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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><a href="">pyerrors</a></code> is a python package for error computation and propagation of Markov chain Monte Carlo data.
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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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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><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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<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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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><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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<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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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><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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<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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<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>
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<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>
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@ -284,7 +284,7 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
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<h1 id="correlators">Correlators</h1>
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<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>
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<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>
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<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>
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<span class="nb">print</span><span class="p">(</span><span class="n">my_corr</span><span class="p">)</span>
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<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>
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</code></pre></div>
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<p><code><a href="">pyerrors</a></code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>
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<p><code>pyerrors</code> provides the user with a set of regularly used methods for the manipulation of correlator objects:</p>
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<ul>
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<li><code>Corr.gamma_method</code> applies the gamma method to all entries of the correlator.</li>
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@ -338,13 +338,13 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
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<li><code>Corr.reweight</code> reweights the correlator.</li>
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</ul>
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<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>
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<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>
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<p>For the full API see <code><a href="pyerrors/correlators.html#Corr">pyerrors.correlators.Corr</a></code>.</p>
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<h1 id="complex-valued-observables">Complex valued observables</h1>
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<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>.
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<p><code>pyerrors</code> can handle complex valued observables via the class <code><a href="pyerrors/obs.html#CObs">pyerrors.obs.CObs</a></code>.
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<code>CObs</code> are initialized with a real and an imaginary part which both can be <code>Obs</code> valued.</p>
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<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>
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@ -366,11 +366,11 @@ Make sure to check the autocorrelation time with e.g. <code><a href="pyerrors/ob
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<h1 id="the-covobs-class">The <code>Covobs</code> class</h1>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<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>
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<span class="n">mpi</span><span class="o">.</span><span class="n">gamma_method</span><span class="p">()</span>
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@ -401,7 +401,7 @@ where the Jacobian is computed for each derived quantity via automatic different
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<h1 id="error-propagation-in-iterative-algorithms">Error propagation in iterative algorithms</h1>
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<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>
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<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>
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<h2 id="least-squares-fits">Least squares fits</h2>
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@ -453,13 +453,13 @@ where the Jacobian is computed for each derived quantity via automatic different
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<h2 id="total-least-squares-fits">Total least squares fits</h2>
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<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>
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<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>
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<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>
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<p>For the full API see <code>pyerrors.fits</code> for fits and <code>pyerrors.roots</code> for finding roots of functions.</p>
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<h1 id="matrix-operations">Matrix operations</h1>
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<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>
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<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>
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<ul>
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<li><code>inv</code> for the matrix inverse.</li>
