
+</span><span id="L-131"><a href="#L-131"><span class="linenos">131</span></a>
+</span><span id="L-132"><a href="#L-132"><span class="linenos">132</span></a><span class="sd">Error propagation for multiple ensembles (Markov chains with different simulation parameters) is handled automatically. Ensembles are uniquely identified by their `name`.</span>
+</span><span id="L-133"><a href="#L-133"><span class="linenos">133</span></a>
+</span><span id="L-134"><a href="#L-134"><span class="linenos">134</span></a><span class="sd">```python</span>
+</span><span id="L-135"><a href="#L-135"><span class="linenos">135</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1&#39;])</span>
+</span><span id="L-136"><a href="#L-136"><span class="linenos">136</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble2&#39;])</span>
+</span><span id="L-137"><a href="#L-137"><span class="linenos">137</span></a>
+</span><span id="L-138"><a href="#L-138"><span class="linenos">138</span></a><span class="sd">my_sum = obs1 + obs2</span>
+</span><span id="L-139"><a href="#L-139"><span class="linenos">139</span></a><span class="sd">my_sum.details()</span>
+</span><span id="L-140"><a href="#L-140"><span class="linenos">140</span></a><span class="sd">&gt; Result   2.00697958e+00</span>
+</span><span id="L-141"><a href="#L-141"><span class="linenos">141</span></a><span class="sd">&gt; 1500 samples in 2 ensembles:</span>
+</span><span id="L-142"><a href="#L-142"><span class="linenos">142</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 1000 configurations (from 1 to 1000)</span>
+</span><span id="L-143"><a href="#L-143"><span class="linenos">143</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble2&#39; : 500 configurations (from 1 to 500)</span>
+</span><span id="L-144"><a href="#L-144"><span class="linenos">144</span></a><span class="sd">```</span>
+</span><span id="L-145"><a href="#L-145"><span class="linenos">145</span></a>
+</span><span id="L-146"><a href="#L-146"><span class="linenos">146</span></a><span class="sd">`pyerrors` identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar `|` in the name of the data set.</span>
+</span><span id="L-147"><a href="#L-147"><span class="linenos">147</span></a>
+</span><span id="L-148"><a href="#L-148"><span class="linenos">148</span></a><span class="sd">```python</span>
+</span><span id="L-149"><a href="#L-149"><span class="linenos">149</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1|r01&#39;])</span>
+</span><span id="L-150"><a href="#L-150"><span class="linenos">150</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble1|r02&#39;])</span>
+</span><span id="L-151"><a href="#L-151"><span class="linenos">151</span></a>
+</span><span id="L-152"><a href="#L-152"><span class="linenos">152</span></a><span class="sd">&gt; my_sum = obs1 + obs2</span>
+</span><span id="L-153"><a href="#L-153"><span class="linenos">153</span></a><span class="sd">&gt; my_sum.details()</span>
+</span><span id="L-154"><a href="#L-154"><span class="linenos">154</span></a><span class="sd">&gt; Result   2.00697958e+00</span>
+</span><span id="L-155"><a href="#L-155"><span class="linenos">155</span></a><span class="sd">&gt; 1500 samples in 1 ensemble:</span>
+</span><span id="L-156"><a href="#L-156"><span class="linenos">156</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39;</span>
+</span><span id="L-157"><a href="#L-157"><span class="linenos">157</span></a><span class="sd">&gt;     · Replicum &#39;r01&#39; : 1000 configurations (from 1 to 1000)</span>
+</span><span id="L-158"><a href="#L-158"><span class="linenos">158</span></a><span class="sd">&gt;     · Replicum &#39;r02&#39; : 500 configurations (from 1 to 500)</span>
+</span><span id="L-159"><a href="#L-159"><span class="linenos">159</span></a><span class="sd">```</span>
+</span><span id="L-160"><a href="#L-160"><span class="linenos">160</span></a>
+</span><span id="L-161"><a href="#L-161"><span class="linenos">161</span></a><span class="sd">### Error estimation for multiple ensembles</span>
+</span><span id="L-162"><a href="#L-162"><span class="linenos">162</span></a>
+</span><span id="L-163"><a href="#L-163"><span class="linenos">163</span></a><span class="sd">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.</span>
+</span><span id="L-164"><a href="#L-164"><span class="linenos">164</span></a>
+</span><span id="L-165"><a href="#L-165"><span class="linenos">165</span></a><span class="sd">```python</span>
+</span><span id="L-166"><a href="#L-166"><span class="linenos">166</span></a><span class="sd">pe.Obs.S_dict[&#39;ensemble1&#39;] = 2.5</span>
+</span><span id="L-167"><a href="#L-167"><span class="linenos">167</span></a><span class="sd">pe.Obs.tau_exp_dict[&#39;ensemble2&#39;] = 8.0</span>
+</span><span id="L-168"><a href="#L-168"><span class="linenos">168</span></a><span class="sd">pe.Obs.tau_exp_dict[&#39;ensemble3&#39;] = 2.0</span>
+</span><span id="L-169"><a href="#L-169"><span class="linenos">169</span></a><span class="sd">```</span>
+</span><span id="L-170"><a href="#L-170"><span class="linenos">170</span></a>
+</span><span id="L-171"><a href="#L-171"><span class="linenos">171</span></a><span class="sd">In case the `gamma_method` is called without any parameters it will use the values specified in the dictionaries for the respective ensembles.</span>
+</span><span id="L-172"><a href="#L-172"><span class="linenos">172</span></a><span class="sd">Passing arguments to the `gamma_method` still dominates over the dictionaries.</span>
 </span><span id="L-173"><a href="#L-173"><span class="linenos">173</span></a>
-</span><span id="L-174"><a href="#L-174"><span class="linenos">174</span></a><span class="sd">## Irregular Monte Carlo chains</span>
-</span><span id="L-175"><a href="#L-175"><span class="linenos">175</span></a>
-</span><span id="L-176"><a href="#L-176"><span class="linenos">176</span></a><span class="sd">`Obs` objects defined on irregular Monte Carlo chains can be initialized with the parameter `idl`.</span>
-</span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a>
-</span><span id="L-178"><a href="#L-178"><span class="linenos">178</span></a><span class="sd">```python</span>
-</span><span id="L-179"><a href="#L-179"><span class="linenos">179</span></a><span class="sd"># Observable defined on configurations 20 to 519</span>
-</span><span id="L-180"><a href="#L-180"><span class="linenos">180</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1&#39;], idl=[range(20, 520)])</span>
-</span><span id="L-181"><a href="#L-181"><span class="linenos">181</span></a><span class="sd">obs1.details()</span>
-</span><span id="L-182"><a href="#L-182"><span class="linenos">182</span></a><span class="sd">&gt; Result	 9.98319881e-01</span>
-</span><span id="L-183"><a href="#L-183"><span class="linenos">183</span></a><span class="sd">&gt; 500 samples in 1 ensemble:</span>
-</span><span id="L-184"><a href="#L-184"><span class="linenos">184</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 500 configurations (from 20 to 519)</span>
-</span><span id="L-185"><a href="#L-185"><span class="linenos">185</span></a>
-</span><span id="L-186"><a href="#L-186"><span class="linenos">186</span></a><span class="sd"># Observable defined on every second configuration between 5 and 1003</span>
-</span><span id="L-187"><a href="#L-187"><span class="linenos">187</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble1&#39;], idl=[range(5, 1005, 2)])</span>
-</span><span id="L-188"><a href="#L-188"><span class="linenos">188</span></a><span class="sd">obs2.details()</span>
-</span><span id="L-189"><a href="#L-189"><span class="linenos">189</span></a><span class="sd">&gt; Result	 9.99100712e-01</span>
-</span><span id="L-190"><a href="#L-190"><span class="linenos">190</span></a><span class="sd">&gt; 500 samples in 1 ensemble:</span>
-</span><span id="L-191"><a href="#L-191"><span class="linenos">191</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 500 configurations (from 5 to 1003 in steps of 2)</span>
-</span><span id="L-192"><a href="#L-192"><span class="linenos">192</span></a>
-</span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a><span class="sd"># Observable defined on configurations 2, 9, 28, 29 and 501</span>
-</span><span id="L-194"><a href="#L-194"><span class="linenos">194</span></a><span class="sd">obs3 = pe.Obs([samples3], [&#39;ensemble1&#39;], idl=[[2, 9, 28, 29, 501]])</span>
-</span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a><span class="sd">obs3.details()</span>
-</span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a><span class="sd">&gt; Result	 1.01718064e+00</span>
-</span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a><span class="sd">&gt; 5 samples in 1 ensemble:</span>
-</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 5 configurations (irregular range)</span>
-</span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a>
-</span><span id="L-200"><a href="#L-200"><span class="linenos">200</span></a><span class="sd">```</span>
-</span><span id="L-201"><a href="#L-201"><span class="linenos">201</span></a>
-</span><span id="L-202"><a href="#L-202"><span class="linenos">202</span></a><span class="sd">`Obs` objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</span>
-</span><span id="L-203"><a href="#L-203"><span class="linenos">203</span></a>
-</span><span id="L-204"><a href="#L-204"><span class="linenos">204</span></a><span class="sd">**Warning:** Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.</span>
-</span><span id="L-205"><a href="#L-205"><span class="linenos">205</span></a><span class="sd">Make sure to check the autocorrelation time with e.g. `pyerrors.obs.Obs.plot_rho` or `pyerrors.obs.Obs.plot_tauint`.</span>
-</span><span id="L-206"><a href="#L-206"><span class="linenos">206</span></a>
-</span><span id="L-207"><a href="#L-207"><span class="linenos">207</span></a><span class="sd">For the full API see `pyerrors.obs.Obs`.</span>
-</span><span id="L-208"><a href="#L-208"><span class="linenos">208</span></a>
-</span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a><span class="sd"># Correlators</span>
-</span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a><span class="sd">When one is not interested in single observables but correlation functions, `pyerrors` offers the `Corr` class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a `Corr` objects one needs to arrange the data as a list of `Obs`</span>
-</span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a><span class="sd">```python</span>
-</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a><span class="sd">my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])</span>
-</span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a><span class="sd">print(my_corr)</span>
-</span><span id="L-214"><a href="#L-214"><span class="linenos">214</span></a><span class="sd">&gt; x0/a	Corr(x0/a)</span>
-</span><span id="L-215"><a href="#L-215"><span class="linenos">215</span></a><span class="sd">&gt; ------------------</span>
-</span><span id="L-216"><a href="#L-216"><span class="linenos">216</span></a><span class="sd">&gt; 0	 0.7957(80)</span>
-</span><span id="L-217"><a href="#L-217"><span class="linenos">217</span></a><span class="sd">&gt; 1	 0.5156(51)</span>
-</span><span id="L-218"><a href="#L-218"><span class="linenos">218</span></a><span class="sd">&gt; 2	 0.3227(33)</span>
-</span><span id="L-219"><a href="#L-219"><span class="linenos">219</span></a><span class="sd">&gt; 3	 0.2041(21)</span>
-</span><span id="L-220"><a href="#L-220"><span class="linenos">220</span></a><span class="sd">```</span>
-</span><span id="L-221"><a href="#L-221"><span class="linenos">221</span></a><span class="sd">In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</span>
-</span><span id="L-222"><a href="#L-222"><span class="linenos">222</span></a><span class="sd">```python</span>
-</span><span id="L-223"><a href="#L-223"><span class="linenos">223</span></a><span class="sd">my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])</span>
-</span><span id="L-224"><a href="#L-224"><span class="linenos">224</span></a><span class="sd">print(my_corr)</span>
-</span><span id="L-225"><a href="#L-225"><span class="linenos">225</span></a><span class="sd">&gt; x0/a	Corr(x0/a)</span>
-</span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a><span class="sd">&gt; ------------------</span>
-</span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a><span class="sd">&gt; 0</span>
-</span><span id="L-228"><a href="#L-228"><span class="linenos">228</span></a><span class="sd">&gt; 1	 0.7957(80)</span>
-</span><span id="L-229"><a href="#L-229"><span class="linenos">229</span></a><span class="sd">&gt; 2	 0.5156(51)</span>
-</span><span id="L-230"><a href="#L-230"><span class="linenos">230</span></a><span class="sd">&gt; 3	 0.3227(33)</span>
-</span><span id="L-231"><a href="#L-231"><span class="linenos">231</span></a><span class="sd">&gt; 4	 0.2041(21)</span>
-</span><span id="L-232"><a href="#L-232"><span class="linenos">232</span></a><span class="sd">&gt; 5</span>
-</span><span id="L-233"><a href="#L-233"><span class="linenos">233</span></a><span class="sd">```</span>
-</span><span id="L-234"><a href="#L-234"><span class="linenos">234</span></a><span class="sd">The individual entries of a correlator can be accessed via slicing</span>
-</span><span id="L-235"><a href="#L-235"><span class="linenos">235</span></a><span class="sd">```python</span>
-</span><span id="L-236"><a href="#L-236"><span class="linenos">236</span></a><span class="sd">print(my_corr[3])</span>
-</span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a><span class="sd">&gt; 0.3227(33)</span>
-</span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a><span class="sd">```</span>
-</span><span id="L-239"><a href="#L-239"><span class="linenos">239</span></a><span class="sd">Error propagation with the `Corr` class works very similar to `Obs` objects. Mathematical operations are overloaded and `Corr` objects can be computed together with other `Corr` objects, `Obs` objects or real numbers and integers.</span>
-</span><span id="L-240"><a href="#L-240"><span class="linenos">240</span></a><span class="sd">```python</span>
-</span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a><span class="sd">my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr</span>
-</span><span id="L-242"><a href="#L-242"><span class="linenos">242</span></a><span class="sd">```</span>
-</span><span id="L-243"><a href="#L-243"><span class="linenos">243</span></a>
-</span><span id="L-244"><a href="#L-244"><span class="linenos">244</span></a><span class="sd">`pyerrors` provides the user with a set of regularly used methods for the manipulation of correlator objects:</span>
-</span><span id="L-245"><a href="#L-245"><span class="linenos">245</span></a><span class="sd">- `Corr.gamma_method` applies the gamma method to all entries of the correlator.</span>
-</span><span id="L-246"><a href="#L-246"><span class="linenos">246</span></a><span class="sd">- `Corr.m_eff` to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</span>
-</span><span id="L-247"><a href="#L-247"><span class="linenos">247</span></a><span class="sd">- `Corr.deriv` returns the first derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available.</span>
-</span><span id="L-248"><a href="#L-248"><span class="linenos">248</span></a><span class="sd">- `Corr.second_deriv` returns the second derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available.</span>
-</span><span id="L-249"><a href="#L-249"><span class="linenos">249</span></a><span class="sd">- `Corr.symmetric` symmetrizes parity even correlations functions, assuming periodic boundary conditions.</span>
-</span><span id="L-250"><a href="#L-250"><span class="linenos">250</span></a><span class="sd">- `Corr.anti_symmetric` anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</span>
-</span><span id="L-251"><a href="#L-251"><span class="linenos">251</span></a><span class="sd">- `Corr.T_symmetry` averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</span>
-</span><span id="L-252"><a href="#L-252"><span class="linenos">252</span></a><span class="sd">- `Corr.plateau` extracts a plateau value from the correlator in a given range.</span>
-</span><span id="L-253"><a href="#L-253"><span class="linenos">253</span></a><span class="sd">- `Corr.roll` periodically shifts the correlator.</span>
-</span><span id="L-254"><a href="#L-254"><span class="linenos">254</span></a><span class="sd">- `Corr.reverse` reverses the time ordering of the correlator.</span>
-</span><span id="L-255"><a href="#L-255"><span class="linenos">255</span></a><span class="sd">- `Corr.correlate` constructs a disconnected correlation function from the correlator and another `Corr` or `Obs` object.</span>
-</span><span id="L-256"><a href="#L-256"><span class="linenos">256</span></a><span class="sd">- `Corr.reweight` reweights the correlator.</span>
-</span><span id="L-257"><a href="#L-257"><span class="linenos">257</span></a>
-</span><span id="L-258"><a href="#L-258"><span class="linenos">258</span></a><span class="sd">`pyerrors` can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see `pyerrors.correlators.Corr.GEVP`).</span>
-</span><span id="L-259"><a href="#L-259"><span class="linenos">259</span></a>
-</span><span id="L-260"><a href="#L-260"><span class="linenos">260</span></a><span class="sd">For the full API see `pyerrors.correlators.Corr`.</span>
-</span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a>
-</span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a><span class="sd"># Complex valued observables</span>
-</span><span id="L-263"><a href="#L-263"><span class="linenos">263</span></a>
-</span><span id="L-264"><a href="#L-264"><span class="linenos">264</span></a><span class="sd">`pyerrors` can handle complex valued observables via the class `pyerrors.obs.CObs`.</span>
-</span><span id="L-265"><a href="#L-265"><span class="linenos">265</span></a><span class="sd">`CObs` are initialized with a real and an imaginary part which both can be `Obs` valued.</span>
-</span><span id="L-266"><a href="#L-266"><span class="linenos">266</span></a>
-</span><span id="L-267"><a href="#L-267"><span class="linenos">267</span></a><span class="sd">```python</span>
-</span><span id="L-268"><a href="#L-268"><span class="linenos">268</span></a><span class="sd">my_real_part = pe.Obs([samples1], [&#39;ensemble1&#39;])</span>
-</span><span id="L-269"><a href="#L-269"><span class="linenos">269</span></a><span class="sd">my_imag_part = pe.Obs([samples2], [&#39;ensemble1&#39;])</span>
-</span><span id="L-270"><a href="#L-270"><span class="linenos">270</span></a>
-</span><span id="L-271"><a href="#L-271"><span class="linenos">271</span></a><span class="sd">my_cobs = pe.CObs(my_real_part, my_imag_part)</span>
-</span><span id="L-272"><a href="#L-272"><span class="linenos">272</span></a><span class="sd">my_cobs.gamma_method()</span>
-</span><span id="L-273"><a href="#L-273"><span class="linenos">273</span></a><span class="sd">print(my_cobs)</span>
-</span><span id="L-274"><a href="#L-274"><span class="linenos">274</span></a><span class="sd">&gt; (0.9959(91)+0.659(28)j)</span>
-</span><span id="L-275"><a href="#L-275"><span class="linenos">275</span></a><span class="sd">```</span>
-</span><span id="L-276"><a href="#L-276"><span class="linenos">276</span></a>
-</span><span id="L-277"><a href="#L-277"><span class="linenos">277</span></a><span class="sd">Elementary mathematical operations are overloaded and samples are properly propagated as for the `Obs` class.</span>
-</span><span id="L-278"><a href="#L-278"><span class="linenos">278</span></a><span class="sd">```python</span>
-</span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a><span class="sd">my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)</span>
-</span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a><span class="sd">my_derived_cobs.gamma_method()</span>
-</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a><span class="sd">print(my_derived_cobs)</span>
-</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a><span class="sd">&gt; (1.668(23)+0.0j)</span>
-</span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a><span class="sd">```</span>
-</span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a>
-</span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a><span class="sd"># The `Covobs` class</span>
-</span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a><span class="sd">In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The `Covobs` class allows to define such quantities in `pyerrors`. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</span>
-</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a>
-</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a><span class="sd">This concept is built into the definition of `Covobs`. In `pyerrors`, external input is defined by $M$ mean values, a $M\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters `cov_Obs`, since the second argument of this function is the covariance matrix of the `Covobs`.</span>
-</span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a>
-</span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a><span class="sd">```python</span>
-</span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a><span class="sd">import pyerrors.obs as pe</span>
-</span><span id="L-292"><a href="#L-292"><span class="linenos">292</span></a>
-</span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a><span class="sd">mpi = pe.cov_Obs(134.9768, 0.0005**2, &#39;pi^0 mass&#39;)</span>
-</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a><span class="sd">mpi.gamma_method()</span>
-</span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a><span class="sd">mpi.details()</span>
-</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a><span class="sd">&gt; Result	 1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)</span>
-</span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a><span class="sd">&gt;  pi^0 mass 	 5.00000000e-04</span>
-</span><span id="L-298"><a href="#L-298"><span class="linenos">298</span></a><span class="sd">&gt; 0 samples in 1 ensemble:</span>
-</span><span id="L-299"><a href="#L-299"><span class="linenos">299</span></a><span class="sd">&gt;   · Covobs   &#39;pi^0 mass&#39;</span>
-</span><span id="L-300"><a href="#L-300"><span class="linenos">300</span></a><span class="sd">```</span>
-</span><span id="L-301"><a href="#L-301"><span class="linenos">301</span></a><span class="sd">The resulting object `mpi` is an `Obs` that contains a `Covobs`. In the following, it may be handled as any other `Obs`. The contribution of the covariance matrix to the error of an `Obs` is determined from the $M \times M$ covariance matrix $\Sigma$ and the gradient of the `Obs` with respect to the external quantities, which is the $1\times M$ Jacobian matrix $J$, via</span>
-</span><span id="L-302"><a href="#L-302"><span class="linenos">302</span></a><span class="sd">$$s = \sqrt{J^T \Sigma J}\,,$$</span>
-</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a><span class="sd">where the Jacobian is computed for each derived quantity via automatic differentiation.</span>
-</span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a>
-</span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a><span class="sd">Correlated auxiliary data is defined similarly to above, e.g., via</span>
-</span><span id="L-306"><a href="#L-306"><span class="linenos">306</span></a><span class="sd">```python</span>
-</span><span id="L-307"><a href="#L-307"><span class="linenos">307</span></a><span class="sd">RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], &#39;R_AP, 1906.03445, (5.3a)&#39;)</span>
-</span><span id="L-308"><a href="#L-308"><span class="linenos">308</span></a><span class="sd">print(RAP)</span>
-</span><span id="L-309"><a href="#L-309"><span class="linenos">309</span></a><span class="sd">&gt; [Obs[16.7(1.9)], Obs[-19.0(3.3)]]</span>
-</span><span id="L-310"><a href="#L-310"><span class="linenos">310</span></a><span class="sd">```</span>
-</span><span id="L-311"><a href="#L-311"><span class="linenos">311</span></a><span class="sd">where `RAP` now is a list of two `Obs` that contains the two correlated parameters.</span>
-</span><span id="L-312"><a href="#L-312"><span class="linenos">312</span></a>
-</span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a><span class="sd">Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the `Covobs` class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an `Obs` `o` with respect to a covariance matrix with the identifying string `k` may be accessed via</span>
-</span><span id="L-314"><a href="#L-314"><span class="linenos">314</span></a><span class="sd">```python</span>
-</span><span id="L-315"><a href="#L-315"><span class="linenos">315</span></a><span class="sd">o.covobs[k].grad</span>
-</span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a><span class="sd">```</span>
-</span><span id="L-317"><a href="#L-317"><span class="linenos">317</span></a>
-</span><span id="L-318"><a href="#L-318"><span class="linenos">318</span></a><span class="sd"># Error propagation in iterative algorithms</span>
-</span><span id="L-319"><a href="#L-319"><span class="linenos">319</span></a>
-</span><span id="L-320"><a href="#L-320"><span class="linenos">320</span></a><span class="sd">`pyerrors` supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span>
-</span><span id="L-321"><a href="#L-321"><span class="linenos">321</span></a>
-</span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a><span class="sd">## Least squares fits</span>
-</span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a>
-</span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a><span class="sd">Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with `pyerrors.fits.least_squares`. As default solver the Levenberg-Marquardt algorithm implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html) is used.</span>
-</span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a>
-</span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a><span class="sd">Fit functions have to be of the following form</span>
-</span><span id="L-327"><a href="#L-327"><span class="linenos">327</span></a><span class="sd">```python</span>
-</span><span id="L-328"><a href="#L-328"><span class="linenos">328</span></a><span class="sd">import autograd.numpy as anp</span>
-</span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a>
-</span><span id="L-330"><a href="#L-330"><span class="linenos">330</span></a><span class="sd">def func(a, x):</span>
-</span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a><span class="sd">    return a[1] * anp.exp(-a[0] * x)</span>
-</span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a><span class="sd">```</span>
-</span><span id="L-333"><a href="#L-333"><span class="linenos">333</span></a><span class="sd">**It is important that numerical functions refer to `autograd.numpy` instead of `numpy` for the automatic differentiation in iterative algorithms to work properly.**</span>
-</span><span id="L-334"><a href="#L-334"><span class="linenos">334</span></a>
-</span><span id="L-335"><a href="#L-335"><span class="linenos">335</span></a><span class="sd">Fits can then be performed via</span>
-</span><span id="L-336"><a href="#L-336"><span class="linenos">336</span></a><span class="sd">```python</span>
-</span><span id="L-337"><a href="#L-337"><span class="linenos">337</span></a><span class="sd">fit_result = pe.fits.least_squares(x, y, func)</span>
-</span><span id="L-338"><a href="#L-338"><span class="linenos">338</span></a><span class="sd">print(&quot;\n&quot;, fit_result)</span>
-</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a><span class="sd">&gt; Fit with 2 parameters</span>
-</span><span id="L-340"><a href="#L-340"><span class="linenos">340</span></a><span class="sd">&gt; Method: Levenberg-Marquardt</span>
-</span><span id="L-341"><a href="#L-341"><span class="linenos">341</span></a><span class="sd">&gt; `ftol` termination condition is satisfied.</span>
