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window.MathJax = {
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tex: {
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@ -99,7 +99,7 @@ pyerrors </h1>
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<div class="docstring"><h1 id="what-is-pyerrors">What is pyerrors?</h1>
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<p><code>pyerrors</code> is a python package for error computation and propagation of Markov chain Monte Carlo data.
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<p><code><a href="">pyerrors</a></code> is a python package for error computation and propagation of Markov chain Monte Carlo data.
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It 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>
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<ul>
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@ -126,7 +126,7 @@ It is based on the gamma method <a href="https://arxiv.org/abs/hep-lat/0306017">
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<h1 id="the-obs-class">The <code>Obs</code> class</h1>
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<p><code>pyerrors</code> introduces a new datatype, <code>Obs</code>, which simplifies error propagation and estimation for auto- and cross-correlated data.
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<p><code><a href="">pyerrors</a></code> introduces a new datatype, <code>Obs</code>, which simplifies error propagation and estimation for auto- and cross-correlated data.
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An <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.
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The samples can either be provided as python list or as numpy array.
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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.</p>
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@ -163,7 +163,7 @@ The required derivatives $\bar{f}_\alpha$ are evaluated up to machine precision
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<h2 id="error-estimation">Error estimation</h2>
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<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>.
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<p>The error estimation within <code><a href="">pyerrors</a></code> is based on the gamma method introduced in <a href="https://arxiv.org/abs/hep-lat/0306017">arXiv:hep-lat/0306017</a>.
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After having arrived at the derived quantity of interest the <code>gamma_method</code> can be called as detailed in the following example.</p>
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<div class="pdoc-code codehilite"><pre><span></span><code><span class="n">my_sum</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span>
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@ -223,7 +223,7 @@ In this case the error estimate is identical to the sample standard error.</p>
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<span class="o">></span> <span class="err">·</span> <span class="n">Ensemble</span> <span class="s1">'ensemble2'</span> <span class="p">:</span> <span class="mi">500</span> <span class="n">configurations</span> <span class="p">(</span><span class="kn">from</span> <span class="mi">1</span> <span class="n">to</span> <span class="mi">500</span><span class="p">)</span>
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</code></pre></div>
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<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>
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<p><code><a href="">pyerrors</a></code> identifies multiple replica (independent Markov chains with identical simulation parameters) by the vertical bar <code>|</code> in the name of the data set.</p>
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<div class="pdoc-code codehilite"><pre><span></span><code><span class="n">obs1</span> <span class="o">=</span> <span class="n">pe</span><span class="o">.</span><span class="n">Obs</span><span class="p">([</span><span class="n">samples1</span><span class="p">],</span> <span class="p">[</span><span class="s1">'ensemble1|r01'</span><span class="p">])</span>
|
||||
<span class="n">obs2</span> <span class="o">=</span> <span class="n">pe</span><span class="o">.</span><span class="n">Obs</span><span class="p">([</span><span class="n">samples2</span><span class="p">],</span> <span class="p">[</span><span class="s1">'ensemble1|r02'</span><span class="p">])</span>
|
||||
|
|
@ -284,7 +284,7 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
|
|||
|
||||
<h1 id="correlators">Correlators</h1>
|
||||
|
||||
<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>
|
||||
<p>When one is not interested in single observables but correlation functions, <code><a href="">pyerrors</a></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>
|
||||
|
||||
<div class="pdoc-code codehilite"><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="nb">print</span><span class="p">(</span><span class="n">my_corr</span><span class="p">)</span>
|
||||
|
|
@ -321,7 +321,7 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
|
|||
<div class="pdoc-code codehilite"><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>
|
||||
</code></pre></div>
|
||||
|
||||
<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>
|
||||
<p><code><a href="">pyerrors</a></code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>
|
||||
|
||||
<ul>
|
||||
<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>
|
||||
|
|
@ -338,13 +338,13 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
|
|||
<li><code>Corr.reweight</code> reweights the correlator.</li>
|
||||
</ul>
|
||||
|
||||
<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><a href="pyerrors/correlators.html#Corr.GEVP">pyerrors.correlators.Corr.GEVP</a></code>).</p>
|
||||
<p><code><a href="">pyerrors</a></code> can also handle matrices of correlation functions and extract energy states from these matrices via a generalized eigenvalue problem (see <code><a href="pyerrors/correlators.html#Corr.GEVP">pyerrors.correlators.Corr.GEVP</a></code>).</p>
|
||||
|
||||
<p>For the full API see <code><a href="pyerrors/correlators.html#Corr">pyerrors.correlators.Corr</a></code>.</p>
|
||||
|
||||
<h1 id="complex-valued-observables">Complex valued observables</h1>
|
||||
|
||||
<p><code>pyerrors</code> can handle complex valued observables via the class <code><a href="pyerrors/obs.html#CObs">pyerrors.obs.CObs</a></code>.