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@ -471,11 +471,11 @@ where the Jacobian is computed for each derived quantity via automatic different
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<li><code>svd</code> for the singular-value-decomposition.</li>
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</ul>
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<p>For the full API see <code><a href="pyerrors/linalg.html">pyerrors.linalg</a></code>.</p>
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<p>For the full API see <code>pyerrors.linalg</code>.</p>
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<h1 id="export-data">Export data</h1>
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<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>
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<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>
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<ul>
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<li>What observables are stored? Possibly: How exactly are they defined.</li>
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@ -483,7 +483,7 @@ where the Jacobian is computed for each derived quantity via automatic different
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<li>Who did write the file when and on which machine?</li>
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</ul>
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<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>
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<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>
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<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>
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<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>
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@ -510,7 +510,7 @@ where the Jacobian is computed for each derived quantity via automatic different
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<li><code>who</code> is a string that specifies the user name of the creator of the file.</li>
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<li><code>date</code> is a string and contains the creation date of the file.</li>
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<li><code>host</code> is a string and contains the hostname of the machine where the file has been written.</li>
|
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<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>
|
||||
<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>
|
||||
</ul>
|
||||
|
||||
<p>The only necessary entry of the file is the field
|
||||
|
|
@ -523,10 +523,10 @@ where the Jacobian is computed for each derived quantity via automatic different
|
|||
<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><a href="">pyerrors</a></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>pyerrors</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><a href="">pyerrors</a></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>pyerrors</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>
|
||||
|
|
@ -542,7 +542,7 @@ 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><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>
|
||||
<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>
|
||||
|
||||
<ul>
|
||||
<li><code>id</code>, a string that identifies the covariance matrix</li>
|
||||
|
|
@ -557,7 +557,7 @@ The following entries are optional:</li>
|
|||
|
||||
<h1 id="citing">Citing</h1>
|
||||
|
||||
<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>pyerrors</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>
|
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|
||||
<style>/*! * Bootstrap Reboot v5.0.0 (https://getbootstrap.com/) * Copyright 2011-2021 The Bootstrap Authors * Copyright 2011-2021 Twitter, Inc. * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE) * Forked from Normalize.css, licensed MIT (https://github.com/necolas/normalize.css/blob/master/LICENSE.md) */*,::after,::before{box-sizing:border-box}@media (prefers-reduced-motion:no-preference){:root{scroll-behavior:smooth}}body{margin:0;font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans","Liberation Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;-webkit-text-size-adjust:100%;-webkit-tap-highlight-color:transparent}hr{margin:1rem 0;color:inherit;background-color:currentColor;border:0;opacity:.25}hr:not([size]){height:1px}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}h1{font-size:calc(1.375rem + 1.5vw)}@media (min-width:1200px){h1{font-size:2.5rem}}h2{font-size:calc(1.325rem + .9vw)}@media (min-width:1200px){h2{font-size:2rem}}h3{font-size:calc(1.3rem + .6vw)}@media (min-width:1200px){h3{font-size:1.75rem}}h4{font-size:calc(1.275rem + .3vw)}@media (min-width:1200px){h4{font-size:1.5rem}}h5{font-size:1.25rem}h6{font-size:1rem}p{margin-top:0;margin-bottom:1rem}abbr[data-bs-original-title],abbr[title]{-webkit-text-decoration:underline dotted;text-decoration:underline dotted;cursor:help;-webkit-text-decoration-skip-ink:none;text-decoration-skip-ink:none}address{margin-bottom:1rem;font-style:normal;line-height:inherit}ol,ul{padding-left:2rem}dl,ol,ul{margin-top:0;margin-bottom:1rem}ol ol,ol ul,ul ol,ul ul{margin-bottom:0}dt{font-weight:700}dd{margin-bottom:.5rem;margin-left:0}blockquote{margin:0 0 1rem}b,strong{font-weight:bolder}small{font-size:.875em}mark{padding:.2em;background-color:#fcf8e3}sub,sup{position:relative;font-size:.75em;line-height:0;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:#0d6efd;text-decoration:underline}a:hover{color:#0a58ca}a:not([href]):not([class]),a:not([href]):not([class]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace;font-size:1em;direction:ltr;unicode-bidi:bidi-override}pre{display:block;margin-top:0;margin-bottom:1rem;overflow:auto;font-size:.875em}pre code{font-size:inherit;color:inherit;word-break:normal}code{font-size:.875em;color:#d63384;word-wrap:break-word}a>code{color:inherit}kbd{padding:.2rem .4rem;font-size:.875em;color:#fff;background-color:#212529;border-radius:.2rem}kbd kbd{padding:0;font-size:1em;font-weight:700}figure{margin:0 0 1rem}img,svg{vertical-align:middle}table{caption-side:bottom;border-collapse:collapse}caption{padding-top:.5rem;padding-bottom:.5rem;color:#6c757d;text-align:left}th{text-align:inherit;text-align:-webkit-match-parent}tbody,td,tfoot,th,thead,tr{border-color:inherit;border-style:solid;border-width:0}label{display:inline-block}button{border-radius:0}button:focus:not(:focus-visible){outline:0}button,input,optgroup,select,textarea{margin:0;font-family:inherit;font-size:inherit;line-height:inherit}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}select:disabled{opacity:1}[list]::-webkit-calendar-picker-indicator{display:none}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}::-moz-focus-inner{padding:0;border-style:none}textarea{resize:vertical}fieldset{min-width:0;padding:0;margin:0;border:0}legend{float:left;width:100%;padding:0;margin-bottom:.5rem;font-size:calc(1.275rem + .3vw);line-height:inherit}@media (min-width:1200px){legend{font-size:1.5rem}}legend+*{clear:left}::-webkit-datetime-edit-day-field,::-webkit-datetime-edit-fields-wrapper,::-webkit-datetime-edit-hour-field,::-webkit-datetime-edit-minute,::-webkit-datetime-edit-month-field,::-webkit-datetime-edit-text,::-webkit-datetime-edit-year-field{padding:0}::-webkit-inner-spin-button{height:auto}[type=search]{outline-offset:-2px;-webkit-appearance:textfield}::-webkit-search-decoration{-webkit-appearance:none}::-webkit-color-swatch-wrapper{padding:0}::file-selector-button{font:inherit}::-webkit-file-upload-button{font:inherit;-webkit-appearance:button}output{display:inline-block}iframe{border:0}summary{display:list-item;cursor:pointer}progress{vertical-align:baseline}[hidden]{display:none!important}</style>
|
||||
|
|
@ -74,9 +74,6 @@
|
|||
<li>
|
||||
<a class="function" href="#residual_plot">residual_plot</a>
|
||||
</li>
|
||||
<li>
|
||||
<a class="function" href="#covariance_matrix">covariance_matrix</a>
|
||||
</li>
|
||||
<li>
|
||||
<a class="function" href="#error_band">error_band</a>
|
||||
</li>
|
||||
|
|
@ -343,7 +340,7 @@
|
|||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||||
|
||||
<span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||||
|
||||
|
|
@ -559,7 +556,7 @@
|
|||
<span class="n">x0</span> <span class="o">=</span> <span class="p">[</span><span class="mf">0.1</span><span class="p">]</span> <span class="o">*</span> <span class="n">n_parms</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<span class="n">cov</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">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="mf">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">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span>
|
||||
<span class="n">corr</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">copy</span><span class="p">(</span><span class="n">cov</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)):</span>
|
||||
|
|
@ -631,7 +628,7 @@
|
|||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'expected_chisquare'</span><span class="p">)</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'correlated_fit'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="n">W</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">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<span class="n">cov</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">A</span> <span class="o">=</span> <span class="n">W</span> <span class="o">@</span> <span class="n">jacobian</span><span class="p">(</span><span class="n">func</span><span class="p">)(</span><span class="n">fit_result</span><span class="o">.</span><span class="n">x</span><span class="p">,</span> <span class="n">x</span><span class="p">)</span>
|
||||
<span class="n">P_phi</span> <span class="o">=</span> <span class="n">A</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">A</span><span class="o">.</span><span class="n">T</span> <span class="o">@</span> <span class="n">A</span><span class="p">)</span> <span class="o">@</span> <span class="n">A</span><span class="o">.</span><span class="n">T</span>
|
||||
<span class="n">expected_chisquare</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">trace</span><span class="p">((</span><span class="n">np</span><span class="o">.</span><span class="n">identity</span><span class="p">(</span><span class="n">x</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span> <span class="o">-</span> <span class="n">P_phi</span><span class="p">)</span> <span class="o">@</span> <span class="n">W</span> <span class="o">@</span> <span class="n">cov</span> <span class="o">@</span> <span class="n">W</span><span class="p">)</span>
|
||||
|
|
@ -755,33 +752,9 @@
|
|||
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
||||
<span class="sd">"""Returns the covariance matrix of y.</span>
|
||||
|
||||
<span class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
<span class="sd"> y : list or numpy.ndarray</span>
|
||||
<span class="sd"> List or one dimensional array of Obs</span>
|
||||
<span class="sd"> """</span>
|
||||
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">jtem</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">[:</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">**</span> <span class="mi">2</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">jtem</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">cov</span> <span class="o">+</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</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="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
||||
<span class="n">eigenvalues</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">eigh</span><span class="p">(</span><span class="n">cov</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">eigenvalues</span> <span class="o">>=</span> <span class="mi">0</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">"Covariance matrix is not positive semi-definite"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Eigenvalues of the covariance matrix:"</span><span class="p">,</span> <span class="n">eigenvalues</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">cov</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">error_band</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
|
||||
<span class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">cov</span> <span class="o">-</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">></span> <span class="mi">1000</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="n">np</span><span class="o">.</span><span class="n">float64</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">"Covariance matrix is not symmetric within floating point precision"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
|
||||
|
|
@ -1220,7 +1193,7 @@ If true, use the full correlation matrix in the definition of the chisquare
|
|||
<span class="k">if</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span> <span class="ow">is</span> <span class="ow">not</span> <span class="kc">None</span><span class="p">:</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">kwargs</span><span class="o">.</span><span class="n">get</span><span class="p">(</span><span class="s1">'covariance'</span><span class="p">)</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">((</span><span class="n">y</span><span class="p">,</span> <span class="n">x</span><span class="o">.</span><span class="n">ravel</span><span class="p">())))</span>