-</span><span id="L-342"><a href="#L-342"><span class="linenos">342</span></a><span class="sd">&gt; chisquare/d.o.f.: 0.9593035785160936</span>
-</span><span id="L-343"><a href="#L-343"><span class="linenos">343</span></a>
-</span><span id="L-344"><a href="#L-344"><span class="linenos">344</span></a><span class="sd">&gt;  Goodness of fit:</span>
-</span><span id="L-345"><a href="#L-345"><span class="linenos">345</span></a><span class="sd">&gt; χ²/d.o.f. = 0.959304</span>
-</span><span id="L-346"><a href="#L-346"><span class="linenos">346</span></a><span class="sd">&gt; p-value   = 0.5673</span>
-</span><span id="L-347"><a href="#L-347"><span class="linenos">347</span></a><span class="sd">&gt; Fit parameters:</span>
-</span><span id="L-348"><a href="#L-348"><span class="linenos">348</span></a><span class="sd">&gt; 0	 0.0548(28)</span>
-</span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a><span class="sd">&gt; 1	 1.933(64)</span>
-</span><span id="L-350"><a href="#L-350"><span class="linenos">350</span></a><span class="sd">```</span>
-</span><span id="L-351"><a href="#L-351"><span class="linenos">351</span></a><span class="sd">where x is a `list` or `numpy.array` of `floats` and y is a `list` or `numpy.array` of `Obs`.</span>
-</span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a>
-</span><span id="L-353"><a href="#L-353"><span class="linenos">353</span></a><span class="sd">Data stored in `Corr` objects can be fitted directly using the `Corr.fit` method.</span>
-</span><span id="L-354"><a href="#L-354"><span class="linenos">354</span></a><span class="sd">```python</span>
-</span><span id="L-355"><a href="#L-355"><span class="linenos">355</span></a><span class="sd">my_corr = pe.Corr(y)</span>
-</span><span id="L-356"><a href="#L-356"><span class="linenos">356</span></a><span class="sd">fit_result = my_corr.fit(func, fitrange=[12, 25])</span>
-</span><span id="L-357"><a href="#L-357"><span class="linenos">357</span></a><span class="sd">```</span>
-</span><span id="L-358"><a href="#L-358"><span class="linenos">358</span></a><span class="sd">this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</span>
-</span><span id="L-359"><a href="#L-359"><span class="linenos">359</span></a>
-</span><span id="L-360"><a href="#L-360"><span class="linenos">360</span></a><span class="sd">For fit functions with multiple independent variables the fit function can be of the form</span>
-</span><span id="L-361"><a href="#L-361"><span class="linenos">361</span></a>
-</span><span id="L-362"><a href="#L-362"><span class="linenos">362</span></a><span class="sd">```python</span>
-</span><span id="L-363"><a href="#L-363"><span class="linenos">363</span></a><span class="sd">def func(a, x):</span>
-</span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a><span class="sd">    (x1, x2) = x</span>
-</span><span id="L-365"><a href="#L-365"><span class="linenos">365</span></a><span class="sd">    return a[0] * x1 ** 2 + a[1] * x2</span>
-</span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a><span class="sd">```</span>
-</span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a>
-</span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a><span class="sd">`pyerrors` also supports correlated fits which can be triggered via the parameter `correlated_fit=True`.</span>
-</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a><span class="sd">Details about how the required covariance matrix is estimated can be found in `pyerrors.obs.covariance`.</span>
-</span><span id="L-370"><a href="#L-370"><span class="linenos">370</span></a>
-</span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a><span class="sd">Direct visualizations of the performed fits can be triggered via `resplot=True` or `qqplot=True`. For all available options see `pyerrors.fits.least_squares`.</span>
-</span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a>
-</span><span id="L-373"><a href="#L-373"><span class="linenos">373</span></a><span class="sd">## Total least squares fits</span>
-</span><span id="L-374"><a href="#L-374"><span class="linenos">374</span></a><span class="sd">`pyerrors` can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/odr.html), see `pyerrors.fits.least_squares`. The syntax is identical to the standard least squares case, the only difference being that `x` also has to be a `list` or `numpy.array` of `Obs`.</span>
-</span><span id="L-375"><a href="#L-375"><span class="linenos">375</span></a>
-</span><span id="L-376"><a href="#L-376"><span class="linenos">376</span></a><span class="sd">For the full API see `pyerrors.fits` for fits and `pyerrors.roots` for finding roots of functions.</span>
-</span><span id="L-377"><a href="#L-377"><span class="linenos">377</span></a>
-</span><span id="L-378"><a href="#L-378"><span class="linenos">378</span></a><span class="sd"># Matrix operations</span>
-</span><span id="L-379"><a href="#L-379"><span class="linenos">379</span></a><span class="sd">`pyerrors` provides wrappers for `Obs`- and `CObs`-valued matrix operations based on `numpy.linalg`. The supported functions include:</span>
-</span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a><span class="sd">- `inv` for the matrix inverse.</span>
-</span><span id="L-381"><a href="#L-381"><span class="linenos">381</span></a><span class="sd">- `cholseky` for the Cholesky decomposition.</span>
-</span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a><span class="sd">- `det` for the matrix determinant.</span>
-</span><span id="L-383"><a href="#L-383"><span class="linenos">383</span></a><span class="sd">- `eigh` for eigenvalues and eigenvectors of hermitean matrices.</span>
-</span><span id="L-384"><a href="#L-384"><span class="linenos">384</span></a><span class="sd">- `eig` for eigenvalues of general matrices.</span>
-</span><span id="L-385"><a href="#L-385"><span class="linenos">385</span></a><span class="sd">- `pinv` for the Moore-Penrose pseudoinverse.</span>
-</span><span id="L-386"><a href="#L-386"><span class="linenos">386</span></a><span class="sd">- `svd` for the singular-value-decomposition.</span>
-</span><span id="L-387"><a href="#L-387"><span class="linenos">387</span></a>
-</span><span id="L-388"><a href="#L-388"><span class="linenos">388</span></a><span class="sd">For the full API see `pyerrors.linalg`.</span>
-</span><span id="L-389"><a href="#L-389"><span class="linenos">389</span></a>
-</span><span id="L-390"><a href="#L-390"><span class="linenos">390</span></a><span class="sd"># Export data</span>
-</span><span id="L-391"><a href="#L-391"><span class="linenos">391</span></a>
-</span><span id="L-392"><a href="#L-392"><span class="linenos">392</span></a><span class="sd">The preferred exported file format within `pyerrors` is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</span>
-</span><span id="L-393"><a href="#L-393"><span class="linenos">393</span></a><span class="sd">- What observables are stored? Possibly: How exactly are they defined.</span>
-</span><span id="L-394"><a href="#L-394"><span class="linenos">394</span></a><span class="sd">- How does each single ensemble or external quantity contribute to the error of the observable?</span>
-</span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a><span class="sd">- Who did write the file when and on which machine?</span>
-</span><span id="L-396"><a href="#L-396"><span class="linenos">396</span></a>
-</span><span id="L-397"><a href="#L-397"><span class="linenos">397</span></a><span class="sd">This can be achieved by storing all information in one single file. The export routines of `pyerrors` are written such that as much information as possible is written automatically as described in the following example</span>
-</span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a><span class="sd">```python</span>
-</span><span id="L-399"><a href="#L-399"><span class="linenos">399</span></a><span class="sd">my_obs = pe.Obs([samples], [&quot;test_ensemble&quot;])</span>
-</span><span id="L-400"><a href="#L-400"><span class="linenos">400</span></a><span class="sd">my_obs.tag = &quot;My observable&quot;</span>
-</span><span id="L-401"><a href="#L-401"><span class="linenos">401</span></a>
-</span><span id="L-402"><a href="#L-402"><span class="linenos">402</span></a><span class="sd">pe.input.json.dump_to_json(my_obs, &quot;test_output_file&quot;, description=&quot;This file contains a test observable&quot;)</span>
-</span><span id="L-403"><a href="#L-403"><span class="linenos">403</span></a><span class="sd"># For a single observable one can equivalently use the class method dump</span>
-</span><span id="L-404"><a href="#L-404"><span class="linenos">404</span></a><span class="sd">my_obs.dump(&quot;test_output_file&quot;, description=&quot;This file contains a test observable&quot;)</span>
-</span><span id="L-405"><a href="#L-405"><span class="linenos">405</span></a>
-</span><span id="L-406"><a href="#L-406"><span class="linenos">406</span></a><span class="sd">check = pe.input.json.load_json(&quot;test_output_file&quot;)</span>
-</span><span id="L-407"><a href="#L-407"><span class="linenos">407</span></a>
-</span><span id="L-408"><a href="#L-408"><span class="linenos">408</span></a><span class="sd">print(my_obs == check)</span>
-</span><span id="L-409"><a href="#L-409"><span class="linenos">409</span></a><span class="sd">&gt; True</span>
-</span><span id="L-410"><a href="#L-410"><span class="linenos">410</span></a><span class="sd">```</span>
-</span><span id="L-411"><a href="#L-411"><span class="linenos">411</span></a><span class="sd">The format also allows to directly write out the content of `Corr` objects or lists and arrays of `Obs` objects by passing the desired data to `pyerrors.input.json.dump_to_json`.</span>
-</span><span id="L-412"><a href="#L-412"><span class="linenos">412</span></a>
-</span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a><span class="sd">## json.gz format specification</span>
-</span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a><span class="sd">The first entries of the file provide optional auxiliary information:</span>
-</span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a><span class="sd">- `program` is a string that indicates which program was used to write the file.</span>
-</span><span id="L-416"><a href="#L-416"><span class="linenos">416</span></a><span class="sd">- `version` is a string that specifies the version of the format.</span>
-</span><span id="L-417"><a href="#L-417"><span class="linenos">417</span></a><span class="sd">- `who` is a string that specifies the user name of the creator of the file.</span>
-</span><span id="L-418"><a href="#L-418"><span class="linenos">418</span></a><span class="sd">- `date` is a string and contains the creation date of the file.</span>
-</span><span id="L-419"><a href="#L-419"><span class="linenos">419</span></a><span class="sd">- `host` is a string and contains the hostname of the machine where the file has been written.</span>
-</span><span id="L-420"><a href="#L-420"><span class="linenos">420</span></a><span class="sd">- `description` contains information on the content of the file. This field is not filled automatically in `pyerrors`. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</span>
-</span><span id="L-421"><a href="#L-421"><span class="linenos">421</span></a>
-</span><span id="L-422"><a href="#L-422"><span class="linenos">422</span></a><span class="sd">The only necessary entry of the file is the field</span>
-</span><span id="L-423"><a href="#L-423"><span class="linenos">423</span></a><span class="sd">-`obsdata`, an array that contains the actual data.</span>
-</span><span id="L-424"><a href="#L-424"><span class="linenos">424</span></a>
-</span><span id="L-425"><a href="#L-425"><span class="linenos">425</span></a><span class="sd">Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of `Obs`, `list`, `numpy.ndarray`, `Corr`. All `Obs` inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array `obsdata`, are treated independently. Each entry of the array `obsdata` has the following required entries:</span>
-</span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a><span class="sd">- `type` is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</span>
-</span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a><span class="sd">- `value` is an array that contains the mean values of the Obs inside the structure.</span>
-</span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a><span class="sd">The following entries are optional:</span>
-</span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a><span class="sd">- `layout` is a string that specifies the layout of multi-dimensional structures. Examples are &quot;2, 2&quot; for a 2x2 dimensional matrix or  &quot;64, 4, 4&quot; for a Corr with $T=64$ and 4x4 matrices on each time slices. &quot;1&quot; denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</span>
-</span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a><span class="sd">- `tag` is any JSON type. It contains additional information concerning the structure. The `tag` of an `Obs` in `pyerrors` is written here.</span>
-</span><span id="L-431"><a href="#L-431"><span class="linenos">431</span></a><span class="sd">- `reweighted` is a Bool that may be used to specify, whether the `Obs` in the structure have been reweighted.</span>
-</span><span id="L-432"><a href="#L-432"><span class="linenos">432</span></a><span class="sd">- `data` is an array that contains the data from MC chains. We will define it below.</span>
-</span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a><span class="sd">- `cdata` is an array that contains the data from external quantities with an error (`Covobs` in `pyerrors`). We will define it below.</span>
-</span><span id="L-434"><a href="#L-434"><span class="linenos">434</span></a>
-</span><span id="L-435"><a href="#L-435"><span class="linenos">435</span></a><span class="sd">The array `data` contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</span>
-</span><span id="L-436"><a href="#L-436"><span class="linenos">436</span></a><span class="sd">- `id`, a string that contains the name of the ensemble</span>
-</span><span id="L-437"><a href="#L-437"><span class="linenos">437</span></a><span class="sd">- `replica`, an array that contains an entry per replica of the ensemble.</span>
-</span><span id="L-438"><a href="#L-438"><span class="linenos">438</span></a>
-</span><span id="L-439"><a href="#L-439"><span class="linenos">439</span></a><span class="sd">Each entry of `replica` contains</span>
-</span><span id="L-440"><a href="#L-440"><span class="linenos">440</span></a><span class="sd">`name`, a string that contains the name of the replica</span>
-</span><span id="L-441"><a href="#L-441"><span class="linenos">441</span></a><span class="sd">`deltas`, an array that contains the actual data.</span>
-</span><span id="L-442"><a href="#L-442"><span class="linenos">442</span></a>
-</span><span id="L-443"><a href="#L-443"><span class="linenos">443</span></a><span class="sd">Each entry in `deltas` corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each `Obs` inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</span>
-</span><span id="L-444"><a href="#L-444"><span class="linenos">444</span></a>
-</span><span id="L-445"><a href="#L-445"><span class="linenos">445</span></a><span class="sd">The array `cdata` contains information about the contribution of auxiliary observables, represented by `Covobs` in `pyerrors`, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</span>
-</span><span id="L-446"><a href="#L-446"><span class="linenos">446</span></a><span class="sd">- `id`, a string that identifies the covariance matrix</span>
-</span><span id="L-447"><a href="#L-447"><span class="linenos">447</span></a><span class="sd">- `layout`, a string that defines the dimensions of the $M\times M$ covariance matrix (has to be &quot;M, M&quot; or &quot;1&quot;).</span>
-</span><span id="L-448"><a href="#L-448"><span class="linenos">448</span></a><span class="sd">- `cov`, an array that contains the $M\times M$ many entries of the covariance matrix, stored in row-major format.</span>
-</span><span id="L-449"><a href="#L-449"><span class="linenos">449</span></a><span class="sd">- `grad`, an array that contains N entries, one for each `Obs` inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</span>
-</span><span id="L-450"><a href="#L-450"><span class="linenos">450</span></a>
-</span><span id="L-451"><a href="#L-451"><span class="linenos">451</span></a><span class="sd">A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</span>
-</span><span id="L-452"><a href="#L-452"><span class="linenos">452</span></a>
-</span><span id="L-453"><a href="#L-453"><span class="linenos">453</span></a><span class="sd">Julia I/O routines for the json.gz format, compatible with [ADerrors.jl](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl), can be found [here](https://github.com/fjosw/ADjson.jl).</span>
-</span><span id="L-454"><a href="#L-454"><span class="linenos">454</span></a><span class="sd">&#39;&#39;&#39;</span>
-</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a><span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="o">*</span>
-</span><span id="L-456"><a href="#L-456"><span class="linenos">456</span></a><span class="kn">from</span> <span class="nn">.correlators</span> <span class="kn">import</span> <span class="o">*</span>
-</span><span id="L-457"><a href="#L-457"><span class="linenos">457</span></a><span class="kn">from</span> <span class="nn">.fits</span> <span class="kn">import</span> <span class="o">*</span>
-</span><span id="L-458"><a href="#L-458"><span class="linenos">458</span></a><span class="kn">from</span> <span class="nn">.misc</span> <span class="kn">import</span> <span class="o">*</span>
-</span><span id="L-459"><a href="#L-459"><span class="linenos">459</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">dirac</span>
-</span><span id="L-460"><a href="#L-460"><span class="linenos">460</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="nb">input</span>
-</span><span id="L-461"><a href="#L-461"><span class="linenos">461</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span>
-</span><span id="L-462"><a href="#L-462"><span class="linenos">462</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">mpm</span>
-</span><span id="L-463"><a href="#L-463"><span class="linenos">463</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">roots</span>
-</span><span id="L-464"><a href="#L-464"><span class="linenos">464</span></a>
-</span><span id="L-465"><a href="#L-465"><span class="linenos">465</span></a><span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">__version__</span>
+</span><span id="L-174"><a href="#L-174"><span class="linenos">174</span></a>
+</span><span id="L-175"><a href="#L-175"><span class="linenos">175</span></a><span class="sd">## Irregular Monte Carlo chains</span>
+</span><span id="L-176"><a href="#L-176"><span class="linenos">176</span></a>
+</span><span id="L-177"><a href="#L-177"><span class="linenos">177</span></a><span class="sd">`Obs` objects defined on irregular Monte Carlo chains can be initialized with the parameter `idl`.</span>
+</span><span id="L-178"><a href="#L-178"><span class="linenos">178</span></a>
+</span><span id="L-179"><a href="#L-179"><span class="linenos">179</span></a><span class="sd">```python</span>
+</span><span id="L-180"><a href="#L-180"><span class="linenos">180</span></a><span class="sd"># Observable defined on configurations 20 to 519</span>
+</span><span id="L-181"><a href="#L-181"><span class="linenos">181</span></a><span class="sd">obs1 = pe.Obs([samples1], [&#39;ensemble1&#39;], idl=[range(20, 520)])</span>
+</span><span id="L-182"><a href="#L-182"><span class="linenos">182</span></a><span class="sd">obs1.details()</span>
+</span><span id="L-183"><a href="#L-183"><span class="linenos">183</span></a><span class="sd">&gt; Result	 9.98319881e-01</span>
+</span><span id="L-184"><a href="#L-184"><span class="linenos">184</span></a><span class="sd">&gt; 500 samples in 1 ensemble:</span>
+</span><span id="L-185"><a href="#L-185"><span class="linenos">185</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 500 configurations (from 20 to 519)</span>
+</span><span id="L-186"><a href="#L-186"><span class="linenos">186</span></a>
+</span><span id="L-187"><a href="#L-187"><span class="linenos">187</span></a><span class="sd"># Observable defined on every second configuration between 5 and 1003</span>
+</span><span id="L-188"><a href="#L-188"><span class="linenos">188</span></a><span class="sd">obs2 = pe.Obs([samples2], [&#39;ensemble1&#39;], idl=[range(5, 1005, 2)])</span>
+</span><span id="L-189"><a href="#L-189"><span class="linenos">189</span></a><span class="sd">obs2.details()</span>
+</span><span id="L-190"><a href="#L-190"><span class="linenos">190</span></a><span class="sd">&gt; Result	 9.99100712e-01</span>
+</span><span id="L-191"><a href="#L-191"><span class="linenos">191</span></a><span class="sd">&gt; 500 samples in 1 ensemble:</span>
+</span><span id="L-192"><a href="#L-192"><span class="linenos">192</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 500 configurations (from 5 to 1003 in steps of 2)</span>
+</span><span id="L-193"><a href="#L-193"><span class="linenos">193</span></a>
+</span><span id="L-194"><a href="#L-194"><span class="linenos">194</span></a><span class="sd"># Observable defined on configurations 2, 9, 28, 29 and 501</span>
+</span><span id="L-195"><a href="#L-195"><span class="linenos">195</span></a><span class="sd">obs3 = pe.Obs([samples3], [&#39;ensemble1&#39;], idl=[[2, 9, 28, 29, 501]])</span>
+</span><span id="L-196"><a href="#L-196"><span class="linenos">196</span></a><span class="sd">obs3.details()</span>
+</span><span id="L-197"><a href="#L-197"><span class="linenos">197</span></a><span class="sd">&gt; Result	 1.01718064e+00</span>
+</span><span id="L-198"><a href="#L-198"><span class="linenos">198</span></a><span class="sd">&gt; 5 samples in 1 ensemble:</span>
+</span><span id="L-199"><a href="#L-199"><span class="linenos">199</span></a><span class="sd">&gt;   · Ensemble &#39;ensemble1&#39; : 5 configurations (irregular range)</span>
+</span><span id="L-200"><a href="#L-200"><span class="linenos">200</span></a>
+</span><span id="L-201"><a href="#L-201"><span class="linenos">201</span></a><span class="sd">```</span>
+</span><span id="L-202"><a href="#L-202"><span class="linenos">202</span></a>
+</span><span id="L-203"><a href="#L-203"><span class="linenos">203</span></a><span class="sd">`Obs` objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</span>
+</span><span id="L-204"><a href="#L-204"><span class="linenos">204</span></a>
+</span><span id="L-205"><a href="#L-205"><span class="linenos">205</span></a><span class="sd">**Warning:** Irregular Monte Carlo chains can result in odd patterns in the autocorrelation functions.</span>
+</span><span id="L-206"><a href="#L-206"><span class="linenos">206</span></a><span class="sd">Make sure to check the autocorrelation time with e.g. `pyerrors.obs.Obs.plot_rho` or `pyerrors.obs.Obs.plot_tauint`.</span>
+</span><span id="L-207"><a href="#L-207"><span class="linenos">207</span></a>
+</span><span id="L-208"><a href="#L-208"><span class="linenos">208</span></a><span class="sd">For the full API see `pyerrors.obs.Obs`.</span>
+</span><span id="L-209"><a href="#L-209"><span class="linenos">209</span></a>
+</span><span id="L-210"><a href="#L-210"><span class="linenos">210</span></a><span class="sd"># Correlators</span>
+</span><span id="L-211"><a href="#L-211"><span class="linenos">211</span></a><span class="sd">When one is not interested in single observables but correlation functions, `pyerrors` offers the `Corr` class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a `Corr` objects one needs to arrange the data as a list of `Obs`</span>
+</span><span id="L-212"><a href="#L-212"><span class="linenos">212</span></a><span class="sd">```python</span>
+</span><span id="L-213"><a href="#L-213"><span class="linenos">213</span></a><span class="sd">my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3])</span>
+</span><span id="L-214"><a href="#L-214"><span class="linenos">214</span></a><span class="sd">print(my_corr)</span>
+</span><span id="L-215"><a href="#L-215"><span class="linenos">215</span></a><span class="sd">&gt; x0/a	Corr(x0/a)</span>
+</span><span id="L-216"><a href="#L-216"><span class="linenos">216</span></a><span class="sd">&gt; ------------------</span>
+</span><span id="L-217"><a href="#L-217"><span class="linenos">217</span></a><span class="sd">&gt; 0	 0.7957(80)</span>
+</span><span id="L-218"><a href="#L-218"><span class="linenos">218</span></a><span class="sd">&gt; 1	 0.5156(51)</span>
+</span><span id="L-219"><a href="#L-219"><span class="linenos">219</span></a><span class="sd">&gt; 2	 0.3227(33)</span>
+</span><span id="L-220"><a href="#L-220"><span class="linenos">220</span></a><span class="sd">&gt; 3	 0.2041(21)</span>
+</span><span id="L-221"><a href="#L-221"><span class="linenos">221</span></a><span class="sd">```</span>
+</span><span id="L-222"><a href="#L-222"><span class="linenos">222</span></a><span class="sd">In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</span>
+</span><span id="L-223"><a href="#L-223"><span class="linenos">223</span></a><span class="sd">```python</span>
+</span><span id="L-224"><a href="#L-224"><span class="linenos">224</span></a><span class="sd">my_corr = pe.Corr([obs_0, obs_1, obs_2, obs_3], padding=[1, 1])</span>
+</span><span id="L-225"><a href="#L-225"><span class="linenos">225</span></a><span class="sd">print(my_corr)</span>
+</span><span id="L-226"><a href="#L-226"><span class="linenos">226</span></a><span class="sd">&gt; x0/a	Corr(x0/a)</span>
+</span><span id="L-227"><a href="#L-227"><span class="linenos">227</span></a><span class="sd">&gt; ------------------</span>
+</span><span id="L-228"><a href="#L-228"><span class="linenos">228</span></a><span class="sd">&gt; 0</span>
+</span><span id="L-229"><a href="#L-229"><span class="linenos">229</span></a><span class="sd">&gt; 1	 0.7957(80)</span>
+</span><span id="L-230"><a href="#L-230"><span class="linenos">230</span></a><span class="sd">&gt; 2	 0.5156(51)</span>
+</span><span id="L-231"><a href="#L-231"><span class="linenos">231</span></a><span class="sd">&gt; 3	 0.3227(33)</span>
+</span><span id="L-232"><a href="#L-232"><span class="linenos">232</span></a><span class="sd">&gt; 4	 0.2041(21)</span>
+</span><span id="L-233"><a href="#L-233"><span class="linenos">233</span></a><span class="sd">&gt; 5</span>
+</span><span id="L-234"><a href="#L-234"><span class="linenos">234</span></a><span class="sd">```</span>
+</span><span id="L-235"><a href="#L-235"><span class="linenos">235</span></a><span class="sd">The individual entries of a correlator can be accessed via slicing</span>
+</span><span id="L-236"><a href="#L-236"><span class="linenos">236</span></a><span class="sd">```python</span>
+</span><span id="L-237"><a href="#L-237"><span class="linenos">237</span></a><span class="sd">print(my_corr[3])</span>
+</span><span id="L-238"><a href="#L-238"><span class="linenos">238</span></a><span class="sd">&gt; 0.3227(33)</span>
+</span><span id="L-239"><a href="#L-239"><span class="linenos">239</span></a><span class="sd">```</span>
+</span><span id="L-240"><a href="#L-240"><span class="linenos">240</span></a><span class="sd">Error propagation with the `Corr` class works very similar to `Obs` objects. Mathematical operations are overloaded and `Corr` objects can be computed together with other `Corr` objects, `Obs` objects or real numbers and integers.</span>
+</span><span id="L-241"><a href="#L-241"><span class="linenos">241</span></a><span class="sd">```python</span>
+</span><span id="L-242"><a href="#L-242"><span class="linenos">242</span></a><span class="sd">my_new_corr = 0.3 * my_corr[2] * my_corr * my_corr + 12 / my_corr</span>
+</span><span id="L-243"><a href="#L-243"><span class="linenos">243</span></a><span class="sd">```</span>
+</span><span id="L-244"><a href="#L-244"><span class="linenos">244</span></a>