|
||||
<p><code><a href="">pyerrors</a></code> can handle complex valued observables via the class <code><a href="pyerrors/obs.html#CObs">pyerrors.obs.CObs</a></code>.
|
||||
<code>CObs</code> are initialized with a real and an imaginary part which both can be <code>Obs</code> valued.</p>
|
||||
|
||||
<div class="pdoc-code codehilite"><pre><span></span><code><span class="n">my_real_part</span> <span class="o">=</span> <span class="n">pe</span><span class="o">.</span><span class="n">Obs</span><span class="p">([</span><span class="n">samples1</span><span class="p">],</span> <span class="p">[</span><span class="s1">'ensemble1'</span><span class="p">])</span>
|
||||
|
|
@ -366,11 +366,11 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
|
|||
|
||||
<h1 id="the-covobs-class">The <code>Covobs</code> class</h1>
|
||||
|
||||
<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>
|
||||
<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><a href="">pyerrors</a></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>
|
||||
|
||||
<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>
|
||||
<p>This concept is built into the definition of <code>Covobs</code>. In <code><a href="">pyerrors</a></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>
|
||||
|
||||
<div class="pdoc-code codehilite"><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>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><code><span class="kn">import</span> <span class="nn"><a href="pyerrors/obs.html">pyerrors.obs</a></span> <span class="k">as</span> <span class="nn">pe</span>
|
||||
|
||||
<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">'pi^0 mass'</span><span class="p">)</span>
|
||||
<span class="n">mpi</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span>
|
||||
|
|
@ -401,7 +401,7 @@ where the Jacobian is computed for each derived quantity via automatic different
|
|||
|
||||
<h1 id="error-propagation-in-iterative-algorithms">Error propagation in iterative algorithms</h1>
|
||||
|
||||
<p><code>pyerrors</code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures 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>
|
||||
<p><code><a href="">pyerrors</a></code> supports exact linear error propagation for iterative algorithms like various variants of non-linear least sqaures 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>
|
||||
|
||||
<h2 id="least-squares-fits">Least squares fits</h2>
|
||||
|
||||
|
|
@ -451,20 +451,20 @@ where the Jacobian is computed for each derived quantity via automatic different
|
|||
<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>
|
||||
</code></pre></div>
|
||||
|
||||
<p><code>pyerrors</code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.
|
||||
<p><code><a href="">pyerrors</a></code> also supports correlated fits which can be triggered via the parameter <code>correlated_fit=True</code>.