+</span><span id="L-245"><a href="#L-245"><span class="linenos">245</span></a><span class="sd">`pyerrors` provides the user with a set of regularly used methods for the manipulation of correlator objects:</span>
+</span><span id="L-246"><a href="#L-246"><span class="linenos">246</span></a><span class="sd">- `Corr.gamma_method` applies the gamma method to all entries of the correlator.</span>
+</span><span id="L-247"><a href="#L-247"><span class="linenos">247</span></a><span class="sd">- `Corr.m_eff` to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</span>
+</span><span id="L-248"><a href="#L-248"><span class="linenos">248</span></a><span class="sd">- `Corr.deriv` returns the first derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available.</span>
+</span><span id="L-249"><a href="#L-249"><span class="linenos">249</span></a><span class="sd">- `Corr.second_deriv` returns the second derivative of the correlator as `Corr`. Different discretizations of the numerical derivative are available.</span>
+</span><span id="L-250"><a href="#L-250"><span class="linenos">250</span></a><span class="sd">- `Corr.symmetric` symmetrizes parity even correlations functions, assuming periodic boundary conditions.</span>
+</span><span id="L-251"><a href="#L-251"><span class="linenos">251</span></a><span class="sd">- `Corr.anti_symmetric` anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</span>
+</span><span id="L-252"><a href="#L-252"><span class="linenos">252</span></a><span class="sd">- `Corr.T_symmetry` averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</span>
+</span><span id="L-253"><a href="#L-253"><span class="linenos">253</span></a><span class="sd">- `Corr.plateau` extracts a plateau value from the correlator in a given range.</span>
+</span><span id="L-254"><a href="#L-254"><span class="linenos">254</span></a><span class="sd">- `Corr.roll` periodically shifts the correlator.</span>
+</span><span id="L-255"><a href="#L-255"><span class="linenos">255</span></a><span class="sd">- `Corr.reverse` reverses the time ordering of the correlator.</span>
+</span><span id="L-256"><a href="#L-256"><span class="linenos">256</span></a><span class="sd">- `Corr.correlate` constructs a disconnected correlation function from the correlator and another `Corr` or `Obs` object.</span>
+</span><span id="L-257"><a href="#L-257"><span class="linenos">257</span></a><span class="sd">- `Corr.reweight` reweights the correlator.</span>
+</span><span id="L-258"><a href="#L-258"><span class="linenos">258</span></a>
+</span><span id="L-259"><a href="#L-259"><span class="linenos">259</span></a><span class="sd">`pyerrors` can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see `pyerrors.correlators.Corr.GEVP`).</span>
+</span><span id="L-260"><a href="#L-260"><span class="linenos">260</span></a>
+</span><span id="L-261"><a href="#L-261"><span class="linenos">261</span></a><span class="sd">For the full API see `pyerrors.correlators.Corr`.</span>
+</span><span id="L-262"><a href="#L-262"><span class="linenos">262</span></a>
+</span><span id="L-263"><a href="#L-263"><span class="linenos">263</span></a><span class="sd"># Complex valued observables</span>
+</span><span id="L-264"><a href="#L-264"><span class="linenos">264</span></a>
+</span><span id="L-265"><a href="#L-265"><span class="linenos">265</span></a><span class="sd">`pyerrors` can handle complex valued observables via the class `pyerrors.obs.CObs`.</span>
+</span><span id="L-266"><a href="#L-266"><span class="linenos">266</span></a><span class="sd">`CObs` are initialized with a real and an imaginary part which both can be `Obs` valued.</span>
+</span><span id="L-267"><a href="#L-267"><span class="linenos">267</span></a>
+</span><span id="L-268"><a href="#L-268"><span class="linenos">268</span></a><span class="sd">```python</span>
+</span><span id="L-269"><a href="#L-269"><span class="linenos">269</span></a><span class="sd">my_real_part = pe.Obs([samples1], [&#39;ensemble1&#39;])</span>
+</span><span id="L-270"><a href="#L-270"><span class="linenos">270</span></a><span class="sd">my_imag_part = pe.Obs([samples2], [&#39;ensemble1&#39;])</span>
+</span><span id="L-271"><a href="#L-271"><span class="linenos">271</span></a>
+</span><span id="L-272"><a href="#L-272"><span class="linenos">272</span></a><span class="sd">my_cobs = pe.CObs(my_real_part, my_imag_part)</span>
+</span><span id="L-273"><a href="#L-273"><span class="linenos">273</span></a><span class="sd">my_cobs.gamma_method()</span>
+</span><span id="L-274"><a href="#L-274"><span class="linenos">274</span></a><span class="sd">print(my_cobs)</span>
+</span><span id="L-275"><a href="#L-275"><span class="linenos">275</span></a><span class="sd">&gt; (0.9959(91)+0.659(28)j)</span>
+</span><span id="L-276"><a href="#L-276"><span class="linenos">276</span></a><span class="sd">```</span>
+</span><span id="L-277"><a href="#L-277"><span class="linenos">277</span></a>
+</span><span id="L-278"><a href="#L-278"><span class="linenos">278</span></a><span class="sd">Elementary mathematical operations are overloaded and samples are properly propagated as for the `Obs` class.</span>
+</span><span id="L-279"><a href="#L-279"><span class="linenos">279</span></a><span class="sd">```python</span>
+</span><span id="L-280"><a href="#L-280"><span class="linenos">280</span></a><span class="sd">my_derived_cobs = (my_cobs + my_cobs.conjugate()) / np.abs(my_cobs)</span>
+</span><span id="L-281"><a href="#L-281"><span class="linenos">281</span></a><span class="sd">my_derived_cobs.gamma_method()</span>
+</span><span id="L-282"><a href="#L-282"><span class="linenos">282</span></a><span class="sd">print(my_derived_cobs)</span>
+</span><span id="L-283"><a href="#L-283"><span class="linenos">283</span></a><span class="sd">&gt; (1.668(23)+0.0j)</span>
+</span><span id="L-284"><a href="#L-284"><span class="linenos">284</span></a><span class="sd">```</span>
+</span><span id="L-285"><a href="#L-285"><span class="linenos">285</span></a>
+</span><span id="L-286"><a href="#L-286"><span class="linenos">286</span></a><span class="sd"># The `Covobs` class</span>
+</span><span id="L-287"><a href="#L-287"><span class="linenos">287</span></a><span class="sd">In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The `Covobs` class allows to define such quantities in `pyerrors`. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</span>
+</span><span id="L-288"><a href="#L-288"><span class="linenos">288</span></a>
+</span><span id="L-289"><a href="#L-289"><span class="linenos">289</span></a><span class="sd">This concept is built into the definition of `Covobs`. In `pyerrors`, external input is defined by $M$ mean values, a $M\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters `cov_Obs`, since the second argument of this function is the covariance matrix of the `Covobs`.</span>
+</span><span id="L-290"><a href="#L-290"><span class="linenos">290</span></a>
+</span><span id="L-291"><a href="#L-291"><span class="linenos">291</span></a><span class="sd">```python</span>
+</span><span id="L-292"><a href="#L-292"><span class="linenos">292</span></a><span class="sd">import pyerrors.obs as pe</span>
+</span><span id="L-293"><a href="#L-293"><span class="linenos">293</span></a>
+</span><span id="L-294"><a href="#L-294"><span class="linenos">294</span></a><span class="sd">mpi = pe.cov_Obs(134.9768, 0.0005**2, &#39;pi^0 mass&#39;)</span>
+</span><span id="L-295"><a href="#L-295"><span class="linenos">295</span></a><span class="sd">mpi.gamma_method()</span>
+</span><span id="L-296"><a href="#L-296"><span class="linenos">296</span></a><span class="sd">mpi.details()</span>
+</span><span id="L-297"><a href="#L-297"><span class="linenos">297</span></a><span class="sd">&gt; Result	 1.34976800e+02 +/- 5.00000000e-04 +/- 0.00000000e+00 (0.000%)</span>
+</span><span id="L-298"><a href="#L-298"><span class="linenos">298</span></a><span class="sd">&gt;  pi^0 mass 	 5.00000000e-04</span>
+</span><span id="L-299"><a href="#L-299"><span class="linenos">299</span></a><span class="sd">&gt; 0 samples in 1 ensemble:</span>
+</span><span id="L-300"><a href="#L-300"><span class="linenos">300</span></a><span class="sd">&gt;   · Covobs   &#39;pi^0 mass&#39;</span>
+</span><span id="L-301"><a href="#L-301"><span class="linenos">301</span></a><span class="sd">```</span>
+</span><span id="L-302"><a href="#L-302"><span class="linenos">302</span></a><span class="sd">The resulting object `mpi` is an `Obs` that contains a `Covobs`. In the following, it may be handled as any other `Obs`. The contribution of the covariance matrix to the error of an `Obs` is determined from the $M \times M$ covariance matrix $\Sigma$ and the gradient of the `Obs` with respect to the external quantities, which is the $1\times M$ Jacobian matrix $J$, via</span>
+</span><span id="L-303"><a href="#L-303"><span class="linenos">303</span></a><span class="sd">$$s = \sqrt{J^T \Sigma J}\,,$$</span>
+</span><span id="L-304"><a href="#L-304"><span class="linenos">304</span></a><span class="sd">where the Jacobian is computed for each derived quantity via automatic differentiation.</span>
+</span><span id="L-305"><a href="#L-305"><span class="linenos">305</span></a>
+</span><span id="L-306"><a href="#L-306"><span class="linenos">306</span></a><span class="sd">Correlated auxiliary data is defined similarly to above, e.g., via</span>
+</span><span id="L-307"><a href="#L-307"><span class="linenos">307</span></a><span class="sd">```python</span>
+</span><span id="L-308"><a href="#L-308"><span class="linenos">308</span></a><span class="sd">RAP = pe.cov_Obs([16.7457, -19.0475], [[3.49591, -6.07560], [-6.07560, 10.5834]], &#39;R_AP, 1906.03445, (5.3a)&#39;)</span>
+</span><span id="L-309"><a href="#L-309"><span class="linenos">309</span></a><span class="sd">print(RAP)</span>
+</span><span id="L-310"><a href="#L-310"><span class="linenos">310</span></a><span class="sd">&gt; [Obs[16.7(1.9)], Obs[-19.0(3.3)]]</span>
+</span><span id="L-311"><a href="#L-311"><span class="linenos">311</span></a><span class="sd">```</span>
+</span><span id="L-312"><a href="#L-312"><span class="linenos">312</span></a><span class="sd">where `RAP` now is a list of two `Obs` that contains the two correlated parameters.</span>
+</span><span id="L-313"><a href="#L-313"><span class="linenos">313</span></a>
+</span><span id="L-314"><a href="#L-314"><span class="linenos">314</span></a><span class="sd">Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the `Covobs` class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an `Obs` `o` with respect to a covariance matrix with the identifying string `k` may be accessed via</span>
+</span><span id="L-315"><a href="#L-315"><span class="linenos">315</span></a><span class="sd">```python</span>
+</span><span id="L-316"><a href="#L-316"><span class="linenos">316</span></a><span class="sd">o.covobs[k].grad</span>
+</span><span id="L-317"><a href="#L-317"><span class="linenos">317</span></a><span class="sd">```</span>
+</span><span id="L-318"><a href="#L-318"><span class="linenos">318</span></a>
+</span><span id="L-319"><a href="#L-319"><span class="linenos">319</span></a><span class="sd"># Error propagation in iterative algorithms</span>
+</span><span id="L-320"><a href="#L-320"><span class="linenos">320</span></a>
+</span><span id="L-321"><a href="#L-321"><span class="linenos">321</span></a><span class="sd">`pyerrors` supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in [arXiv:1809.01289](https://arxiv.org/abs/1809.01289).</span>
+</span><span id="L-322"><a href="#L-322"><span class="linenos">322</span></a>
+</span><span id="L-323"><a href="#L-323"><span class="linenos">323</span></a><span class="sd">## Least squares fits</span>
+</span><span id="L-324"><a href="#L-324"><span class="linenos">324</span></a>
+</span><span id="L-325"><a href="#L-325"><span class="linenos">325</span></a><span class="sd">Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with `pyerrors.fits.least_squares`. As default solver the Levenberg-Marquardt algorithm implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html) is used.</span>
+</span><span id="L-326"><a href="#L-326"><span class="linenos">326</span></a>
+</span><span id="L-327"><a href="#L-327"><span class="linenos">327</span></a><span class="sd">Fit functions have to be of the following form</span>
+</span><span id="L-328"><a href="#L-328"><span class="linenos">328</span></a><span class="sd">```python</span>
+</span><span id="L-329"><a href="#L-329"><span class="linenos">329</span></a><span class="sd">import autograd.numpy as anp</span>
+</span><span id="L-330"><a href="#L-330"><span class="linenos">330</span></a>
+</span><span id="L-331"><a href="#L-331"><span class="linenos">331</span></a><span class="sd">def func(a, x):</span>
+</span><span id="L-332"><a href="#L-332"><span class="linenos">332</span></a><span class="sd">    return a[1] * anp.exp(-a[0] * x)</span>
+</span><span id="L-333"><a href="#L-333"><span class="linenos">333</span></a><span class="sd">```</span>
+</span><span id="L-334"><a href="#L-334"><span class="linenos">334</span></a><span class="sd">**It is important that numerical functions refer to `autograd.numpy` instead of `numpy` for the automatic differentiation in iterative algorithms to work properly.**</span>
+</span><span id="L-335"><a href="#L-335"><span class="linenos">335</span></a>
+</span><span id="L-336"><a href="#L-336"><span class="linenos">336</span></a><span class="sd">Fits can then be performed via</span>
+</span><span id="L-337"><a href="#L-337"><span class="linenos">337</span></a><span class="sd">```python</span>
+</span><span id="L-338"><a href="#L-338"><span class="linenos">338</span></a><span class="sd">fit_result = pe.fits.least_squares(x, y, func)</span>
+</span><span id="L-339"><a href="#L-339"><span class="linenos">339</span></a><span class="sd">print(&quot;\n&quot;, fit_result)</span>
+</span><span id="L-340"><a href="#L-340"><span class="linenos">340</span></a><span class="sd">&gt; Fit with 2 parameters</span>
+</span><span id="L-341"><a href="#L-341"><span class="linenos">341</span></a><span class="sd">&gt; Method: Levenberg-Marquardt</span>
+</span><span id="L-342"><a href="#L-342"><span class="linenos">342</span></a><span class="sd">&gt; `ftol` termination condition is satisfied.</span>
+</span><span id="L-343"><a href="#L-343"><span class="linenos">343</span></a><span class="sd">&gt; chisquare/d.o.f.: 0.9593035785160936</span>
+</span><span id="L-344"><a href="#L-344"><span class="linenos">344</span></a>
+</span><span id="L-345"><a href="#L-345"><span class="linenos">345</span></a><span class="sd">&gt;  Goodness of fit:</span>
+</span><span id="L-346"><a href="#L-346"><span class="linenos">346</span></a><span class="sd">&gt; χ²/d.o.f. = 0.959304</span>
+</span><span id="L-347"><a href="#L-347"><span class="linenos">347</span></a><span class="sd">&gt; p-value   = 0.5673</span>
+</span><span id="L-348"><a href="#L-348"><span class="linenos">348</span></a><span class="sd">&gt; Fit parameters:</span>
+</span><span id="L-349"><a href="#L-349"><span class="linenos">349</span></a><span class="sd">&gt; 0	 0.0548(28)</span>
+</span><span id="L-350"><a href="#L-350"><span class="linenos">350</span></a><span class="sd">&gt; 1	 1.933(64)</span>
+</span><span id="L-351"><a href="#L-351"><span class="linenos">351</span></a><span class="sd">```</span>
+</span><span id="L-352"><a href="#L-352"><span class="linenos">352</span></a><span class="sd">where x is a `list` or `numpy.array` of `floats` and y is a `list` or `numpy.array` of `Obs`.</span>
+</span><span id="L-353"><a href="#L-353"><span class="linenos">353</span></a>
+</span><span id="L-354"><a href="#L-354"><span class="linenos">354</span></a><span class="sd">Data stored in `Corr` objects can be fitted directly using the `Corr.fit` method.</span>
+</span><span id="L-355"><a href="#L-355"><span class="linenos">355</span></a><span class="sd">```python</span>
+</span><span id="L-356"><a href="#L-356"><span class="linenos">356</span></a><span class="sd">my_corr = pe.Corr(y)</span>
+</span><span id="L-357"><a href="#L-357"><span class="linenos">357</span></a><span class="sd">fit_result = my_corr.fit(func, fitrange=[12, 25])</span>
+</span><span id="L-358"><a href="#L-358"><span class="linenos">358</span></a><span class="sd">```</span>
+</span><span id="L-359"><a href="#L-359"><span class="linenos">359</span></a><span class="sd">this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</span>
+</span><span id="L-360"><a href="#L-360"><span class="linenos">360</span></a>
+</span><span id="L-361"><a href="#L-361"><span class="linenos">361</span></a><span class="sd">For fit functions with multiple independent variables the fit function can be of the form</span>
+</span><span id="L-362"><a href="#L-362"><span class="linenos">362</span></a>
+</span><span id="L-363"><a href="#L-363"><span class="linenos">363</span></a><span class="sd">```python</span>
+</span><span id="L-364"><a href="#L-364"><span class="linenos">364</span></a><span class="sd">def func(a, x):</span>
+</span><span id="L-365"><a href="#L-365"><span class="linenos">365</span></a><span class="sd">    (x1, x2) = x</span>
+</span><span id="L-366"><a href="#L-366"><span class="linenos">366</span></a><span class="sd">    return a[0] * x1 ** 2 + a[1] * x2</span>
+</span><span id="L-367"><a href="#L-367"><span class="linenos">367</span></a><span class="sd">```</span>
+</span><span id="L-368"><a href="#L-368"><span class="linenos">368</span></a>
+</span><span id="L-369"><a href="#L-369"><span class="linenos">369</span></a><span class="sd">`pyerrors` also supports correlated fits which can be triggered via the parameter `correlated_fit=True`.</span>
+</span><span id="L-370"><a href="#L-370"><span class="linenos">370</span></a><span class="sd">Details about how the required covariance matrix is estimated can be found in `pyerrors.obs.covariance`.</span>
+</span><span id="L-371"><a href="#L-371"><span class="linenos">371</span></a>
+</span><span id="L-372"><a href="#L-372"><span class="linenos">372</span></a><span class="sd">Direct visualizations of the performed fits can be triggered via `resplot=True` or `qqplot=True`. For all available options see `pyerrors.fits.least_squares`.</span>
+</span><span id="L-373"><a href="#L-373"><span class="linenos">373</span></a>
+</span><span id="L-374"><a href="#L-374"><span class="linenos">374</span></a><span class="sd">## Total least squares fits</span>
+</span><span id="L-375"><a href="#L-375"><span class="linenos">375</span></a><span class="sd">`pyerrors` can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in [scipy](https://docs.scipy.org/doc/scipy/reference/odr.html), see `pyerrors.fits.least_squares`. The syntax is identical to the standard least squares case, the only difference being that `x` also has to be a `list` or `numpy.array` of `Obs`.</span>
+</span><span id="L-376"><a href="#L-376"><span class="linenos">376</span></a>
+</span><span id="L-377"><a href="#L-377"><span class="linenos">377</span></a><span class="sd">For the full API see `pyerrors.fits` for fits and `pyerrors.roots` for finding roots of functions.</span>
+</span><span id="L-378"><a href="#L-378"><span class="linenos">378</span></a>
+</span><span id="L-379"><a href="#L-379"><span class="linenos">379</span></a><span class="sd"># Matrix operations</span>
+</span><span id="L-380"><a href="#L-380"><span class="linenos">380</span></a><span class="sd">`pyerrors` provides wrappers for `Obs`- and `CObs`-valued matrix operations based on `numpy.linalg`. The supported functions include:</span>
+</span><span id="L-381"><a href="#L-381"><span class="linenos">381</span></a><span class="sd">- `inv` for the matrix inverse.</span>
+</span><span id="L-382"><a href="#L-382"><span class="linenos">382</span></a><span class="sd">- `cholseky` for the Cholesky decomposition.</span>
+</span><span id="L-383"><a href="#L-383"><span class="linenos">383</span></a><span class="sd">- `det` for the matrix determinant.</span>
+</span><span id="L-384"><a href="#L-384"><span class="linenos">384</span></a><span class="sd">- `eigh` for eigenvalues and eigenvectors of hermitean matrices.</span>
+</span><span id="L-385"><a href="#L-385"><span class="linenos">385</span></a><span class="sd">- `eig` for eigenvalues of general matrices.</span>
+</span><span id="L-386"><a href="#L-386"><span class="linenos">386</span></a><span class="sd">- `pinv` for the Moore-Penrose pseudoinverse.</span>
+</span><span id="L-387"><a href="#L-387"><span class="linenos">387</span></a><span class="sd">- `svd` for the singular-value-decomposition.</span>
+</span><span id="L-388"><a href="#L-388"><span class="linenos">388</span></a>
+</span><span id="L-389"><a href="#L-389"><span class="linenos">389</span></a><span class="sd">For the full API see `pyerrors.linalg`.</span>
+</span><span id="L-390"><a href="#L-390"><span class="linenos">390</span></a>
+</span><span id="L-391"><a href="#L-391"><span class="linenos">391</span></a><span class="sd"># Export data</span>
+</span><span id="L-392"><a href="#L-392"><span class="linenos">392</span></a>
+</span><span id="L-393"><a href="#L-393"><span class="linenos">393</span></a><span class="sd">The preferred exported file format within `pyerrors` is json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</span>
+</span><span id="L-394"><a href="#L-394"><span class="linenos">394</span></a><span class="sd">- What observables are stored? Possibly: How exactly are they defined.</span>
+</span><span id="L-395"><a href="#L-395"><span class="linenos">395</span></a><span class="sd">- How does each single ensemble or external quantity contribute to the error of the observable?</span>
+</span><span id="L-396"><a href="#L-396"><span class="linenos">396</span></a><span class="sd">- Who did write the file when and on which machine?</span>
+</span><span id="L-397"><a href="#L-397"><span class="linenos">397</span></a>
+</span><span id="L-398"><a href="#L-398"><span class="linenos">398</span></a><span class="sd">This can be achieved by storing all information in one single file. The export routines of `pyerrors` are written such that as much information as possible is written automatically as described in the following example</span>
+</span><span id="L-399"><a href="#L-399"><span class="linenos">399</span></a><span class="sd">```python</span>
+</span><span id="L-400"><a href="#L-400"><span class="linenos">400</span></a><span class="sd">my_obs = pe.Obs([samples], [&quot;test_ensemble&quot;])</span>
+</span><span id="L-401"><a href="#L-401"><span class="linenos">401</span></a><span class="sd">my_obs.tag = &quot;My observable&quot;</span>
+</span><span id="L-402"><a href="#L-402"><span class="linenos">402</span></a>
+</span><span id="L-403"><a href="#L-403"><span class="linenos">403</span></a><span class="sd">pe.input.json.dump_to_json(my_obs, &quot;test_output_file&quot;, description=&quot;This file contains a test observable&quot;)</span>
+</span><span id="L-404"><a href="#L-404"><span class="linenos">404</span></a><span class="sd"># For a single observable one can equivalently use the class method dump</span>
+</span><span id="L-405"><a href="#L-405"><span class="linenos">405</span></a><span class="sd">my_obs.dump(&quot;test_output_file&quot;, description=&quot;This file contains a test observable&quot;)</span>
+</span><span id="L-406"><a href="#L-406"><span class="linenos">406</span></a>
+</span><span id="L-407"><a href="#L-407"><span class="linenos">407</span></a><span class="sd">check = pe.input.json.load_json(&quot;test_output_file&quot;)</span>
+</span><span id="L-408"><a href="#L-408"><span class="linenos">408</span></a>
+</span><span id="L-409"><a href="#L-409"><span class="linenos">409</span></a><span class="sd">print(my_obs == check)</span>
+</span><span id="L-410"><a href="#L-410"><span class="linenos">410</span></a><span class="sd">&gt; True</span>
+</span><span id="L-411"><a href="#L-411"><span class="linenos">411</span></a><span class="sd">```</span>
+</span><span id="L-412"><a href="#L-412"><span class="linenos">412</span></a><span class="sd">The format also allows to directly write out the content of `Corr` objects or lists and arrays of `Obs` objects by passing the desired data to `pyerrors.input.json.dump_to_json`.</span>
+</span><span id="L-413"><a href="#L-413"><span class="linenos">413</span></a>
+</span><span id="L-414"><a href="#L-414"><span class="linenos">414</span></a><span class="sd">## json.gz format specification</span>
+</span><span id="L-415"><a href="#L-415"><span class="linenos">415</span></a><span class="sd">The first entries of the file provide optional auxiliary information:</span>
+</span><span id="L-416"><a href="#L-416"><span class="linenos">416</span></a><span class="sd">- `program` is a string that indicates which program was used to write the file.</span>
+</span><span id="L-417"><a href="#L-417"><span class="linenos">417</span></a><span class="sd">- `version` is a string that specifies the version of the format.</span>
+</span><span id="L-418"><a href="#L-418"><span class="linenos">418</span></a><span class="sd">- `who` is a string that specifies the user name of the creator of the file.</span>
+</span><span id="L-419"><a href="#L-419"><span class="linenos">419</span></a><span class="sd">- `date` is a string and contains the creation date of the file.</span>
+</span><span id="L-420"><a href="#L-420"><span class="linenos">420</span></a><span class="sd">- `host` is a string and contains the hostname of the machine where the file has been written.</span>
+</span><span id="L-421"><a href="#L-421"><span class="linenos">421</span></a><span class="sd">- `description` contains information on the content of the file. This field is not filled automatically in `pyerrors`. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</span>
+</span><span id="L-422"><a href="#L-422"><span class="linenos">422</span></a>
+</span><span id="L-423"><a href="#L-423"><span class="linenos">423</span></a><span class="sd">The only necessary entry of the file is the field</span>
+</span><span id="L-424"><a href="#L-424"><span class="linenos">424</span></a><span class="sd">-`obsdata`, an array that contains the actual data.</span>
+</span><span id="L-425"><a href="#L-425"><span class="linenos">425</span></a>
+</span><span id="L-426"><a href="#L-426"><span class="linenos">426</span></a><span class="sd">Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of `Obs`, `list`, `numpy.ndarray`, `Corr`. All `Obs` inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array `obsdata`, are treated independently. Each entry of the array `obsdata` has the following required entries:</span>
+</span><span id="L-427"><a href="#L-427"><span class="linenos">427</span></a><span class="sd">- `type` is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</span>
+</span><span id="L-428"><a href="#L-428"><span class="linenos">428</span></a><span class="sd">- `value` is an array that contains the mean values of the Obs inside the structure.</span>
+</span><span id="L-429"><a href="#L-429"><span class="linenos">429</span></a><span class="sd">The following entries are optional:</span>
+</span><span id="L-430"><a href="#L-430"><span class="linenos">430</span></a><span class="sd">- `layout` is a string that specifies the layout of multi-dimensional structures. Examples are &quot;2, 2&quot; for a 2x2 dimensional matrix or  &quot;64, 4, 4&quot; for a Corr with $T=64$ and 4x4 matrices on each time slices. &quot;1&quot; denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</span>
+</span><span id="L-431"><a href="#L-431"><span class="linenos">431</span></a><span class="sd">- `tag` is any JSON type. It contains additional information concerning the structure. The `tag` of an `Obs` in `pyerrors` is written here.</span>
+</span><span id="L-432"><a href="#L-432"><span class="linenos">432</span></a><span class="sd">- `reweighted` is a Bool that may be used to specify, whether the `Obs` in the structure have been reweighted.</span>
+</span><span id="L-433"><a href="#L-433"><span class="linenos">433</span></a><span class="sd">- `data` is an array that contains the data from MC chains. We will define it below.</span>
+</span><span id="L-434"><a href="#L-434"><span class="linenos">434</span></a><span class="sd">- `cdata` is an array that contains the data from external quantities with an error (`Covobs` in `pyerrors`). We will define it below.</span>
+</span><span id="L-435"><a href="#L-435"><span class="linenos">435</span></a>
+</span><span id="L-436"><a href="#L-436"><span class="linenos">436</span></a><span class="sd">The array `data` contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</span>
+</span><span id="L-437"><a href="#L-437"><span class="linenos">437</span></a><span class="sd">- `id`, a string that contains the name of the ensemble</span>
+</span><span id="L-438"><a href="#L-438"><span class="linenos">438</span></a><span class="sd">- `replica`, an array that contains an entry per replica of the ensemble.</span>
+</span><span id="L-439"><a href="#L-439"><span class="linenos">439</span></a>
+</span><span id="L-440"><a href="#L-440"><span class="linenos">440</span></a><span class="sd">Each entry of `replica` contains</span>
+</span><span id="L-441"><a href="#L-441"><span class="linenos">441</span></a><span class="sd">`name`, a string that contains the name of the replica</span>
+</span><span id="L-442"><a href="#L-442"><span class="linenos">442</span></a><span class="sd">`deltas`, an array that contains the actual data.</span>
+</span><span id="L-443"><a href="#L-443"><span class="linenos">443</span></a>
+</span><span id="L-444"><a href="#L-444"><span class="linenos">444</span></a><span class="sd">Each entry in `deltas` corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each `Obs` inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</span>
+</span><span id="L-445"><a href="#L-445"><span class="linenos">445</span></a>
+</span><span id="L-446"><a href="#L-446"><span class="linenos">446</span></a><span class="sd">The array `cdata` contains information about the contribution of auxiliary observables, represented by `Covobs` in `pyerrors`, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</span>
+</span><span id="L-447"><a href="#L-447"><span class="linenos">447</span></a><span class="sd">- `id`, a string that identifies the covariance matrix</span>
+</span><span id="L-448"><a href="#L-448"><span class="linenos">448</span></a><span class="sd">- `layout`, a string that defines the dimensions of the $M\times M$ covariance matrix (has to be &quot;M, M&quot; or &quot;1&quot;).</span>
+</span><span id="L-449"><a href="#L-449"><span class="linenos">449</span></a><span class="sd">- `cov`, an array that contains the $M\times M$ many entries of the covariance matrix, stored in row-major format.</span>
+</span><span id="L-450"><a href="#L-450"><span class="linenos">450</span></a><span class="sd">- `grad`, an array that contains N entries, one for each `Obs` inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</span>
+</span><span id="L-451"><a href="#L-451"><span class="linenos">451</span></a>
+</span><span id="L-452"><a href="#L-452"><span class="linenos">452</span></a><span class="sd">A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</span>
+</span><span id="L-453"><a href="#L-453"><span class="linenos">453</span></a>
+</span><span id="L-454"><a href="#L-454"><span class="linenos">454</span></a><span class="sd">Julia I/O routines for the json.gz format, compatible with [ADerrors.jl](https://gitlab.ift.uam-csic.es/alberto/aderrors.jl), can be found [here](https://github.com/fjosw/ADjson.jl).</span>
+</span><span id="L-455"><a href="#L-455"><span class="linenos">455</span></a><span class="sd">&#39;&#39;&#39;</span>
+</span><span id="L-456"><a href="#L-456"><span class="linenos">456</span></a><span class="kn">from</span> <span class="nn">.obs</span> <span class="kn">import</span> <span class="o">*</span>
+</span><span id="L-457"><a href="#L-457"><span class="linenos">457</span></a><span class="kn">from</span> <span class="nn">.correlators</span> <span class="kn">import</span> <span class="o">*</span>
+</span><span id="L-458"><a href="#L-458"><span class="linenos">458</span></a><span class="kn">from</span> <span class="nn">.fits</span> <span class="kn">import</span> <span class="o">*</span>
+</span><span id="L-459"><a href="#L-459"><span class="linenos">459</span></a><span class="kn">from</span> <span class="nn">.misc</span> <span class="kn">import</span> <span class="o">*</span>
+</span><span id="L-460"><a href="#L-460"><span class="linenos">460</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">dirac</span>
+</span><span id="L-461"><a href="#L-461"><span class="linenos">461</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="nb">input</span>
+</span><span id="L-462"><a href="#L-462"><span class="linenos">462</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">linalg</span>
+</span><span id="L-463"><a href="#L-463"><span class="linenos">463</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">mpm</span>
+</span><span id="L-464"><a href="#L-464"><span class="linenos">464</span></a><span class="kn">from</span> <span class="nn">.</span> <span class="kn">import</span> <span class="n">roots</span>
+</span><span id="L-465"><a href="#L-465"><span class="linenos">465</span></a>
+</span><span id="L-466"><a href="#L-466"><span class="linenos">466</span></a><span class="kn">from</span> <span class="nn">.version</span> <span class="kn">import</span> <span class="n">__version__</span>
 </span></pre></div>
 
 
diff --git a/docs/search.js b/docs/search.js
index 32e58fa0..a2963391 100644
--- a/docs/search.js
+++ b/docs/search.js
@@ -1,6 +1,6 @@
 window.pdocSearch = (function(){
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-    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "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 gamma method <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>automatic differentiation for exact linear error propagation 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>treatment of slow modes in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>.</li>\n<li>coherent error propagation for data from different Markov chains.</li>\n<li>non-linear fits with x- and y-errors 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>real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).</li>\n</ul>\n\n<p>More detailed examples can found in the <a href=\"https://github.com/fjosw/pyerrors/tree/develop/examples\">GitHub repository</a> <a href=\"https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples\"><img src=\"https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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\" alt=\"badge\" /></a>.</p>\n\n<p>If you use <code>pyerrors</code> for research that leads to a publication please consider citing:</p>\n\n<ul>\n<li>Ulli Wolff, <em>Monte Carlo errors with less errors</em>. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</li>\n<li>Alberto Ramos, <em>Automatic differentiation for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 238 (2019) 19-35.</li>\n</ul>\n\n<p>and</p>\n\n<ul>\n<li>Stefan Schaefer, Rainer Sommer, Francesco Virotta, <em>Critical slowing down and error analysis in lattice QCD simulations</em>. Nucl.Phys.B 845 (2011) 93-119.</li>\n</ul>\n\n<p>where applicable.</p>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a>, <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a> and <a href=\"https://github.com/mbruno46/pyobs\">Python</a>.</p>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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 of 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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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_rho</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size 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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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><code>Obs</code> objects defined on irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p><code>Obs</code> objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</p>\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>When one is not interested in single observables but correlation functions, <code>pyerrors</code> offers the <code>Corr</code> class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a <code>Corr</code> objects one needs to arrange the data as a list of <code>Obs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">],</span> <span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">4</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span>\n</code></pre>\n</div>\n\n<p>The individual entries of a correlator can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Error propagation with the <code>Corr</code> class works very similar to <code>Obs</code> objects. Mathematical operations are overloaded and <code>Corr</code> objects can be computed together with other <code>Corr</code> objects, <code>Obs</code> objects or real numbers and integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_new_corr</span> <span class=\"o\">=</span> <span class=\"mf\">0.3</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">+</span> <span class=\"mi\">12</span> <span class=\"o\">/</span> <span class=\"n\">my_corr</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>\n\n<ul>\n<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>\n<li><code>Corr.m_eff</code> to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</li>\n<li><code>Corr.deriv</code> returns the first derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.second_deriv</code> returns the second derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.symmetric</code> symmetrizes parity even correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.anti_symmetric</code> anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.T_symmetry</code> averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</li>\n<li><code>Corr.plateau</code> extracts a plateau value from the correlator in a given range.</li>\n<li><code>Corr.roll</code> periodically shifts the correlator.</li>\n<li><code>Corr.reverse</code> reverses the time ordering of the correlator.</li>\n<li><code>Corr.correlate</code> constructs a disconnected correlation function from the correlator and another <code>Corr</code> or <code>Obs</code> object.</li>\n<li><code>Corr.reweight</code> reweights the correlator.</li>\n</ul>\n\n<p><code>pyerrors</code> can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see <code>pyerrors.correlators.Corr.GEVP</code>).</p>\n\n<p>For the full API see <code>pyerrors.correlators.Corr</code>.</p>\n\n<h1 id=\"complex-valued-observables\">Complex valued 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<div class=\"pdoc-code codehilite\">\n<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>\n</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=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<h1 id=\"the-covobs-class\">The <code>Covobs</code> class</h1>\n\n<p>In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The <code>Covobs</code> class allows to define such quantities in <code>pyerrors</code>. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</p>\n\n<p>This concept is built into the definition of <code>Covobs</code>. In <code>pyerrors</code>, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters <code>cov_Obs</code>, since the second argument of this function is the covariance matrix of the <code>Covobs</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">pyerrors.obs</span> <span class=\"k\">as</span> <span class=\"nn\">pe</span>\n\n<span class=\"n\">mpi</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">(</span><span class=\"mf\">134.9768</span><span class=\"p\">,</span> <span class=\"mf\">0.0005</span><span class=\"o\">**</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s1\">&#39;pi^0 mass&#39;</span><span class=\"p\">)</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"n\">mpi</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\">1.34976800e+02</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.00000000e-04</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>\n<span class=\"o\">&gt;</span>  <span class=\"n\">pi</span><span class=\"o\">^</span><span class=\"mi\">0</span> <span class=\"n\">mass</span>     <span class=\"mf\">5.00000000e-04</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</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\">Covobs</span>   <span class=\"s1\">&#39;pi^0 mass&#39;</span>\n</code></pre>\n</div>\n\n<p>The resulting object <code>mpi</code> is an <code>Obs</code> that contains a <code>Covobs</code>. In the following, it may be handled as any other <code>Obs</code>. The contribution of the covariance matrix to the error of an <code>Obs</code> is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the <code>Obs</code> with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.</p>\n\n<p>Correlated auxiliary data is defined similarly to above, e.g., via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">RAP</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">([</span><span class=\"mf\">16.7457</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">19.0475</span><span class=\"p\">],</span> <span class=\"p\">[[</span><span class=\"mf\">3.49591</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">,</span> <span class=\"mf\">10.5834</span><span class=\"p\">]],</span> <span class=\"s1\">&#39;R_AP, 1906.03445, (5.3a)&#39;</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">RAP</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">[</span><span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"mf\">16.7</span><span class=\"p\">(</span><span class=\"mf\">1.9</span><span class=\"p\">)],</span> <span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">19.0</span><span class=\"p\">(</span><span class=\"mf\">3.3</span><span class=\"p\">)]]</span>\n</code></pre>\n</div>\n\n<p>where <code>RAP</code> now is a list of two <code>Obs</code> that contains the two correlated parameters.</p>\n\n<p>Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the <code>Covobs</code> class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an <code>Obs</code> <code>o</code> with respect to a covariance matrix with the identifying string <code>k</code> may be accessed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">covobs</span><span class=\"p\">[</span><span class=\"n\">k</span><span class=\"p\">]</span><span class=\"o\">.</span><span class=\"n\">grad</span>\n</code></pre>\n</div>\n\n<h1 id=\"error-propagation-in-iterative-algorithms\">Error propagation in iterative algorithms</h1>\n\n<p><code>pyerrors</code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<h2 id=\"least-squares-fits\">Least squares fits</h2>\n\n<p>Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with <code>pyerrors.fits.least_squares</code>. As default solver the Levenberg-Marquardt algorithm implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html\">scipy</a> is used.</p>\n\n<p>Fit functions have to be of the following form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"k\">return</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\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</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\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><strong>It is important that numerical functions refer to <code>autograd.numpy</code> instead of <code>numpy</code> for the automatic differentiation in iterative algorithms to work properly.</strong></p>\n\n<p>Fits can then be performed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">fits</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">func</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"s2\">&quot;</span><span class=\"se\">\\n</span><span class=\"s2\">&quot;</span><span class=\"p\">,</span> <span class=\"n\">fit_result</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"k\">with</span> <span class=\"mi\">2</span> <span class=\"n\">parameters</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Method</span><span class=\"p\">:</span> <span class=\"n\">Levenberg</span><span class=\"o\">-</span><span class=\"n\">Marquardt</span>\n<span class=\"o\">&gt;</span> <span class=\"err\">`</span><span class=\"n\">ftol</span><span class=\"err\">`</span> <span class=\"n\">termination</span> <span class=\"n\">condition</span> <span class=\"ow\">is</span> <span class=\"n\">satisfied</span><span class=\"o\">.</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">chisquare</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span><span class=\"p\">:</span> <span class=\"mf\">0.9593035785160936</span>\n\n<span class=\"o\">&gt;</span>  <span class=\"n\">Goodness</span> <span class=\"n\">of</span> <span class=\"n\">fit</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">\u03c7</span><span class=\"err\">\u00b2</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span> <span class=\"o\">=</span> <span class=\"mf\">0.959304</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">p</span><span class=\"o\">-</span><span class=\"n\">value</span>   <span class=\"o\">=</span> <span class=\"mf\">0.5673</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"n\">parameters</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.0548</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">1.933</span><span class=\"p\">(</span><span class=\"mi\">64</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is a <code>list</code> or <code>numpy.array</code> of <code>floats</code> and y is a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>Data stored in <code>Corr</code> objects can be fitted directly using the <code>Corr.fit</code> method.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">my_corr</span><span class=\"o\">.</span><span class=\"n\">fit</span><span class=\"p\">(</span><span class=\"n\">func</span><span class=\"p\">,</span> <span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">12</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<p>this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</p>\n\n<p>For fit functions with multiple independent variables the fit function can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p><code>pyerrors</code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.\nDetails about how the required covariance matrix is estimated can be found in <code>pyerrors.obs.covariance</code>.</p>\n\n<p>Direct visualizations of the performed fits can be triggered via <code>resplot=True</code> or <code>qqplot=True</code>. For all available options see <code>pyerrors.fits.least_squares</code>.</p>\n\n<h2 id=\"total-least-squares-fits\">Total least squares fits</h2>\n\n<p><code>pyerrors</code> can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/odr.html\">scipy</a>, see <code>pyerrors.fits.least_squares</code>. The syntax is identical to the standard least squares case, the only difference being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors</code> provides wrappers for <code>Obs</code>- and <code>CObs</code>-valued matrix operations based on <code>numpy.linalg</code>. The supported functions include:</p>\n\n<ul>\n<li><code>inv</code> for the matrix inverse.</li>\n<li><code>cholseky</code> for the Cholesky decomposition.</li>\n<li><code>det</code> for the matrix determinant.</li>\n<li><code>eigh</code> for eigenvalues and eigenvectors of hermitean matrices.</li>\n<li><code>eig</code> for eigenvalues of general matrices.</li>\n<li><code>pinv</code> for the Moore-Penrose pseudoinverse.</li>\n<li><code>svd</code> for the singular-value-decomposition.</li>\n</ul>\n\n<p>For the full API see <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 json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</p>\n\n<ul>\n<li>What observables are stored? Possibly: How exactly are they defined.</li>\n<li>How does each single ensemble or external quantity contribute to the error of the observable?</li>\n<li>Who did write the file when and on which machine?</li>\n</ul>\n\n<p>This can be achieved by storing all information in one single file. The export routines of <code>pyerrors</code> are written such that as much information as possible is written automatically as described in the following example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><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=\"s2\">&quot;test_ensemble&quot;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">tag</span> <span class=\"o\">=</span> <span class=\"s2\">&quot;My observable&quot;</span>\n\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">dump_to_json</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">,</span> <span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n<span class=\"c1\"># For a single observable one can equivalently use the class method dump</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">dump</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n\n<span class=\"n\">check</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">load_json</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">)</span>\n\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_obs</span> <span class=\"o\">==</span> <span class=\"n\">check</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<p>The format also allows to directly write out the content of <code>Corr</code> objects or lists and arrays of <code>Obs</code> objects by passing the desired data to <code>pyerrors.input.json.dump_to_json</code>.</p>\n\n<h2 id=\"jsongz-format-specification\">json.gz format specification</h2>\n\n<p>The first entries of the file provide optional auxiliary information:</p>\n\n<ul>\n<li><code>program</code> is a string that indicates which program was used to write the file.</li>\n<li><code>version</code> is a string that specifies the version of the format.</li>\n<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>\n<li><code>date</code> is a string and contains the creation date of the file.</li>\n<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>\n<li><code>description</code> contains information on the content of the file. This field is not filled automatically in <code>pyerrors</code>. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</li>\n</ul>\n\n<p>The only necessary entry of the file is the field\n-<code>obsdata</code>, an array that contains the actual data.</p>\n\n<p>Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of <code>Obs</code>, <code>list</code>, <code>numpy.ndarray</code>, <code>Corr</code>. All <code>Obs</code> inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array <code>obsdata</code>, are treated independently. Each entry of the array <code>obsdata</code> has the following required entries:</p>\n\n<ul>\n<li><code>type</code> is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</li>\n<li><code>value</code> is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:</li>\n<li><code>layout</code> is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</li>\n<li><code>tag</code> is any JSON type. It contains additional information concerning the structure. The <code>tag</code> of an <code>Obs</code> in <code>pyerrors</code> is written here.</li>\n<li><code>reweighted</code> is a Bool that may be used to specify, whether the <code>Obs</code> in the structure have been reweighted.</li>\n<li><code>data</code> is an array that contains the data from MC chains. We will define it below.</li>\n<li><code>cdata</code> is an array that contains the data from external quantities with an error (<code>Covobs</code> in <code>pyerrors</code>). We will define it below.</li>\n</ul>\n\n<p>The array <code>data</code> contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that contains the name of the ensemble</li>\n<li><code>replica</code>, an array that contains an entry per replica of the ensemble.</li>\n</ul>\n\n<p>Each entry of <code>replica</code> contains\n<code>name</code>, a string that contains the name of the replica\n<code>deltas</code>, an array that contains the actual data.</p>\n\n<p>Each entry in <code>deltas</code> corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each <code>Obs</code> inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</p>\n\n<p>The array <code>cdata</code> contains information about the contribution of auxiliary observables, represented by <code>Covobs</code> in <code>pyerrors</code>, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that identifies the covariance matrix</li>\n<li><code>layout</code>, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").</li>\n<li><code>cov</code>, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.</li>\n<li><code>grad</code>, an array that contains N entries, one for each <code>Obs</code> inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</li>\n</ul>\n\n<p>A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</p>\n\n<p>Julia I/O routines for the json.gz format, compatible with <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">ADerrors.jl</a>, can be found <a href=\"https://github.com/fjosw/ADjson.jl\">here</a>.</p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "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 matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "<p>Initialize a Corr object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data_input</strong> (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs</li>\n<li><strong>padding</strong> (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.</li>\n<li><strong>prange</strong> (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">data_input</span>, </span><span class=\"param\"><span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">prange</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "<p>We need to project the Correlator with a Vector to get a single value at each timeslice.</p>\n\n<p>The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">vector_l</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vector_r</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">normalize</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "<p>Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>i</strong> (int):\nFirst index to be picked.</li>\n<li><strong>j</strong> (int):\nSecond index to be picked.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "type": "function", "doc": "<p>Checks whether a correlator matrices is symmetric on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "<p>Symmetrizes the correlator matrices on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "<p>Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.</p>\n\n<p>The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</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=\"c1\"># Ground state vector(s)</span>\n<span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[:</span><span class=\"mi\">3</span><span class=\"p\">]</span>  <span class=\"c1\"># Vectors for the lowest three states</span>\n</code></pre>\n</div>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t0</strong> (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$</li>\n<li><strong>ts</strong> (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.</li>\n<li><strong>sort</strong> (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n<ul>\n<li>\"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.</li>\n<li>\"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.</li>\n</ul></li>\n</ul>\n\n<h6 id=\"other-parameters\">Other Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "<p>Determines the eigenvalue of the GEVP by solving and projecting the correlator</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nThe state one is interested in ordered by energy. The lowest state is zero.</li>\n<li><strong>All other parameters are identical to the ones of Corr.GEVP.