|
||||
Details about how the required covariance matrix is estimated can be found in <code><a href="pyerrors/obs.html#covariance">pyerrors.obs.covariance</a></code>.</p>
|
||||
|
||||
<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><a href="pyerrors/fits.html#least_squares">pyerrors.fits.least_squares</a></code>.</p>
|
||||
|
||||
<h2 id="total-least-squares-fits">Total least squares fits</h2>
|
||||
|
||||
<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><a href="pyerrors/fits.html#least_squares">pyerrors.fits.least_squares</a></code>. The syntax is identical to the standard least squares case, the only diffrence being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>
|
||||
<p><code><a href="">pyerrors</a></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><a href="pyerrors/fits.html#least_squares">pyerrors.fits.least_squares</a></code>. The syntax is identical to the standard least squares case, the only diffrence being that <code>x</code> also has to be a <code>list</code> or <code>numpy.array</code> of <code>Obs</code>.</p>
|
||||
|
||||
<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>
|
||||
<p>For the full API see <code><a href="pyerrors/fits.html">pyerrors.fits</a></code> for fits and <code><a href="pyerrors/roots.html">pyerrors.roots</a></code> for finding roots of functions.</p>
|
||||
|
||||
<h1 id="matrix-operations">Matrix operations</h1>
|
||||
|
||||
<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>
|
||||
<p><code><a href="">pyerrors</a></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>
|
||||
|
||||
<ul>
|
||||
<li><code>inv</code> for the matrix inverse.</li>
|
||||
|
|
@ -476,11 +476,11 @@ Details about how the required covariance matrix is estimated can be found in <c
|
|||
<li><code>svd</code> for the singular-value-decomposition.</li>
|
||||
</ul>
|
||||
|
||||
<p>For the full API see <code>pyerrors.linalg</code>.</p>
|
||||
<p>For the full API see <code><a href="pyerrors/linalg.html">pyerrors.linalg</a></code>.</p>
|
||||
|
||||
<h1 id="export-data">Export data</h1>
|
||||
|
||||
<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>
|
||||
<p>The preferred exported file format within <code><a href="">pyerrors</a></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>
|
||||
|
||||
<ul>
|
||||
<li>What observables are stored? Possibly: How exactly are they defined.</li>
|
||||
|
|
@ -488,7 +488,7 @@ Details about how the required covariance matrix is estimated can be found in <c
|
|||
<li>Who did write the file when and on which machine?</li>
|
||||
</ul>
|
||||
|
||||
<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>
|
||||
<p>This can be achieved by storing all information in one single file. The export routines of <code><a href="">pyerrors</a></code> are written such that as much information as possible is written automatically as described in the following example</p>
|
||||
|
||||
<div class="pdoc-code codehilite"><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">"test_ensemble"</span><span class="p">])</span>
|
||||
<span class="n">my_obs</span><span class="o">.</span><span class="n">tag</span> <span class="o">=</span> <span class="s2">"My observable"</span>
|
||||
|
|
@ -515,7 +515,7 @@ Details about how the required covariance matrix is estimated can be found in <c
|
|||
<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>
|
||||
<li><code>date</code> is a string and contains the creation date of the file.</li>
|
||||
<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>
|
||||
<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>
|
||||
<li><code>description</code> contains information on the content of the file. This field is not filled automatically in <code><a href="">pyerrors</a></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>
|
||||
</ul>
|
||||
|
||||
<p>The only necessary entry of the file is the field
|
||||
|
|
@ -528,10 +528,10 @@ Details about how the required covariance matrix is estimated can be found in <c
|
|||
<li><code>value</code> is an array that contains the mean values of the Obs inside the structure.