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">state</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "<p>Constructs an NxN Hankel matrix</p>\n\n<p>C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>N</strong> (int):\nDimension of the Hankel matrix</li>\n<li><strong>periodic</strong> (bool, optional):\ndetermines whether the matrix is extended periodically</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">N</span>, </span><span class=\"param\"><span class=\"n\">periodic</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">dt</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "<p>Thin out a correlator to suppress correlations</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>spacing</strong> (int):\nKeep only every 'spacing'th entry of the correlator</li>\n<li><strong>offset</strong> (int):\nOffset the equal spacing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">spacing</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span>, </span><span class=\"param\"><span class=\"n\">parity</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "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\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;log&#39;</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span></span><span class=\"return-annotation\">):</span></span>", "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):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\n<code>fitrange=[4, 6]</code> corresponds to the three entries 4, 5 and 6.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">function</span>, </span><span class=\"param\"><span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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<li><strong>auto_gamma</strong> (bool):\napply gamma_method with default parameters to the Corr. Defaults to None</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">plateau_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">method</span><span class=\"o\">=</span><span class=\"s1\">&#39;fit&#39;</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">prange</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "<p>Plots the correlator using the tag of the correlator 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.\nThe tags of these correlators are used as labels if available.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale.</li>\n<li><strong>plateau</strong> (Obs):\nPlateau value 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<li><strong>auto_gamma</strong> (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.</li>\n<li><strong>hide_sigma</strong> (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.</li>\n<li><strong>references</strong> (list):\nList of floating point values that are displayed as horizontal lines for reference.</li>\n<li><strong>title</strong> (string):\nOptional title of the figure.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"bp\">self</span>,</span><span class=\"param\">\t<span class=\"n\">x_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">comp</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">y_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">plateau</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_res</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">ylabel</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">hide_sigma</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">references</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">title</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "<p>Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>logscale</strong> (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "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 file of chosen type</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">print_range</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "<p>Project large correlation matrix to lowest states</p>\n\n<p>This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>Ntrunc</strong> (int):\nRank of the target matrix.</li>\n<li><strong>tproj</strong> (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.</li>\n<li><strong>t0proj</strong> (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.</li>\n<li><strong>basematrix</strong> (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">Ntrunc</span>, </span><span class=\"param\"><span class=\"n\">tproj</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">t0proj</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">basematrix</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">mean</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">pos</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "<p>Rank-3 epsilon tensor</p>\n\n<p>Based on <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "<p>Rank-4 epsilon tensor</p>\n\n<p>Extension of <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span>, </span><span class=\"param\"><span class=\"n\">o</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">gamma_tag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "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", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">()</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"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\">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</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.</li>\n<li><strong>method</strong> (str, optional):\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>correlated_fit</strong> (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see <code>pyerrors.obs.covariance</code>.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for <code>prior==None</code> and when no <code>method</code> is given.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).</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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">priors</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"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\">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</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Based on the orthogonal distance regression module of scipy</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nCan 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.</li>\n<li><strong>y</strong> (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">o_y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">fit_res</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">beta</span></span><span class=\"return-annotation\">):</span></span>", "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 p-values of all fit object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>objects</strong> (list):\nList of fit results to include in the analysis (optional).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">objects</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "<p><code>pyerrors</code> includes an <code>input</code> submodule in which input routines and parsers for the output of various numerical programs are contained.</p>\n\n<h1 id=\"jackknife-samples\">Jackknife samples</h1>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can also generate jackknife samples from an <code>Obs</code> object or import jackknife samples into an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> and <code>pyerrors.obs.import_jackknife</code> for details.</p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_list</span>, </span><span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obsl</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>, </span><span class=\"param\"><span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically.</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>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "<p>Import a list of Obs from a string in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>content</strong> (str):\nXML string containing the data</li>\n<li><strong>noemtpy</strong> (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.</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 as list.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">content</span>, </span><span class=\"param\"><span class=\"n\">noempty</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</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>noemtpy</strong> (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the 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 as list.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">noempty</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>,</span><span class=\"param\">\t<span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator |is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "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>gammas</strong> (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">meson</span><span class=\"o\">=</span><span class=\"s1\">&#39;meson_0&#39;</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">gammas</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "<p>Read hadrons DistillationContraction hdf5 files in given directory structure</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the directories to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>diagrams</strong> (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">diagrams</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;direct&#39;</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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>:  An ndarray alias :term:<code>generic &lt;generic type&gt;</code>\nw.r.t. its <code>dtype.type &lt;numpy.dtype.type&gt;</code>.  </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=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p>Second mode:</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n", "bases": "numpy.ndarray"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">()</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vertices</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;VA&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;AV&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "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 moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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 moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "<p>Reconstruct a list of Obs or structures containing Obs from a json string.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\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>json_string</strong> (str):\njson string containing the data.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the 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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">json_string</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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, Corr\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "<p>Export a dict 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>od</strong> (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\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>reps</strong> (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.</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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">od</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "<p>Import a dict of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr</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<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "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=\"parameters\">Parameters</h6>\n\n<ul>\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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "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>path</strong> (str):\npath that contains the data files</li>\n<li><strong>prefix</strong> (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.</li>\n<li><strong>version</strong> (str):\nversion of openQCD, default 2.0</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</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>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>print_err</strong> (bool):\nPrint additional information that is useful for debugging.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;2.0&#39;</span>, </span><span class=\"param\"><span class=\"n\">names</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</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\nwhen 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\neffects 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\ncrossing 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>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">dtr_read</span>, </span><span class=\"param\"><span class=\"n\">xmin</span>, </span><span class=\"param\"><span class=\"n\">spatial_extent</span>, </span><span class=\"param\"><span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "<p>Read the topologial charge based on openQCD gradient flow measurements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nEither openQCD or sfqcd, depending on the data.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</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>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n<li><strong>integer_charge</strong> (bool):\nIf True, the charge is rounded towards the nearest integer on each config.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;openQCD&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "function", "doc": "<p>Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.</p>\n\n<p>Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</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>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">Zeuthen_flow</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "<p>Returns the projection to the topological charge sector defined by target.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (Obs):\nTopological charge.</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">qtop</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "<p>Constructs reweighting factors to a specified topological sector.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs</li>\n<li><strong>r_stop</strong> (list):\nlast configurations that need to be read (per replicum)</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "function", "doc": "<p>Write DataFrame including Obs or Corr valued columns to sqlite database.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be written to the database.</li>\n<li><strong>table_name</strong> (str):\nName of the table in the database.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>if exists</strong> (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.</li>\n<li><strong>gz</strong> (bool):\nIf True the json strings are gzipped.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">table_name</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">if_exists</span><span class=\"o\">=</span><span class=\"s1\">&#39;fail&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "type": "function", "doc": "<p>Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sql</strong> (str):\nSQL query to be executed.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">sql</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "type": "function", "doc": "<p>Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.</p>\n\n<p>Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be dumped to a file.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "type": "function", "doc": "<p>Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.</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>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "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>quarks</strong> (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>noffset</strong> (int):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf</strong> (int):\nID of wave function</li>\n<li><strong>wf2</strong> (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>corr_type</strong> (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs:</strong>: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">quarks</span><span class=\"o\">=</span><span class=\"s1\">&#39;.*&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type</span><span class=\"o\">=</span><span class=\"s1\">&#39;bi&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">noffset</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf2</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "<p>Utilities for the input</p>\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "<p>Checks if list of configurations is contained in an idl</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>idl</strong> (range or list):\nidl of the current replicum</li>\n<li><strong>che</strong> (list):\nlist of configurations to be checked against</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">idl</span>, </span><span class=\"param\"><span class=\"n\">che</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">subscripts</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "<p>Cholesky decomposition of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "<p>Determinant of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obj</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "<p>Generate an Obs object with given value, dvalue and name for test purposes</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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">value</span>, </span><span class=\"param\"><span class=\"n\">dvalue</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">tau</span><span class=\"o\">=</span><span class=\"mf\">0.5</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corrs</span>, </span><span class=\"param\"><span class=\"n\">k</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">p</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">samples</span>, </span><span class=\"param\"><span class=\"n\">names</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">ens_content</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "function", "doc": "<p>Reweight the obs with given rewighting factors.</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. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">sigma</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">atol</span><span class=\"o\">=</span><span class=\"mf\">1e-10</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">expand</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "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\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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 file 'name' of chosen format.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nname of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>description</strong> (str):\nDescription for output file, only relevant for json.gz format.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">real</span>, </span><span class=\"param\"><span class=\"n\">imag</span><span class=\"o\">=</span><span class=\"mf\">0.0</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">data</span>, </span><span class=\"param\"><span class=\"n\">array_mode</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_a</span>, </span><span class=\"param\"><span class=\"n\">obs_b</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "<p>Calculates the error covariance matrix of a set of observables.</p>\n\n<p>The gamma method has to be applied first to all observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs</strong> (list or numpy.ndarray):\nList or one dimensional array of Obs</li>\n<li><strong>visualize</strong> (bool):\nIf True plots the corresponding normalized correlation matrix (default False).</li>\n<li><strong>correlation</strong> (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).</li>\n<li><strong>smooth</strong> (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"n\">visualize</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">smooth</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">jacks</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is not possible to combine obs which are based on the same replicum</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">list_of_obs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "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><p><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n<span class=\"k\">def</span> <span class=\"nf\">root_func</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">):</span>\n   <span class=\"k\">return</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">x</span> <span class=\"o\">**</span> <span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">d</span>\n</code></pre>\n</div></li>\n<li><p><strong>guess</strong> (float):\nInitial guess for the minimization.</p></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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">d</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 7978}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 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+    /** pdoc search index */const docs = {"version": "0.9.5", "fields": ["qualname", "fullname", "annotation", "default_value", "signature", "bases", "doc"], "ref": "fullname", "documentStore": {"docs": {"pyerrors": {"fullname": "pyerrors", "modulename": "pyerrors", "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 gamma method <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>automatic differentiation for exact linear error propagation 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>treatment of slow modes in the simulation as suggested in <a href=\"https://arxiv.org/abs/1009.5228\">arXiv:1009.5228</a>.</li>\n<li>coherent error propagation for data from different Markov chains.</li>\n<li>non-linear fits with x- and y-errors 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>real and complex matrix operations and their error propagation based on automatic differentiation (Matrix inverse, Cholesky decomposition, calculation of eigenvalues and eigenvectors, singular value decomposition...).</li>\n</ul>\n\n<p>More detailed examples can found in the <a href=\"https://github.com/fjosw/pyerrors/tree/develop/examples\">GitHub repository</a> <a href=\"https://mybinder.org/v2/gh/fjosw/pyerrors/HEAD?labpath=examples\"><img src=\"https://img.shields.io/badge/-try%20it%20out-579ACA.svg?logo=data:image/png;base64,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\" alt=\"badge\" /></a>.</p>\n\n<p>If you use <code>pyerrors</code> for research that leads to a publication please consider citing:\nFabian Joswig, Simon Kuberski, Justus T. Kuhlmann, Jan Neuendorf, <em>pyerrors: a python framework for error analysis of Monte Carlo data</em>. [arXiv:2209.14371 [hep-lat]].</p>\n\n<ul>\n<li>Ulli Wolff, <em>Monte Carlo errors with less errors</em>. Comput.Phys.Commun. 156 (2004) 143-153, Comput.Phys.Commun. 176 (2007) 383 (erratum).</li>\n<li>Alberto Ramos, <em>Automatic differentiation for error analysis of Monte Carlo data</em>. Comput.Phys.Commun. 238 (2019) 19-35.</li>\n</ul>\n\n<p>and</p>\n\n<ul>\n<li>Stefan Schaefer, Rainer Sommer, Francesco Virotta, <em>Critical slowing down and error analysis in lattice QCD simulations</em>. Nucl.Phys.B 845 (2011) 93-119.</li>\n</ul>\n\n<p>where applicable.</p>\n\n<p>There exist similar publicly available implementations of gamma method error analysis suites in <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors\">Fortran</a>, <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">Julia</a> and <a href=\"https://github.com/mbruno46/pyobs\">Python</a>.</p>\n\n<h2 id=\"basic-example\">Basic example</h2>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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 of 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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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_rho</code>.</p>\n\n<p>If the parameter $S$ is set to zero it is assumed that the dataset does not exhibit any autocorrelation and the window size 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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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<div class=\"pdoc-code codehilite\">\n<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>\n</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><code>Obs</code> objects defined on irregular Monte Carlo chains can be initialized with the parameter <code>idl</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p><code>Obs</code> objects defined on regular and irregular histories of the same ensemble can be combined with each other and the correct error propagation and estimation is automatically taken care of.</p>\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>When one is not interested in single observables but correlation functions, <code>pyerrors</code> offers the <code>Corr</code> class which simplifies the corresponding error propagation and provides the user with a set of standard methods. In order to initialize a <code>Corr</code> objects one needs to arrange the data as a list of <code>Obs</code></p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>In case the correlation functions are not defined on the outermost timeslices, for example because of fixed boundary conditions, a padding can be introduced.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">([</span><span class=\"n\">obs_0</span><span class=\"p\">,</span> <span class=\"n\">obs_1</span><span class=\"p\">,</span> <span class=\"n\">obs_2</span><span class=\"p\">,</span> <span class=\"n\">obs_3</span><span class=\"p\">],</span> <span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">1</span><span class=\"p\">,</span> <span class=\"mi\">1</span><span class=\"p\">])</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span>  <span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">x0</span><span class=\"o\">/</span><span class=\"n\">a</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"o\">------------------</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">0.7957</span><span class=\"p\">(</span><span class=\"mi\">80</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">2</span>      <span class=\"mf\">0.5156</span><span class=\"p\">(</span><span class=\"mi\">51</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">3</span>      <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">4</span>      <span class=\"mf\">0.2041</span><span class=\"p\">(</span><span class=\"mi\">21</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">5</span>\n</code></pre>\n</div>\n\n<p>The individual entries of a correlator can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">3</span><span class=\"p\">])</span>\n<span class=\"o\">&gt;</span> <span class=\"mf\">0.3227</span><span class=\"p\">(</span><span class=\"mi\">33</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>Error propagation with the <code>Corr</code> class works very similar to <code>Obs</code> objects. Mathematical operations are overloaded and <code>Corr</code> objects can be computed together with other <code>Corr</code> objects, <code>Obs</code> objects or real numbers and integers.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_new_corr</span> <span class=\"o\">=</span> <span class=\"mf\">0.3</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span><span class=\"p\">[</span><span class=\"mi\">2</span><span class=\"p\">]</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">*</span> <span class=\"n\">my_corr</span> <span class=\"o\">+</span> <span class=\"mi\">12</span> <span class=\"o\">/</span> <span class=\"n\">my_corr</span>\n</code></pre>\n</div>\n\n<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>\n\n<ul>\n<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>\n<li><code>Corr.m_eff</code> to construct effective masses. Various variants for periodic and fixed temporal boundary conditions are available.</li>\n<li><code>Corr.deriv</code> returns the first derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.second_deriv</code> returns the second derivative of the correlator as <code>Corr</code>. Different discretizations of the numerical derivative are available.</li>\n<li><code>Corr.symmetric</code> symmetrizes parity even correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.anti_symmetric</code> anti-symmetrizes parity odd correlations functions, assuming periodic boundary conditions.</li>\n<li><code>Corr.T_symmetry</code> averages a correlator with its time symmetry partner, assuming fixed boundary conditions.</li>\n<li><code>Corr.plateau</code> extracts a plateau value from the correlator in a given range.</li>\n<li><code>Corr.roll</code> periodically shifts the correlator.</li>\n<li><code>Corr.reverse</code> reverses the time ordering of the correlator.</li>\n<li><code>Corr.correlate</code> constructs a disconnected correlation function from the correlator and another <code>Corr</code> or <code>Obs</code> object.</li>\n<li><code>Corr.reweight</code> reweights the correlator.</li>\n</ul>\n\n<p><code>pyerrors</code> can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see <code>pyerrors.correlators.Corr.GEVP</code>).</p>\n\n<p>For the full API see <code>pyerrors.correlators.Corr</code>.</p>\n\n<h1 id=\"complex-valued-observables\">Complex valued 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<div class=\"pdoc-code codehilite\">\n<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>\n</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=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<h1 id=\"the-covobs-class\">The <code>Covobs</code> class</h1>\n\n<p>In many projects, auxiliary data that is not based on Monte Carlo chains enters. Examples are experimentally determined mesons masses which are used to set the scale or renormalization constants. These numbers come with an error that has to be propagated through the analysis. The <code>Covobs</code> class allows to define such quantities in <code>pyerrors</code>. Furthermore, external input might consist of correlated quantities. An example are the parameters of an interpolation formula, which are defined via mean values and a covariance matrix between all parameters. The contribution of the interpolation formula to the error of a derived quantity therefore might depend on the complete covariance matrix.</p>\n\n<p>This concept is built into the definition of <code>Covobs</code>. In <code>pyerrors</code>, external input is defined by $M$ mean values, a $M\\times M$ covariance matrix, where $M=1$ is permissible, and a name that uniquely identifies the covariance matrix. Below, we define the pion mass, based on its mean value and error, 134.9768(5). Note, that the square of the error enters <code>cov_Obs</code>, since the second argument of this function is the covariance matrix of the <code>Covobs</code>.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">pyerrors.obs</span> <span class=\"k\">as</span> <span class=\"nn\">pe</span>\n\n<span class=\"n\">mpi</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">(</span><span class=\"mf\">134.9768</span><span class=\"p\">,</span> <span class=\"mf\">0.0005</span><span class=\"o\">**</span><span class=\"mi\">2</span><span class=\"p\">,</span> <span class=\"s1\">&#39;pi^0 mass&#39;</span><span class=\"p\">)</span>\n<span class=\"n\">mpi</span><span class=\"o\">.</span><span class=\"n\">gamma_method</span><span class=\"p\">()</span>\n<span class=\"n\">mpi</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\">1.34976800e+02</span> <span class=\"o\">+/-</span> <span class=\"mf\">5.00000000e-04</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>\n<span class=\"o\">&gt;</span>  <span class=\"n\">pi</span><span class=\"o\">^</span><span class=\"mi\">0</span> <span class=\"n\">mass</span>     <span class=\"mf\">5.00000000e-04</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</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\">Covobs</span>   <span class=\"s1\">&#39;pi^0 mass&#39;</span>\n</code></pre>\n</div>\n\n<p>The resulting object <code>mpi</code> is an <code>Obs</code> that contains a <code>Covobs</code>. In the following, it may be handled as any other <code>Obs</code>. The contribution of the covariance matrix to the error of an <code>Obs</code> is determined from the $M \\times M$ covariance matrix $\\Sigma$ and the gradient of the <code>Obs</code> with respect to the external quantities, which is the $1\\times M$ Jacobian matrix $J$, via\n$$s = \\sqrt{J^T \\Sigma J}\\,,$$\nwhere the Jacobian is computed for each derived quantity via automatic differentiation.</p>\n\n<p>Correlated auxiliary data is defined similarly to above, e.g., via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">RAP</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">cov_Obs</span><span class=\"p\">([</span><span class=\"mf\">16.7457</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">19.0475</span><span class=\"p\">],</span> <span class=\"p\">[[</span><span class=\"mf\">3.49591</span><span class=\"p\">,</span> <span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">],</span> <span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">6.07560</span><span class=\"p\">,</span> <span class=\"mf\">10.5834</span><span class=\"p\">]],</span> <span class=\"s1\">&#39;R_AP, 1906.03445, (5.3a)&#39;</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">RAP</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"p\">[</span><span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"mf\">16.7</span><span class=\"p\">(</span><span class=\"mf\">1.9</span><span class=\"p\">)],</span> <span class=\"n\">Obs</span><span class=\"p\">[</span><span class=\"o\">-</span><span class=\"mf\">19.0</span><span class=\"p\">(</span><span class=\"mf\">3.3</span><span class=\"p\">)]]</span>\n</code></pre>\n</div>\n\n<p>where <code>RAP</code> now is a list of two <code>Obs</code> that contains the two correlated parameters.</p>\n\n<p>Since the gradient of a derived observable with respect to an external covariance matrix is propagated through the entire analysis, the <code>Covobs</code> class allows to quote the derivative of a result with respect to the external quantities. If these derivatives are published together with the result, small shifts in the definition of external quantities, e.g., the definition of the physical point, can be performed a posteriori based on the published information. This may help to compare results of different groups. The gradient of an <code>Obs</code> <code>o</code> with respect to a covariance matrix with the identifying string <code>k</code> may be accessed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">covobs</span><span class=\"p\">[</span><span class=\"n\">k</span><span class=\"p\">]</span><span class=\"o\">.</span><span class=\"n\">grad</span>\n</code></pre>\n</div>\n\n<h1 id=\"error-propagation-in-iterative-algorithms\">Error propagation in iterative algorithms</h1>\n\n<p><code>pyerrors</code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least squares fits or root finding. The derivatives required for the error propagation are calculated as described in <a href=\"https://arxiv.org/abs/1809.01289\">arXiv:1809.01289</a>.</p>\n\n<h2 id=\"least-squares-fits\">Least squares fits</h2>\n\n<p>Standard non-linear least square fits with errors on the dependent but not the independent variables can be performed with <code>pyerrors.fits.least_squares</code>. As default solver the Levenberg-Marquardt algorithm implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html\">scipy</a> is used.</p>\n\n<p>Fit functions have to be of the following form</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"k\">return</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\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</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\">x</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p><strong>It is important that numerical functions refer to <code>autograd.numpy</code> instead of <code>numpy</code> for the automatic differentiation in iterative algorithms to work properly.</strong></p>\n\n<p>Fits can then be performed via</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">fits</span><span class=\"o\">.</span><span class=\"n\">least_squares</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">y</span><span class=\"p\">,</span> <span class=\"n\">func</span><span class=\"p\">)</span>\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"s2\">&quot;</span><span class=\"se\">\\n</span><span class=\"s2\">&quot;</span><span class=\"p\">,</span> <span class=\"n\">fit_result</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"k\">with</span> <span class=\"mi\">2</span> <span class=\"n\">parameters</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Method</span><span class=\"p\">:</span> <span class=\"n\">Levenberg</span><span class=\"o\">-</span><span class=\"n\">Marquardt</span>\n<span class=\"o\">&gt;</span> <span class=\"err\">`</span><span class=\"n\">ftol</span><span class=\"err\">`</span> <span class=\"n\">termination</span> <span class=\"n\">condition</span> <span class=\"ow\">is</span> <span class=\"n\">satisfied</span><span class=\"o\">.</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">chisquare</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span><span class=\"p\">:</span> <span class=\"mf\">0.9593035785160936</span>\n\n<span class=\"o\">&gt;</span>  <span class=\"n\">Goodness</span> <span class=\"n\">of</span> <span class=\"n\">fit</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">\u03c7</span><span class=\"err\">\u00b2</span><span class=\"o\">/</span><span class=\"n\">d</span><span class=\"o\">.</span><span class=\"n\">o</span><span class=\"o\">.</span><span class=\"n\">f</span><span class=\"o\">.</span> <span class=\"o\">=</span> <span class=\"mf\">0.959304</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">p</span><span class=\"o\">-</span><span class=\"n\">value</span>   <span class=\"o\">=</span> <span class=\"mf\">0.5673</span>\n<span class=\"o\">&gt;</span> <span class=\"n\">Fit</span> <span class=\"n\">parameters</span><span class=\"p\">:</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">0</span>      <span class=\"mf\">0.0548</span><span class=\"p\">(</span><span class=\"mi\">28</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"mi\">1</span>      <span class=\"mf\">1.933</span><span class=\"p\">(</span><span class=\"mi\">64</span><span class=\"p\">)</span>\n</code></pre>\n</div>\n\n<p>where x is a <code>list</code> or <code>numpy.array</code> of <code>floats</code> and y is a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>Data stored in <code>Corr</code> objects can be fitted directly using the <code>Corr.fit</code> method.</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">my_corr</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">Corr</span><span class=\"p\">(</span><span class=\"n\">y</span><span class=\"p\">)</span>\n<span class=\"n\">fit_result</span> <span class=\"o\">=</span> <span class=\"n\">my_corr</span><span class=\"o\">.</span><span class=\"n\">fit</span><span class=\"p\">(</span><span class=\"n\">func</span><span class=\"p\">,</span> <span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">12</span><span class=\"p\">,</span> <span class=\"mi\">25</span><span class=\"p\">])</span>\n</code></pre>\n</div>\n\n<p>this can simplify working with absolute fit ranges and takes care of gaps in the data automatically.</p>\n\n<p>For fit functions with multiple independent variables the fit function can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p><code>pyerrors</code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.\nDetails about how the required covariance matrix is estimated can be found in <code>pyerrors.obs.covariance</code>.</p>\n\n<p>Direct visualizations of the performed fits can be triggered via <code>resplot=True</code> or <code>qqplot=True</code>. For all available options see <code>pyerrors.fits.least_squares</code>.</p>\n\n<h2 id=\"total-least-squares-fits\">Total least squares fits</h2>\n\n<p><code>pyerrors</code> can also fit data with errors on both the dependent and independent variables using the total least squares method also referred to orthogonal distance regression as implemented in <a href=\"https://docs.scipy.org/doc/scipy/reference/odr.html\">scipy</a>, see <code>pyerrors.fits.least_squares</code>. The syntax is identical to the standard least squares case, the only difference being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>\n\n<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>\n\n<h1 id=\"matrix-operations\">Matrix operations</h1>\n\n<p><code>pyerrors</code> provides wrappers for <code>Obs</code>- and <code>CObs</code>-valued matrix operations based on <code>numpy.linalg</code>. The supported functions include:</p>\n\n<ul>\n<li><code>inv</code> for the matrix inverse.</li>\n<li><code>cholseky</code> for the Cholesky decomposition.</li>\n<li><code>det</code> for the matrix determinant.</li>\n<li><code>eigh</code> for eigenvalues and eigenvectors of hermitean matrices.</li>\n<li><code>eig</code> for eigenvalues of general matrices.</li>\n<li><code>pinv</code> for the Moore-Penrose pseudoinverse.</li>\n<li><code>svd</code> for the singular-value-decomposition.</li>\n</ul>\n\n<p>For the full API see <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 json.gz. Files written to this format are valid JSON files that have been compressed using gzip. The structure of the content is inspired by the dobs format of the ALPHA collaboration. The aim of the format is to facilitate the storage of data in a self-contained way such that, even years after the creation of the file, it is possible to extract all necessary information:</p>\n\n<ul>\n<li>What observables are stored? Possibly: How exactly are they defined.</li>\n<li>How does each single ensemble or external quantity contribute to the error of the observable?</li>\n<li>Who did write the file when and on which machine?</li>\n</ul>\n\n<p>This can be achieved by storing all information in one single file. The export routines of <code>pyerrors</code> are written such that as much information as possible is written automatically as described in the following example</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><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=\"s2\">&quot;test_ensemble&quot;</span><span class=\"p\">])</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">tag</span> <span class=\"o\">=</span> <span class=\"s2\">&quot;My observable&quot;</span>\n\n<span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">dump_to_json</span><span class=\"p\">(</span><span class=\"n\">my_obs</span><span class=\"p\">,</span> <span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n<span class=\"c1\"># For a single observable one can equivalently use the class method dump</span>\n<span class=\"n\">my_obs</span><span class=\"o\">.</span><span class=\"n\">dump</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">,</span> <span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s2\">&quot;This file contains a test observable&quot;</span><span class=\"p\">)</span>\n\n<span class=\"n\">check</span> <span class=\"o\">=</span> <span class=\"n\">pe</span><span class=\"o\">.</span><span class=\"n\">input</span><span class=\"o\">.</span><span class=\"n\">json</span><span class=\"o\">.</span><span class=\"n\">load_json</span><span class=\"p\">(</span><span class=\"s2\">&quot;test_output_file&quot;</span><span class=\"p\">)</span>\n\n<span class=\"nb\">print</span><span class=\"p\">(</span><span class=\"n\">my_obs</span> <span class=\"o\">==</span> <span class=\"n\">check</span><span class=\"p\">)</span>\n<span class=\"o\">&gt;</span> <span class=\"kc\">True</span>\n</code></pre>\n</div>\n\n<p>The format also allows to directly write out the content of <code>Corr</code> objects or lists and arrays of <code>Obs</code> objects by passing the desired data to <code>pyerrors.input.json.dump_to_json</code>.</p>\n\n<h2 id=\"jsongz-format-specification\">json.gz format specification</h2>\n\n<p>The first entries of the file provide optional auxiliary information:</p>\n\n<ul>\n<li><code>program</code> is a string that indicates which program was used to write the file.</li>\n<li><code>version</code> is a string that specifies the version of the format.</li>\n<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>\n<li><code>date</code> is a string and contains the creation date of the file.</li>\n<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>\n<li><code>description</code> contains information on the content of the file. This field is not filled automatically in <code>pyerrors</code>. The user is advised to provide as detailed information as possible in this field. Examples are: Input files of measurements or simulations, LaTeX formulae or references to publications to specify how the observables have been computed, details on the analysis strategy, ... This field may be any valid JSON type. Strings, arrays or objects (equivalent to dicts in python) are well suited to provide information.</li>\n</ul>\n\n<p>The only necessary entry of the file is the field\n-<code>obsdata</code>, an array that contains the actual data.</p>\n\n<p>Each entry of the array belongs to a single structure of observables. Currently, these structures can be either of <code>Obs</code>, <code>list</code>, <code>numpy.ndarray</code>, <code>Corr</code>. All <code>Obs</code> inside a structure (with dimension &gt; 0) have to be defined on the same set of configurations. Different structures, that are represented by entries of the array <code>obsdata</code>, are treated independently. Each entry of the array <code>obsdata</code> has the following required entries:</p>\n\n<ul>\n<li><code>type</code> is a string that specifies the type of the structure. This allows to parse the content to the correct form after reading the file. It is always possible to interpret the content as list of Obs.</li>\n<li><code>value</code> is an array that contains the mean values of the Obs inside the structure.\nThe following entries are optional:</li>\n<li><code>layout</code> is a string that specifies the layout of multi-dimensional structures. Examples are \"2, 2\" for a 2x2 dimensional matrix or  \"64, 4, 4\" for a Corr with $T=64$ and 4x4 matrices on each time slices. \"1\" denotes a single Obs. Multi-dimensional structures are stored in row-major format (see below).</li>\n<li><code>tag</code> is any JSON type. It contains additional information concerning the structure. The <code>tag</code> of an <code>Obs</code> in <code>pyerrors</code> is written here.</li>\n<li><code>reweighted</code> is a Bool that may be used to specify, whether the <code>Obs</code> in the structure have been reweighted.</li>\n<li><code>data</code> is an array that contains the data from MC chains. We will define it below.</li>\n<li><code>cdata</code> is an array that contains the data from external quantities with an error (<code>Covobs</code> in <code>pyerrors</code>). We will define it below.</li>\n</ul>\n\n<p>The array <code>data</code> contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that contains the name of the ensemble</li>\n<li><code>replica</code>, an array that contains an entry per replica of the ensemble.</li>\n</ul>\n\n<p>Each entry of <code>replica</code> contains\n<code>name</code>, a string that contains the name of the replica\n<code>deltas</code>, an array that contains the actual data.</p>\n\n<p>Each entry in <code>deltas</code> corresponds to one configuration of the replica and has $1+N$ many entries. The first entry is an integer that specifies the configuration number that, together with ensemble and replica name, may be used to uniquely identify the configuration on which the data has been obtained. The following N entries specify the deltas, i.e., the deviation of the observable from the mean value on this configuration, of each <code>Obs</code> inside the structure. Multi-dimensional structures are stored in a row-major format. For primary observables, such as correlation functions, $value + delta_i$ matches the primary data obtained on the configuration.</p>\n\n<p>The array <code>cdata</code> contains information about the contribution of auxiliary observables, represented by <code>Covobs</code> in <code>pyerrors</code>, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</p>\n\n<ul>\n<li><code>id</code>, a string that identifies the covariance matrix</li>\n<li><code>layout</code>, a string that defines the dimensions of the $M\\times M$ covariance matrix (has to be \"M, M\" or \"1\").</li>\n<li><code>cov</code>, an array that contains the $M\\times M$ many entries of the covariance matrix, stored in row-major format.</li>\n<li><code>grad</code>, an array that contains N entries, one for each <code>Obs</code> inside the structure. Each entry itself is an array, that contains the M gradients of the Nth observable  with respect to the quantity that corresponds to the Mth diagonal entry of the covariance matrix.</li>\n</ul>\n\n<p>A JSON schema that may be used to verify the correctness of a file with respect to the format definition is stored in ./examples/json_schema.json. The schema is a self-descriptive format definition and contains an exemplary file.</p>\n\n<p>Julia I/O routines for the json.gz format, compatible with <a href=\"https://gitlab.ift.uam-csic.es/alberto/aderrors.jl\">ADerrors.jl</a>, can be found <a href=\"https://github.com/fjosw/ADjson.jl\">here</a>.</p>\n"}, "pyerrors.correlators": {"fullname": "pyerrors.correlators", "modulename": "pyerrors.correlators", "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 matrices.</p>\n\n<p>The correlator can have two types of content: An Obs at every timeslice OR a GEVP\nmatrix at every timeslice. Other dependency (eg. spatial) are not supported.</p>\n"}, "pyerrors.correlators.Corr.__init__": {"fullname": "pyerrors.correlators.Corr.__init__", "modulename": "pyerrors.correlators", "qualname": "Corr.__init__", "type": "function", "doc": "<p>Initialize a Corr object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>data_input</strong> (list or array):\nlist of Obs or list of arrays of Obs or array of Corrs</li>\n<li><strong>padding</strong> (list, optional):\nList with two entries where the first labels the padding\nat the front of the correlator and the second the padding\nat the back.</li>\n<li><strong>prange</strong> (list, optional):\nList containing the first and last timeslice of the plateau\nregion indentified for this correlator.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">data_input</span>, </span><span class=\"param\"><span class=\"n\">padding</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"mi\">0</span><span class=\"p\">,</span> <span class=\"mi\">0</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">prange</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.projected": {"fullname": "pyerrors.correlators.Corr.projected", "modulename": "pyerrors.correlators", "qualname": "Corr.projected", "type": "function", "doc": "<p>We need to project the Correlator with a Vector to get a single value at each timeslice.</p>\n\n<p>The method can use one or two vectors.\nIf two are specified it returns v1@G@v2 (the order might be very important.)\nBy default it will return the lowest source, which usually means unsmeared-unsmeared (0,0), but it does not have to</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">vector_l</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vector_r</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">normalize</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.item": {"fullname": "pyerrors.correlators.Corr.item", "modulename": "pyerrors.correlators", "qualname": "Corr.item", "type": "function", "doc": "<p>Picks the element [i,j] from every matrix and returns a correlator containing one Obs per timeslice.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>i</strong> (int):\nFirst index to be picked.</li>\n<li><strong>j</strong> (int):\nSecond index to be picked.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.is_matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.is_matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.is_matrix_symmetric", "type": "function", "doc": "<p>Checks whether a correlator matrices is symmetric on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.matrix_symmetric": {"fullname": "pyerrors.correlators.Corr.matrix_symmetric", "modulename": "pyerrors.correlators", "qualname": "Corr.matrix_symmetric", "type": "function", "doc": "<p>Symmetrizes the correlator matrices on every timeslice.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.GEVP": {"fullname": "pyerrors.correlators.Corr.GEVP", "modulename": "pyerrors.correlators", "qualname": "Corr.GEVP", "type": "function", "doc": "<p>Solve the generalized eigenvalue problem on the correlator matrix and returns the corresponding eigenvectors.</p>\n\n<p>The eigenvectors are sorted according to the descending eigenvalues, the zeroth eigenvector(s) correspond to the\nlargest eigenvalue(s). The eigenvector(s) for the individual states can be accessed via slicing</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</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=\"c1\"># Ground state vector(s)</span>\n<span class=\"n\">C</span><span class=\"o\">.</span><span class=\"n\">GEVP</span><span class=\"p\">(</span><span class=\"n\">t0</span><span class=\"o\">=</span><span class=\"mi\">2</span><span class=\"p\">)[:</span><span class=\"mi\">3</span><span class=\"p\">]</span>  <span class=\"c1\"># Vectors for the lowest three states</span>\n</code></pre>\n</div>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>t0</strong> (int):\nThe time t0 for the right hand side of the GEVP according to $G(t)v_i=\\lambda_i G(t_0)v_i$</li>\n<li><strong>ts</strong> (int):\nfixed time $G(t_s)v_i=\\lambda_i G(t_0)v_i$ if sort=None.\nIf sort=\"Eigenvector\" it gives a reference point for the sorting method.</li>\n<li><strong>sort</strong> (string):\nIf this argument is set, a list of self.T vectors per state is returned. If it is set to None, only one vector is returned.\n<ul>\n<li>\"Eigenvalue\": The eigenvector is chosen according to which eigenvalue it belongs individually on every timeslice.</li>\n<li>\"Eigenvector\": Use the method described in arXiv:2004.10472 to find the set of v(t) belonging to the state.\nThe reference state is identified by its eigenvalue at $t=t_s$.</li>\n</ul></li>\n</ul>\n\n<h6 id=\"other-parameters\">Other Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nReturns only the vector(s) for a specified state. The lowest state is zero.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Eigenvalue": {"fullname": "pyerrors.correlators.Corr.Eigenvalue", "modulename": "pyerrors.correlators", "qualname": "Corr.Eigenvalue", "type": "function", "doc": "<p>Determines the eigenvalue of the GEVP by solving and projecting the correlator</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>state</strong> (int):\nThe state one is interested in ordered by energy. The lowest state is zero.</li>\n<li><strong>All other parameters are identical to the ones of Corr.GEVP.</strong></li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">t0</span>, </span><span class=\"param\"><span class=\"n\">ts</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">state</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"n\">sort</span><span class=\"o\">=</span><span class=\"s1\">&#39;Eigenvalue&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.Hankel": {"fullname": "pyerrors.correlators.Corr.Hankel", "modulename": "pyerrors.correlators", "qualname": "Corr.Hankel", "type": "function", "doc": "<p>Constructs an NxN Hankel matrix</p>\n\n<p>C(t) c(t+1) ... c(t+n-1)\nC(t+1) c(t+2) ... c(t+n)\n.................