|
||||
The following entries are optional:</li>
|
||||
<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>
|
||||
<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>
|
||||
<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><a href="">pyerrors</a></code> is written here.</li>
|
||||
<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>
|
||||
<li><code>data</code> is an array that contains the data from MC chains. We will define it below.</li>
|
||||
<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>
|
||||
<li><code>cdata</code> is an array that contains the data from external quantities with an error (<code>Covobs</code> in <code><a href="">pyerrors</a></code>). We will define it below.</li>
|
||||
</ul>
|
||||
|
||||
<p>The array <code>data</code> contains the data from MC chains. Each entry of the array corresponds to one ensemble and contains:</p>
|
||||
|
|
@ -547,7 +547,7 @@ The following entries are optional:</li>
|
|||
|
||||
<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>
|
||||
|
||||
<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>
|
||||
<p>The array <code>cdata</code> contains information about the contribution of auxiliary observables, represented by <code>Covobs</code> in <code><a href="">pyerrors</a></code>, to the total error of the observables. Each entry of the array belongs to one auxiliary covariance matrix and contains:</p>
|
||||
|
||||
<ul>
|
||||
<li><code>id</code>, a string that identifies the covariance matrix</li>
|
||||
|
|
@ -562,7 +562,7 @@ The following entries are optional:</li>
|
|||
|
||||
<h1 id="citing">Citing</h1>
|
||||
|
||||
<p>If you use <code>pyerrors</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:</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>
|
||||
|
|
|
|||
|
|
@ -3,14 +3,14 @@
|
|||
<head>
|
||||
<meta charset="utf-8">
|
||||
<meta name="viewport" content="width=device-width, initial-scale=1">
|
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<meta name="generator" content="pdoc 10.0.2"/>
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<meta name="generator" content="pdoc 10.0.3"/>
|
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<title>pyerrors.correlators API documentation</title>
|
||||
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window.MathJax = {
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tex: {
|
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|
@ -565,8 +565,10 @@
|
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<span class="n">corr</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">y</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">True</span><span class="p">)</span>
|
||||
<span class="n">covdiag</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">asarray</span><span class="p">(</span><span class="n">dy_f</span><span class="p">))</span>
|
||||
<span class="n">condn</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cond</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mf">1e8</span><span class="p">:</span>
|
||||
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Correlation matrix may be ill-conditioned, condition number: </span><span class="si">%1.2e</span><span class="s2">"</span> <span class="o">%</span> <span class="p">(</span><span class="n">condn</span><span class="p">),</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mf">0.1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">:</span>
|
||||
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="sa">f</span><span class="s2">"Cannot invert correlation matrix as its condition number exceeds machine precision (</span><span class="si">{</span><span class="n">condn</span><span class="si">:</span><span class="s2">1.2e</span><span class="si">}</span><span class="s2">)"</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">condn</span> <span class="o">></span> <span class="mi">1</span> <span class="o">/</span> <span class="n">np</span><span class="o">.</span><span class="n">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">finfo</span><span class="p">(</span><span class="nb">float</span><span class="p">)</span><span class="o">.</span><span class="n">eps</span><span class="p">):</span>
|
||||
<span class="n">warnings</span><span class="o">.</span><span class="n">warn</span><span class="p">(</span><span class="s2">"Correlation matrix may be ill-conditioned, condition number: {</span><span class="si">%1.2e</span><span class="s2">}"</span> <span class="o">%</span> <span class="p">(</span><span class="n">condn</span><span class="p">),</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
<span class="n">chol</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">cholesky</span><span class="p">(</span><span class="n">corr</span><span class="p">)</span>
|
||||
<span class="n">chol_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">linalg</span><span class="o">.</span><span class="n">inv</span><span class="p">(</span><span class="n">chol</span><span class="p">)</span>
|
||||
<span class="n">chol_inv</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">chol_inv</span><span class="p">,</span> <span class="n">covdiag</span><span class="p">)</span>
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<title>pyerrors.input API documentation</title>
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window.MathJax = {
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tex: {
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@ -74,11 +74,11 @@
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<h1 class="modulename">
|
||||
<a href="./../pyerrors.html">pyerrors</a><wbr>.input </h1>
|
||||
|
||||
<div class="docstring"><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>
|
||||
<div class="docstring"><p><code><a href="../pyerrors.html">pyerrors</a></code> includes an <code>input</code> submodule in which input routines and parsers for the output of various numerical programs are contained.</p>
|
||||
|
||||
<h1 id="jackknife-samples">Jackknife samples</h1>
|
||||
|
||||
<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.
|
||||
<p>For comparison with other analysis workflows <code><a href="../pyerrors.html">pyerrors</a></code> can also generate jackknife samples from an <code>Obs</code> object or import jackknife samples into an <code>Obs</code> object.
|
||||
See <code><a href="obs.html#Obs.export_jackknife">pyerrors.obs.Obs.export_jackknife</a></code> and <code><a href="obs.html#import_jackknife">pyerrors.obs.import_jackknife</a></code> for details.</p>
|
||||
</div>
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<title>pyerrors.input.bdio API documentation</title>
|
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