\nC(t+(n-1)) c(t+n) ... c(t+2(n-1))</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>N</strong> (int):\nDimension of the Hankel matrix</li>\n<li><strong>periodic</strong> (bool, optional):\ndetermines whether the matrix is extended periodically</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">N</span>, </span><span class=\"param\"><span class=\"n\">periodic</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">dt</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.thin": {"fullname": "pyerrors.correlators.Corr.thin", "modulename": "pyerrors.correlators", "qualname": "Corr.thin", "type": "function", "doc": "<p>Thin out a correlator to suppress correlations</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>spacing</strong> (int):\nKeep only every 'spacing'th entry of the correlator</li>\n<li><strong>offset</strong> (int):\nOffset the equal spacing</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">spacing</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">offset</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">partner</span>, </span><span class=\"param\"><span class=\"n\">parity</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, forward, backward, improved, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "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\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>variant</strong> (str):\ndecides which definition of the finite differences derivative is used.\nAvailable choice: symmetric, improved, default: symmetric</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;symmetric&#39;</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">variant</span><span class=\"o\">=</span><span class=\"s1\">&#39;log&#39;</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span></span><span class=\"return-annotation\">):</span></span>", "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):\nTwo element list containing the timeslices on which the fit is supposed to start and stop.\nCaution: This range is inclusive as opposed to standard python indexing.\n<code>fitrange=[4, 6]</code> corresponds to the three entries 4, 5 and 6.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">function</span>, </span><span class=\"param\"><span class=\"n\">fitrange</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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<li><strong>auto_gamma</strong> (bool):\napply gamma_method with default parameters to the Corr. Defaults to None</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">plateau_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">method</span><span class=\"o\">=</span><span class=\"s1\">&#39;fit&#39;</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">prange</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.show": {"fullname": "pyerrors.correlators.Corr.show", "modulename": "pyerrors.correlators", "qualname": "Corr.show", "type": "function", "doc": "<p>Plots the correlator using the tag of the correlator 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.\nThe tags of these correlators are used as labels if available.</li>\n<li><strong>logscale</strong> (bool):\nSets y-axis to logscale.</li>\n<li><strong>plateau</strong> (Obs):\nPlateau value 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<li><strong>auto_gamma</strong> (bool):\nApply the gamma method with standard parameters to all correlators and plateau values before plotting.</li>\n<li><strong>hide_sigma</strong> (float):\nHides data points from the first value on which is consistent with zero within 'hide_sigma' standard errors.</li>\n<li><strong>references</strong> (list):\nList of floating point values that are displayed as horizontal lines for reference.</li>\n<li><strong>title</strong> (string):\nOptional title of the figure.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"bp\">self</span>,</span><span class=\"param\">\t<span class=\"n\">x_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">comp</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">y_range</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">plateau</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">fit_res</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">ylabel</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">hide_sigma</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">references</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">title</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.spaghetti_plot": {"fullname": "pyerrors.correlators.Corr.spaghetti_plot", "modulename": "pyerrors.correlators", "qualname": "Corr.spaghetti_plot", "type": "function", "doc": "<p>Produces a spaghetti plot of the correlator suited to monitor exceptional configurations.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>logscale</strong> (bool):\nDetermines whether the scale of the y-axis is logarithmic or standard.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">logscale</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "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 file of chosen type</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nName of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.print": {"fullname": "pyerrors.correlators.Corr.print", "modulename": "pyerrors.correlators", "qualname": "Corr.print", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">print_range</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sqrt": {"fullname": "pyerrors.correlators.Corr.sqrt", "modulename": "pyerrors.correlators", "qualname": "Corr.sqrt", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.log": {"fullname": "pyerrors.correlators.Corr.log", "modulename": "pyerrors.correlators", "qualname": "Corr.log", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.exp": {"fullname": "pyerrors.correlators.Corr.exp", "modulename": "pyerrors.correlators", "qualname": "Corr.exp", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sin": {"fullname": "pyerrors.correlators.Corr.sin", "modulename": "pyerrors.correlators", "qualname": "Corr.sin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cos": {"fullname": "pyerrors.correlators.Corr.cos", "modulename": "pyerrors.correlators", "qualname": "Corr.cos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tan": {"fullname": "pyerrors.correlators.Corr.tan", "modulename": "pyerrors.correlators", "qualname": "Corr.tan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.sinh": {"fullname": "pyerrors.correlators.Corr.sinh", "modulename": "pyerrors.correlators", "qualname": "Corr.sinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.cosh": {"fullname": "pyerrors.correlators.Corr.cosh", "modulename": "pyerrors.correlators", "qualname": "Corr.cosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.tanh": {"fullname": "pyerrors.correlators.Corr.tanh", "modulename": "pyerrors.correlators", "qualname": "Corr.tanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsin": {"fullname": "pyerrors.correlators.Corr.arcsin", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccos": {"fullname": "pyerrors.correlators.Corr.arccos", "modulename": "pyerrors.correlators", "qualname": "Corr.arccos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctan": {"fullname": "pyerrors.correlators.Corr.arctan", "modulename": "pyerrors.correlators", "qualname": "Corr.arctan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arcsinh": {"fullname": "pyerrors.correlators.Corr.arcsinh", "modulename": "pyerrors.correlators", "qualname": "Corr.arcsinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arccosh": {"fullname": "pyerrors.correlators.Corr.arccosh", "modulename": "pyerrors.correlators", "qualname": "Corr.arccosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.arctanh": {"fullname": "pyerrors.correlators.Corr.arctanh", "modulename": "pyerrors.correlators", "qualname": "Corr.arctanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.correlators.Corr.prune": {"fullname": "pyerrors.correlators.Corr.prune", "modulename": "pyerrors.correlators", "qualname": "Corr.prune", "type": "function", "doc": "<p>Project large correlation matrix to lowest states</p>\n\n<p>This method can be used to reduce the size of an (N x N) correlation matrix\nto (Ntrunc x Ntrunc) by solving a GEVP at very early times where the noise\nis still small.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>Ntrunc</strong> (int):\nRank of the target matrix.</li>\n<li><strong>tproj</strong> (int):\nTime where the eigenvectors are evaluated, corresponds to ts in the GEVP method.\nThe default value is 3.</li>\n<li><strong>t0proj</strong> (int):\nTime where the correlation matrix is inverted. Choosing t0proj=1 is strongly\ndiscouraged for O(a) improved theories, since the correctness of the procedure\ncannot be granted in this case. The default value is 2.</li>\n<li><strong>basematrix</strong> (Corr):\nCorrelation matrix that is used to determine the eigenvectors of the\nlowest states based on a GEVP. basematrix is taken to be the Corr itself if\nis is not specified.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>We have the basematrix $C(t)$ and the target matrix $G(t)$. We start by solving\nthe GEVP $$C(t) v_n(t, t_0) = \\lambda_n(t, t_0) C(t_0) v_n(t, t_0)$$ where $t \\equiv t_\\mathrm{proj}$\nand $t_0 \\equiv t_{0, \\mathrm{proj}}$. The target matrix is projected onto the subspace of the\nresulting eigenvectors $v_n, n=1,\\dots,N_\\mathrm{trunc}$ via\n$$G^\\prime_{i, j}(t) = (v_i, G(t) v_j)$$. This allows to reduce the size of a large\ncorrelation matrix and to remove some noise that is added by irrelevant operators.\nThis may allow to use the GEVP on $G(t)$ at late times such that the theoretically motivated\nbound $t_0 \\leq t/2$ holds, since the condition number of $G(t)$ is decreased, compared to $C(t)$.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">Ntrunc</span>, </span><span class=\"param\"><span class=\"n\">tproj</span><span class=\"o\">=</span><span class=\"mi\">3</span>, </span><span class=\"param\"><span class=\"n\">t0proj</span><span class=\"o\">=</span><span class=\"mi\">2</span>, </span><span class=\"param\"><span class=\"n\">basematrix</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.covobs": {"fullname": "pyerrors.covobs", "modulename": "pyerrors.covobs", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">mean</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">pos</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac": {"fullname": "pyerrors.dirac", "modulename": "pyerrors.dirac", "type": "module", "doc": "<p></p>\n"}, "pyerrors.dirac.epsilon_tensor": {"fullname": "pyerrors.dirac.epsilon_tensor", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor", "type": "function", "doc": "<p>Rank-3 epsilon tensor</p>\n\n<p>Based on <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.dirac.epsilon_tensor_rank4": {"fullname": "pyerrors.dirac.epsilon_tensor_rank4", "modulename": "pyerrors.dirac", "qualname": "epsilon_tensor_rank4", "type": "function", "doc": "<p>Rank-4 epsilon tensor</p>\n\n<p>Extension of <a href=\"https://codegolf.stackexchange.com/a/160375\">https://codegolf.stackexchange.com/a/160375</a></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">i</span>, </span><span class=\"param\"><span class=\"n\">j</span>, </span><span class=\"param\"><span class=\"n\">k</span>, </span><span class=\"param\"><span class=\"n\">o</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">gamma_tag</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.fits": {"fullname": "pyerrors.fits", "modulename": "pyerrors.fits", "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", "bases": "collections.abc.Sequence"}, "pyerrors.fits.Fit_result.__init__": {"fullname": "pyerrors.fits.Fit_result.__init__", "modulename": "pyerrors.fits", "qualname": "Fit_result.__init__", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">()</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"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\">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</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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\nnon-linear fits with many parameters. In case of correlated fits the guess is used to perform\nan uncorrelated fit which then serves as guess for the correlated fit.</li>\n<li><strong>method</strong> (str, optional):\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>correlated_fit</strong> (bool):\nIf True, use the full inverse covariance matrix in the definition of the chisquare cost function.\nFor details about how the covariance matrix is estimated see <code>pyerrors.obs.covariance</code>.\nIn practice the correlation matrix is Cholesky decomposed and inverted (instead of the covariance matrix).\nThis procedure should be numerically more stable as the correlation matrix is typically better conditioned (Jacobi preconditioning).\nAt the moment this option only works for <code>prior==None</code> and when no <code>method</code> is given.</li>\n<li><strong>expected_chisquare</strong> (bool):\nIf True estimates the expected chisquare which is\ncorrected by effects caused by correlated input data (default False).</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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">priors</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n\n<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=\"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\">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</code></pre>\n</div>\n\n<p>For multiple x values func can be of the form</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Based on the orthogonal distance regression module of scipy</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">silent</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>x</strong> (list):\nCan 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.</li>\n<li><strong>y</strong> (list):\nList of Obs, the dvalues of the Obs are used as yerror for the fit.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">o_y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">p</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">y</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">fit_res</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">beta</span></span><span class=\"return-annotation\">):</span></span>", "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 p-values of all fit object.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>objects</strong> (list):\nList of fit results to include in the analysis (optional).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">objects</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input": {"fullname": "pyerrors.input", "modulename": "pyerrors.input", "type": "module", "doc": "<p><code>pyerrors</code> includes an <code>input</code> submodule in which input routines and parsers for the output of various numerical programs are contained.</p>\n\n<h1 id=\"jackknife-samples\">Jackknife samples</h1>\n\n<p>For comparison with other analysis workflows <code>pyerrors</code> can also generate jackknife samples from an <code>Obs</code> object or import jackknife samples into an <code>Obs</code> object.\nSee <code>pyerrors.obs.Obs.export_jackknife</code> and <code>pyerrors.obs.import_jackknife</code> for details.</p>\n"}, "pyerrors.input.bdio": {"fullname": "pyerrors.input.bdio", "modulename": "pyerrors.input.bdio", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_list</span>, </span><span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</strong> (str):\npath to the bdio file</li>\n<li><strong>bdio_path</strong> (str):\npath to the shared bdio library libbdio.so (default ./libbdio.so)</li>\n<li><strong>start</strong> (int):\nThe first configuration to be read (default 1)</li>\n<li><strong>stop</strong> (int):\nThe last configuration to be read (default None)</li>\n<li><strong>step</strong> (int):\nFixed step size between two measurements (default 1)</li>\n<li><strong>alternative_ensemble_name</strong> (str):\nManually overwrite ensemble name</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">file_path</span>, </span><span class=\"param\"><span class=\"n\">bdio_path</span><span class=\"o\">=</span><span class=\"s1\">&#39;./libbdio.so&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs": {"fullname": "pyerrors.input.dobs", "modulename": "pyerrors.input.dobs", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.dobs.create_pobs_string": {"fullname": "pyerrors.input.dobs.create_pobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_pobs_string", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to an xml string\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obsl</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>, </span><span class=\"param\"><span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_pobs": {"fullname": "pyerrors.input.dobs.write_pobs", "modulename": "pyerrors.input.dobs", "qualname": "write_pobs", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure have to be defined on the same ensemble.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>enstag</strong> (str):\nEnstag that is written to pobs. If None, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped xml. If False, the output is an xml file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">enstag</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_pobs": {"fullname": "pyerrors.input.dobs.read_pobs", "modulename": "pyerrors.input.dobs", "qualname": "read_pobs", "type": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen pobs format.</p>\n\n<p>Tags are not written or recovered automatically.</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>full_output</strong> (bool):\nIf True, a dict containing auxiliary information and the data is returned.\nIf False, only the data is returned as list.</li>\n<li><strong>separatior_insertion</strong> (str or int):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nNone (default): Replica names remain unchanged.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.import_dobs_string": {"fullname": "pyerrors.input.dobs.import_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "import_dobs_string", "type": "function", "doc": "<p>Import a list of Obs from a string in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>content</strong> (str):\nXML string containing the data</li>\n<li><strong>noemtpy</strong> (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the file, possibly with vanishing entries.</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 as list.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">content</span>, </span><span class=\"param\"><span class=\"n\">noempty</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.read_dobs": {"fullname": "pyerrors.input.dobs.read_dobs", "modulename": "pyerrors.input.dobs", "qualname": "read_dobs", "type": "function", "doc": "<p>Import a list of Obs from an xml.gz file in the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically.</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>noemtpy</strong> (bool):\nIf True, ensembles with no contribution to the Obs are not included.\nIf False, ensembles are included as written in the 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 as list.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes XML file.</li>\n<li><strong>separatior_insertion</strong> (str, int or bool):\nstr: replace all occurences of \"separator_insertion\" within the replica names\nby \"|%s\" % (separator_insertion) when constructing the names of the replica.\nint: Insert the separator \"|\" at the position given by separator_insertion.\nTrue (default): separator \"|\" is inserted after len(ensname), assuming that the\nensemble name is a prefix to the replica name.\nNone or False: No separator is inserted.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">noempty</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>,</span><span class=\"param\">\t<span class=\"n\">separator_insertion</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.create_dobs_string": {"fullname": "pyerrors.input.dobs.create_dobs_string", "modulename": "pyerrors.input.dobs", "qualname": "create_dobs_string", "type": "function", "doc": "<p>Generate the string for the export of a list of Obs or structures containing Obs\nto a .xml.gz file according to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator |is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.dobs.write_dobs": {"fullname": "pyerrors.input.dobs.write_dobs", "modulename": "pyerrors.input.dobs", "qualname": "write_dobs", "type": "function", "doc": "<p>Export a list of Obs or structures containing Obs to a .xml.gz file\naccording to the Zeuthen dobs format.</p>\n\n<p>Tags are not written or recovered automatically. The separator | is removed from the replica names.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obsl</strong> (list):\nList of Obs that will be exported.\nThe Obs inside a structure do not have to be defined on the same set of configurations,\nbut the storage requirement is increased, if this is not the case.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>name</strong> (str):\nThe name of the observable.</li>\n<li><strong>spec</strong> (str):\nOptional string that describes the contents of the file.</li>\n<li><strong>origin</strong> (str):\nSpecify where the data has its origin.</li>\n<li><strong>symbol</strong> (list):\nA list of symbols that describe the observables to be written. May be empty.</li>\n<li><strong>who</strong> (str):\nProvide the name of the person that exports the data.</li>\n<li><strong>enstags</strong> (dict):\nProvide alternative enstag for ensembles in the form enstags = {ename: enstag}\nOtherwise, the ensemble name is used.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped XML. If False, the output is a XML file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">obsl</span>,</span><span class=\"param\">\t<span class=\"n\">fname</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">spec</span><span class=\"o\">=</span><span class=\"s1\">&#39;dobs v1.0&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">origin</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">symbol</span><span class=\"o\">=</span><span class=\"p\">[]</span>,</span><span class=\"param\">\t<span class=\"n\">who</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">enstags</span><span class=\"o\">=</span><span class=\"kc\">None</span>,</span><span class=\"param\">\t<span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons": {"fullname": "pyerrors.input.hadrons", "modulename": "pyerrors.input.hadrons", "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>gammas</strong> (tuple of strings):\nInstrad of a meson label one can also provide a tuple of two strings\nindicating the gamma matrices at source and sink.\n(\"Gamma5\", \"Gamma5\") corresponds to the pseudoscalar pseudoscalar\ntwo-point function. The gammas argument dominateds over meson.</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">meson</span><span class=\"o\">=</span><span class=\"s1\">&#39;meson_0&#39;</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">gammas</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.hadrons.read_DistillationContraction_hd5": {"fullname": "pyerrors.input.hadrons.read_DistillationContraction_hd5", "modulename": "pyerrors.input.hadrons", "qualname": "read_DistillationContraction_hd5", "type": "function", "doc": "<p>Read hadrons DistillationContraction hdf5 files in given directory structure</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath to the directories to read</li>\n<li><strong>ens_id</strong> (str):\nname of the ensemble, required for internal bookkeeping</li>\n<li><strong>diagrams</strong> (list):\nList of strings of the diagrams to extract, e.g. [\"direct\", \"box\", \"cross\"].</li>\n<li><strong>idl</strong> (range):\nIf specified only configurations in the given range are read in.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">diagrams</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;direct&#39;</span><span class=\"p\">]</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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>:  An ndarray alias :term:<code>generic &lt;generic type&gt;</code>\nw.r.t. its <code>dtype.type &lt;numpy.dtype.type&gt;</code>.  </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=\"pdoc-code codehilite\">\n<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>\n</div>\n\n<p>Second mode:</p>\n\n<div class=\"pdoc-code codehilite\">\n<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>\n</div>\n", "bases": "numpy.ndarray"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">()</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">filestem</span>, </span><span class=\"param\"><span class=\"n\">ens_id</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"n\">vertices</span><span class=\"o\">=</span><span class=\"p\">[</span><span class=\"s1\">&#39;VA&#39;</span><span class=\"p\">,</span> <span class=\"s1\">&#39;AV&#39;</span><span class=\"p\">]</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json": {"fullname": "pyerrors.input.json", "modulename": "pyerrors.input.json", "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 moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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 moment, these objects can be\neither of: Obs, list, numpy.ndarray, Corr.\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">ol</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.import_json_string": {"fullname": "pyerrors.input.json.import_json_string", "modulename": "pyerrors.input.json", "qualname": "import_json_string", "type": "function", "doc": "<p>Reconstruct a list of Obs or structures containing Obs from a json string.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr\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>json_string</strong> (str):\njson string containing the data.</li>\n<li><strong>verbose</strong> (bool):\nPrint additional information that was written to the 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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">json_string</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "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, Corr\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.dump_dict_to_json": {"fullname": "pyerrors.input.json.dump_dict_to_json", "modulename": "pyerrors.input.json", "qualname": "dump_dict_to_json", "type": "function", "doc": "<p>Export a dict 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>od</strong> (dict):\nDict of JSON valid structures and objects that will be exported.\nAt the moment, these objects can be either of: Obs, list, numpy.ndarray, Corr.\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>reps</strong> (str):\nSpecify the structure of the placeholder in exported dict to be reps[0-9]+.</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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">od</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"n\">indent</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.json.load_json_dict": {"fullname": "pyerrors.input.json.load_json_dict", "modulename": "pyerrors.input.json", "qualname": "load_json_dict", "type": "function", "doc": "<p>Import a dict of Obs or structures containing Obs from a .json(.gz) file.</p>\n\n<p>The following structures are supported: Obs, list, numpy.ndarray, Corr</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<li><strong>reps</strong> (str):\nSpecify the structure of the placeholder in imported dict to be reps[0-9]+.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">verbose</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"n\">full_output</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">reps</span><span class=\"o\">=</span><span class=\"s1\">&#39;DICTOBS&#39;</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.misc": {"fullname": "pyerrors.input.misc", "modulename": "pyerrors.input.misc", "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=\"parameters\">Parameters</h6>\n\n<ul>\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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD": {"fullname": "pyerrors.input.openQCD", "modulename": "pyerrors.input.openQCD", "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>path</strong> (str):\npath that contains the data files</li>\n<li><strong>prefix</strong> (str):\nall files in path that start with prefix are considered as input files.\nMay be used together postfix to consider only special file endings.\nPrefix is ignored, if the keyword 'files' is used.</li>\n<li><strong>version</strong> (str):\nversion of openQCD, default 2.0</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</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>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>postfix</strong> (str):\npostfix of the file to read, e.g. '.ms1' for openQCD-files</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>print_err</strong> (bool):\nPrint additional information that is useful for debugging.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;2.0&#39;</span>, </span><span class=\"param\"><span class=\"n\">names</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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\nsufficiently decayed at x0=xmin.\nThe data around the zero crossing of t^2<E> - 0.3\nis fitted with a linear function\nfrom which the exact root is extracted.</p>\n\n<p>It is assumed that one measurement is performed for each config.\nIf this is not the case, the resulting idl, as well as the handling\nof r_start, r_stop and r_step is wrong and the user has to correct\nthis in the resulting observable.</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\nwhen 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\neffects 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\ncrossing 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>r_step</strong> (int):\ninteger that defines a fixed step size between two measurements (in units of configs)\nIf not given, r_step=1 is assumed.</li>\n<li><strong>plaquette</strong> (bool):\nIf true extract the plaquette estimate of t0 instead.</li>\n<li><strong>names</strong> (list):\nlist of names that is assigned to the data according according\nto the order in the file list. Use careful, if you do not provide file names!</li>\n<li><strong>files</strong> (list):\nlist which contains the filenames to be read. No automatic detection of\nfiles performed if given.</li>\n<li><strong>plot_fit</strong> (bool):\nIf true, the fit for the extraction of t0 is shown together with the data.</li>\n<li><strong>assume_thermalization</strong> (bool):\nIf True: If the first record divided by the distance between two measurements is larger than\n1, it is assumed that this is due to thermalization and the first measurement belongs\nto the first config (default).\nIf False: The config numbers are assumed to be traj_number // difference</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">dtr_read</span>, </span><span class=\"param\"><span class=\"n\">xmin</span>, </span><span class=\"param\"><span class=\"n\">spatial_extent</span>, </span><span class=\"param\"><span class=\"n\">fit_range</span><span class=\"o\">=</span><span class=\"mi\">5</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop": {"fullname": "pyerrors.input.openQCD.read_qtop", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop", "type": "function", "doc": "<p>Read the topologial charge based on openQCD gradient flow measurements.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nEither openQCD or sfqcd, depending on the data.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</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>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n<li><strong>integer_charge</strong> (bool):\nIf True, the charge is rounded towards the nearest integer on each config.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;openQCD&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_gf_coupling": {"fullname": "pyerrors.input.openQCD.read_gf_coupling", "modulename": "pyerrors.input.openQCD", "qualname": "read_gf_coupling", "type": "function", "doc": "<p>Read the gradient flow coupling based on sfqcd gradient flow measurements. See 1607.06423 for details.</p>\n\n<p>Note: The current implementation only works for c=0.3 and T=L. The definition of the coupling in 1607.06423 requires projection to topological charge zero which is not done within this function but has to be performed in a separate step.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat.\nIgnored if file names are passed explicitly via keyword files.</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L.</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of measurements\nbetween two configs.\nIf it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</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>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length.</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for the coupling. If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">dtr_cnfg</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">Zeuthen_flow</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.qtop_projection": {"fullname": "pyerrors.input.openQCD.qtop_projection", "modulename": "pyerrors.input.openQCD", "qualname": "qtop_projection", "type": "function", "doc": "<p>Returns the projection to the topological charge sector defined by target.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (Obs):\nTopological charge.</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">qtop</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.openQCD.read_qtop_sector": {"fullname": "pyerrors.input.openQCD.read_qtop_sector", "modulename": "pyerrors.input.openQCD", "qualname": "read_qtop_sector", "type": "function", "doc": "<p>Constructs reweighting factors to a specified topological sector.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>path</strong> (str):\npath of the measurement files</li>\n<li><strong>prefix</strong> (str):\nprefix of the measurement files, e.g. <prefix>_id0_r0.ms.dat</li>\n<li><strong>c</strong> (double):\nSmearing radius in units of the lattice extent, c = sqrt(8 t0) / L</li>\n<li><strong>target</strong> (int):\nSpecifies the topological sector to be reweighted to (default 0)</li>\n<li><strong>dtr_cnfg</strong> (int):\n(optional) parameter that specifies the number of trajectories\nbetween two configs.\nif it is not set, the distance between two measurements\nin the file is assumed to be the distance between two configurations.</li>\n<li><strong>steps</strong> (int):\n(optional) Distance between two configurations in units of trajectories /\n cycles. Assumed to be the distance between two measurements * dtr_cnfg if not given</li>\n<li><strong>version</strong> (str):\nversion string of the openQCD (sfqcd) version used to create\nthe ensemble. Default is 2.0. May also be set to sfqcd.</li>\n<li><strong>L</strong> (int):\nspatial length of the lattice in L/a.\nHAS to be set if version != sfqcd, since openQCD does not provide\nthis in the header</li>\n<li><strong>r_start</strong> (list):\noffset of the first ensemble, making it easier to match\nlater on with other Obs</li>\n<li><strong>r_stop</strong> (list):\nlast configurations that need to be read (per replicum)</li>\n<li><strong>files</strong> (list):\nspecify the exact files that need to be read\nfrom path, practical if e.g. only one replicum is needed</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>Zeuthen_flow</strong> (bool):\n(optional) If True, the Zeuthen flow is used for Qtop. Only possible\nfor version=='sfqcd' If False, the Wilson flow is used.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span>, </span><span class=\"param\"><span class=\"n\">prefix</span>, </span><span class=\"param\"><span class=\"n\">c</span>, </span><span class=\"param\"><span class=\"n\">target</span><span class=\"o\">=</span><span class=\"mi\">0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas": {"fullname": "pyerrors.input.pandas", "modulename": "pyerrors.input.pandas", "type": "module", "doc": "<p></p>\n"}, "pyerrors.input.pandas.to_sql": {"fullname": "pyerrors.input.pandas.to_sql", "modulename": "pyerrors.input.pandas", "qualname": "to_sql", "type": "function", "doc": "<p>Write DataFrame including Obs or Corr valued columns to sqlite database.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be written to the database.</li>\n<li><strong>table_name</strong> (str):\nName of the table in the database.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>if exists</strong> (str):\nHow to behave if table already exists. Options 'fail', 'replace', 'append'.</li>\n<li><strong>gz</strong> (bool):\nIf True the json strings are gzipped.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">table_name</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">if_exists</span><span class=\"o\">=</span><span class=\"s1\">&#39;fail&#39;</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.read_sql": {"fullname": "pyerrors.input.pandas.read_sql", "modulename": "pyerrors.input.pandas", "qualname": "read_sql", "type": "function", "doc": "<p>Execute SQL query on sqlite database and obtain DataFrame including Obs or Corr valued columns.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>sql</strong> (str):\nSQL query to be executed.</li>\n<li><strong>db</strong> (str):\nPath to the sqlite database.</li>\n<li><strong>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">sql</span>, </span><span class=\"param\"><span class=\"n\">db</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.dump_df": {"fullname": "pyerrors.input.pandas.dump_df", "modulename": "pyerrors.input.pandas", "qualname": "dump_df", "type": "function", "doc": "<p>Exports a pandas DataFrame containing Obs valued columns to a (gzipped) csv file.</p>\n\n<p>Before making use of pandas to_csv functionality Obs objects are serialized via the standardized\njson format of pyerrors.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>df</strong> (pandas.DataFrame):\nDataframe to be dumped to a file.</li>\n<li><strong>fname</strong> (str):\nFilename of the output file.</li>\n<li><strong>gz</strong> (bool):\nIf True, the output is a gzipped csv file. If False, the output is a csv file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">df</span>, </span><span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.pandas.load_df": {"fullname": "pyerrors.input.pandas.load_df", "modulename": "pyerrors.input.pandas", "qualname": "load_df", "type": "function", "doc": "<p>Imports a pandas DataFrame from a csv.(gz) file in which Obs objects are serialized as json strings.</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>auto_gamma</strong> (bool):\nIf True applies the gamma_method to all imported Obs objects with the default parameters for\nthe error analysis. Default False.</li>\n<li><strong>gz</strong> (bool):\nIf True, assumes that data is gzipped. If False, assumes JSON file.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">fname</span>, </span><span class=\"param\"><span class=\"n\">auto_gamma</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">gz</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.sfcf": {"fullname": "pyerrors.input.sfcf", "modulename": "pyerrors.input.sfcf", "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>quarks</strong> (str):\nLabel of the quarks used in the sfcf input file. e.g. \"quark quark\"\nfor version 0.0 this does NOT need to be given with the typical \" - \"\nthat is present in the output file,\nthis is done automatically for this version</li>\n<li><strong>noffset</strong> (int):\nOffset of the source (only relevant when wavefunctions are used)</li>\n<li><strong>wf</strong> (int):\nID of wave function</li>\n<li><strong>wf2</strong> (int):\nID of the second wavefunction\n(only relevant for boundary-to-boundary correlation functions)</li>\n<li><strong>im</strong> (bool):\nif True, read imaginary instead of real part\nof the correlation function.</li>\n<li><strong>corr_type</strong> (str):\nchange between bi (boundary - inner) (default) bib (boundary - inner - boundary) and bb (boundary - boundary)\ncorrelator types</li>\n<li><strong>names</strong> (list):\nAlternative labeling for replicas/ensembles.\nHas to have the appropriate length</li>\n<li><strong>ens_name</strong> (str):\nreplaces the name of the ensemble</li>\n<li><strong>version</strong> (str):\nversion of SFCF, with which the measurement was done.\nif the compact output option (-c) was specified,\nappend a \"c\" to the version (e.g. \"1.0c\")\nif the append output option (-a) was specified,\nappend an \"a\" to the version</li>\n<li><strong>cfg_separator</strong> (str):\nString that separates the ensemble identifier from the configuration number (default 'n').</li>\n<li><strong>replica</strong> (list):\nlist of replica to be read, default is all</li>\n<li><strong>files</strong> (list):\nlist of files to be read per replica, default is all.\nfor non-compact output format, hand the folders to be read here.</li>\n<li><strong>check_configs:</strong>: list of list of supposed configs, eg. [range(1,1000)]\nfor one replicum with 1000 configs</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code multiline\">(<span class=\"param\">\t<span class=\"n\">path</span>,</span><span class=\"param\">\t<span class=\"n\">prefix</span>,</span><span class=\"param\">\t<span class=\"n\">name</span>,</span><span class=\"param\">\t<span class=\"n\">quarks</span><span class=\"o\">=</span><span class=\"s1\">&#39;.*&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">corr_type</span><span class=\"o\">=</span><span class=\"s1\">&#39;bi&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">noffset</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">wf2</span><span class=\"o\">=</span><span class=\"mi\">0</span>,</span><span class=\"param\">\t<span class=\"n\">version</span><span class=\"o\">=</span><span class=\"s1\">&#39;1.0c&#39;</span>,</span><span class=\"param\">\t<span class=\"n\">cfg_separator</span><span class=\"o\">=</span><span class=\"s1\">&#39;n&#39;</span>,</span><span class=\"param\">\t<span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.input.utils": {"fullname": "pyerrors.input.utils", "modulename": "pyerrors.input.utils", "type": "module", "doc": "<p>Utilities for the input</p>\n"}, "pyerrors.input.utils.check_idl": {"fullname": "pyerrors.input.utils.check_idl", "modulename": "pyerrors.input.utils", "qualname": "check_idl", "type": "function", "doc": "<p>Checks if list of configurations is contained in an idl</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>idl</strong> (range or list):\nidl of the current replicum</li>\n<li><strong>che</strong> (list):\nlist of configurations to be checked against</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">idl</span>, </span><span class=\"param\"><span class=\"n\">che</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg": {"fullname": "pyerrors.linalg", "modulename": "pyerrors.linalg", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">subscripts</span>, </span><span class=\"param\"><span class=\"o\">*</span><span class=\"n\">operands</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.cholesky": {"fullname": "pyerrors.linalg.cholesky", "modulename": "pyerrors.linalg", "qualname": "cholesky", "type": "function", "doc": "<p>Cholesky decomposition of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.linalg.det": {"fullname": "pyerrors.linalg.det", "modulename": "pyerrors.linalg", "qualname": "det", "type": "function", "doc": "<p>Determinant of Obs valued matrices.</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">x</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc": {"fullname": "pyerrors.misc", "modulename": "pyerrors.misc", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obj</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">path</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.misc.pseudo_Obs": {"fullname": "pyerrors.misc.pseudo_Obs", "modulename": "pyerrors.misc", "qualname": "pseudo_Obs", "type": "function", "doc": "<p>Generate an Obs object with given value, dvalue and name for test purposes</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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">value</span>, </span><span class=\"param\"><span class=\"n\">dvalue</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">tau</span><span class=\"o\">=</span><span class=\"mf\">0.5</span>, </span><span class=\"param\"><span class=\"n\">samples</span><span class=\"o\">=</span><span class=\"mi\">1000</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.mpm": {"fullname": "pyerrors.mpm", "modulename": "pyerrors.mpm", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">corrs</span>, </span><span class=\"param\"><span class=\"n\">k</span><span class=\"o\">=</span><span class=\"mi\">1</span>, </span><span class=\"param\"><span class=\"n\">p</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs": {"fullname": "pyerrors.obs", "modulename": "pyerrors.obs", "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</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">samples</span>, </span><span class=\"param\"><span class=\"n\">names</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">ens_content</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.reweight": {"fullname": "pyerrors.obs.Obs.reweight", "modulename": "pyerrors.obs", "qualname": "Obs.reweight", "type": "function", "doc": "<p>Reweight the obs with given rewighting factors.</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. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">weight</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">sigma</span><span class=\"o\">=</span><span class=\"mi\">1</span></span><span class=\"return-annotation\">):</span></span>", "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>atol</strong> (float):\nAbsolute tolerance (for details see numpy documentation).</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">atol</span><span class=\"o\">=</span><span class=\"mf\">1e-10</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">expand</span><span class=\"o\">=</span><span class=\"kc\">True</span></span><span class=\"return-annotation\">):</span></span>", "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\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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">save</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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 file 'name' of chosen format.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>filename</strong> (str):\nname of the file to be saved.</li>\n<li><strong>datatype</strong> (str):\nFormat of the exported file. Supported formats include\n\"json.gz\" and \"pickle\"</li>\n<li><strong>description</strong> (str):\nDescription for output file, only relevant for json.gz format.</li>\n<li><strong>path</strong> (str):\nspecifies a custom path for the file (default '.')</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"n\">filename</span>, </span><span class=\"param\"><span class=\"n\">datatype</span><span class=\"o\">=</span><span class=\"s1\">&#39;json.gz&#39;</span>, </span><span class=\"param\"><span class=\"n\">description</span><span class=\"o\">=</span><span class=\"s1\">&#39;&#39;</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sqrt": {"fullname": "pyerrors.obs.Obs.sqrt", "modulename": "pyerrors.obs", "qualname": "Obs.sqrt", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.log": {"fullname": "pyerrors.obs.Obs.log", "modulename": "pyerrors.obs", "qualname": "Obs.log", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.exp": {"fullname": "pyerrors.obs.Obs.exp", "modulename": "pyerrors.obs", "qualname": "Obs.exp", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sin": {"fullname": "pyerrors.obs.Obs.sin", "modulename": "pyerrors.obs", "qualname": "Obs.sin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cos": {"fullname": "pyerrors.obs.Obs.cos", "modulename": "pyerrors.obs", "qualname": "Obs.cos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tan": {"fullname": "pyerrors.obs.Obs.tan", "modulename": "pyerrors.obs", "qualname": "Obs.tan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsin": {"fullname": "pyerrors.obs.Obs.arcsin", "modulename": "pyerrors.obs", "qualname": "Obs.arcsin", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccos": {"fullname": "pyerrors.obs.Obs.arccos", "modulename": "pyerrors.obs", "qualname": "Obs.arccos", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctan": {"fullname": "pyerrors.obs.Obs.arctan", "modulename": "pyerrors.obs", "qualname": "Obs.arctan", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.sinh": {"fullname": "pyerrors.obs.Obs.sinh", "modulename": "pyerrors.obs", "qualname": "Obs.sinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.cosh": {"fullname": "pyerrors.obs.Obs.cosh", "modulename": "pyerrors.obs", "qualname": "Obs.cosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.tanh": {"fullname": "pyerrors.obs.Obs.tanh", "modulename": "pyerrors.obs", "qualname": "Obs.tanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arcsinh": {"fullname": "pyerrors.obs.Obs.arcsinh", "modulename": "pyerrors.obs", "qualname": "Obs.arcsinh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arccosh": {"fullname": "pyerrors.obs.Obs.arccosh", "modulename": "pyerrors.obs", "qualname": "Obs.arccosh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.Obs.arctanh": {"fullname": "pyerrors.obs.Obs.arctanh", "modulename": "pyerrors.obs", "qualname": "Obs.arctanh", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">real</span>, </span><span class=\"param\"><span class=\"n\">imag</span><span class=\"o\">=</span><span class=\"mf\">0.0</span></span>)</span>"}, "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.CObs.conjugate": {"fullname": "pyerrors.obs.CObs.conjugate", "modulename": "pyerrors.obs", "qualname": "CObs.conjugate", "type": "function", "doc": "<p></p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"bp\">self</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">data</span>, </span><span class=\"param\"><span class=\"n\">array_mode</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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. Default False.</li>\n</ul>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">weight</span>, </span><span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>Keep in mind to only correlate primary observables which have not been reweighted\nyet. The reweighting has to be applied after correlating the observables.\nCurrently only works if ensembles are identical (this is not strictly necessary).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs_a</span>, </span><span class=\"param\"><span class=\"n\">obs_b</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.obs.covariance": {"fullname": "pyerrors.obs.covariance", "modulename": "pyerrors.obs", "qualname": "covariance", "type": "function", "doc": "<p>Calculates the error covariance matrix of a set of observables.</p>\n\n<p>The gamma method has to be applied first to all observables.</p>\n\n<h6 id=\"parameters\">Parameters</h6>\n\n<ul>\n<li><strong>obs</strong> (list or numpy.ndarray):\nList or one dimensional array of Obs</li>\n<li><strong>visualize</strong> (bool):\nIf True plots the corresponding normalized correlation matrix (default False).</li>\n<li><strong>correlation</strong> (bool):\nIf True the correlation matrix instead of the error covariance matrix is returned (default False).</li>\n<li><strong>smooth</strong> (None or int):\nIf smooth is an integer 'E' between 2 and the dimension of the matrix minus 1 the eigenvalue\nsmoothing procedure of hep-lat/9412087 is applied to the correlation matrix which leaves the\nlargest E eigenvalues essentially unchanged and smoothes the smaller eigenvalues to avoid extremely\nsmall ones.</li>\n</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>The error covariance is defined such that it agrees with the squared standard error for two identical observables\n$$\\operatorname{cov}(a,a)=\\sum_{s=1}^N\\delta_a^s\\delta_a^s/N^2=\\Gamma_{aa}(0)/N=\\operatorname{var}(a)/N=\\sigma_a^2$$\nin the absence of autocorrelation.\nThe error covariance is estimated by calculating the correlation matrix assuming no autocorrelation and then rescaling the correlation matrix by the full errors including the previous gamma method estimate for the autocorrelation of the observables. The covariance at windowsize 0 is guaranteed to be positive semi-definite\n$$\\sum_{i,j}v_i\\Gamma_{ij}(0)v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i,j}v_i\\delta_i^s\\delta_j^s v_j=\\frac{1}{N}\\sum_{s=1}^N\\sum_{i}|v_i\\delta_i^s|^2\\geq 0\\,,$$ for every $v\\in\\mathbb{R}^M$, while such an identity does not hold for larger windows/lags.\nFor observables defined on a single ensemble our approximation is equivalent to assuming that the integrated autocorrelation time of an off-diagonal element is equal to the geometric mean of the integrated autocorrelation times of the corresponding diagonal elements.\n$$\\tau_{\\mathrm{int}, ij}=\\sqrt{\\tau_{\\mathrm{int}, i}\\times \\tau_{\\mathrm{int}, j}}$$\nThis construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">obs</span>, </span><span class=\"param\"><span class=\"n\">visualize</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">correlation</span><span class=\"o\">=</span><span class=\"kc\">False</span>, </span><span class=\"param\"><span class=\"n\">smooth</span><span class=\"o\">=</span><span class=\"kc\">None</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">jacks</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">idl</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "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</ul>\n\n<h6 id=\"notes\">Notes</h6>\n\n<p>It is not possible to combine obs which are based on the same replicum</p>\n", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">list_of_obs</span></span><span class=\"return-annotation\">):</span></span>", "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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">means</span>, </span><span class=\"param\"><span class=\"n\">cov</span>, </span><span class=\"param\"><span class=\"n\">name</span>, </span><span class=\"param\"><span class=\"n\">grad</span><span class=\"o\">=</span><span class=\"kc\">None</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.roots": {"fullname": "pyerrors.roots", "modulename": "pyerrors.roots", "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><p><strong>func</strong> (object):\nFunction to be minimized. Any numpy functions have to use the autograd.numpy wrapper.\nExample:</p>\n\n<div class=\"pdoc-code codehilite\">\n<pre><span></span><code><span class=\"kn\">import</span> <span class=\"nn\">autograd.numpy</span> <span class=\"k\">as</span> <span class=\"nn\">anp</span>\n<span class=\"k\">def</span> <span class=\"nf\">root_func</span><span class=\"p\">(</span><span class=\"n\">x</span><span class=\"p\">,</span> <span class=\"n\">d</span><span class=\"p\">):</span>\n   <span class=\"k\">return</span> <span class=\"n\">anp</span><span class=\"o\">.</span><span class=\"n\">exp</span><span class=\"p\">(</span><span class=\"o\">-</span><span class=\"n\">x</span> <span class=\"o\">**</span> <span class=\"mi\">2</span><span class=\"p\">)</span> <span class=\"o\">-</span> <span class=\"n\">d</span>\n</code></pre>\n</div></li>\n<li><p><strong>guess</strong> (float):\nInitial guess for the minimization.</p></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", "signature": "<span class=\"signature pdoc-code condensed\">(<span class=\"param\"><span class=\"n\">d</span>, </span><span class=\"param\"><span class=\"n\">func</span>, </span><span class=\"param\"><span class=\"n\">guess</span><span class=\"o\">=</span><span class=\"mf\">1.0</span>, </span><span class=\"param\"><span class=\"o\">**</span><span class=\"n\">kwargs</span></span><span class=\"return-annotation\">):</span></span>", "funcdef": "def"}, "pyerrors.version": {"fullname": "pyerrors.version", "modulename": "pyerrors.version", "type": "module", "doc": "<p></p>\n"}}, "docInfo": {"pyerrors": {"qualname": 0, "fullname": 1, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 8005}, "pyerrors.correlators": {"qualname": 0, "fullname": 2, "annotation": 0, "default_value": 0, "signature": 0, "bases": 0, "doc": 3}, "pyerrors.correlators.Corr": {"qualname": 1, "fullname": 3, "annotation": 0, "default_value": 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