|
||||
|
||||
<span class="n">number_of_x_parameters</span> <span class="o">=</span> <span class="nb">int</span><span class="p">(</span><span class="n">m</span> <span class="o">/</span> <span class="n">x_f</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">])</span>
|
||||
|
||||
|
|
@ -1451,54 +1424,6 @@ check if the residuals of the fit are gaussian distributed.</p>
|
|||
</div>
|
||||
|
||||
|
||||
</section>
|
||||
<section id="covariance_matrix">
|
||||
<div class="attr function"><a class="headerlink" href="#covariance_matrix">#  </a>
|
||||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">covariance_matrix</span><span class="signature">(y)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span class="k">def</span> <span class="nf">covariance_matrix</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
||||
<span class="sd">"""Returns the covariance matrix of y.</span>
|
||||
|
||||
<span class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
<span class="sd"> y : list or numpy.ndarray</span>
|
||||
<span class="sd"> List or one dimensional array of Obs</span>
|
||||
<span class="sd"> """</span>
|
||||
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">i</span><span class="p">,</span> <span class="n">item</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">j</span><span class="p">,</span> <span class="n">jtem</span> <span class="ow">in</span> <span class="nb">enumerate</span><span class="p">(</span><span class="n">y</span><span class="p">[:</span><span class="n">i</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]):</span>
|
||||
<span class="k">if</span> <span class="n">i</span> <span class="o">==</span> <span class="n">j</span><span class="p">:</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">item</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">**</span> <span class="mi">2</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">item</span><span class="p">,</span> <span class="n">jtem</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">cov</span> <span class="o">+</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</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="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
||||
<span class="n">eigenvalues</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">eigh</span><span class="p">(</span><span class="n">cov</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">eigenvalues</span> <span class="o">>=</span> <span class="mi">0</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">"Covariance matrix is not positive semi-definite"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
<span class="nb">print</span><span class="p">(</span><span class="s2">"Eigenvalues of the covariance matrix:"</span><span class="p">,</span> <span class="n">eigenvalues</span><span class="p">)</span>
|
||||
<span class="k">return</span> <span class="n">cov</span>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
<div class="docstring"><p>Returns the covariance matrix of y.</p>
|
||||
|
||||
<h6 id="parameters">Parameters</h6>
|
||||
|
||||
<ul>
|
||||
<li><strong>y</strong> (list or numpy.ndarray):
|
||||
List or one dimensional array of Obs</li>
|
||||
</ul>
|
||||
</div>
|
||||
|
||||
|
||||
</section>
|
||||
<section id="error_band">
|
||||
<div class="attr function"><a class="headerlink" href="#error_band">#  </a>
|
||||
|
|
@ -1512,7 +1437,7 @@ List or one dimensional array of Obs</li>
|
|||
<summary>View Source</summary>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span class="k">def</span> <span class="nf">error_band</span><span class="p">(</span><span class="n">x</span><span class="p">,</span> <span class="n">func</span><span class="p">,</span> <span class="n">beta</span><span class="p">):</span>
|
||||
<span class="sd">"""Returns the error band for an array of sample values x, for given fit function func with optimized parameters beta."""</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance_matrix</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">covariance</span><span class="p">(</span><span class="n">beta</span><span class="p">)</span>
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">any</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">cov</span> <span class="o">-</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</span><span class="p">)</span> <span class="o">></span> <span class="mi">1000</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="n">np</span><span class="o">.</span><span class="n">float64</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">"Covariance matrix is not symmetric within floating point precision"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@
|
|||
<head>
|
||||
<meta charset="utf-8">
|
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|
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|
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<meta name="generator" content="pdoc 10.0.2"/>
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<title>pyerrors.input API documentation</title>
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<style>/*! * Bootstrap Reboot v5.0.0 (https://getbootstrap.com/) * Copyright 2011-2021 The Bootstrap Authors * Copyright 2011-2021 Twitter, Inc. * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE) * Forked from Normalize.css, licensed MIT (https://github.com/necolas/normalize.css/blob/master/LICENSE.md) */*,::after,::before{box-sizing:border-box}@media (prefers-reduced-motion:no-preference){:root{scroll-behavior:smooth}}body{margin:0;font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans","Liberation Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;-webkit-text-size-adjust:100%;-webkit-tap-highlight-color:transparent}hr{margin:1rem 0;color:inherit;background-color:currentColor;border:0;opacity:.25}hr:not([size]){height:1px}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}h1{font-size:calc(1.375rem + 1.5vw)}@media (min-width:1200px){h1{font-size:2.5rem}}h2{font-size:calc(1.325rem + .9vw)}@media (min-width:1200px){h2{font-size:2rem}}h3{font-size:calc(1.3rem + .6vw)}@media (min-width:1200px){h3{font-size:1.75rem}}h4{font-size:calc(1.275rem + .3vw)}@media (min-width:1200px){h4{font-size:1.5rem}}h5{font-size:1.25rem}h6{font-size:1rem}p{margin-top:0;margin-bottom:1rem}abbr[data-bs-original-title],abbr[title]{-webkit-text-decoration:underline dotted;text-decoration:underline dotted;cursor:help;-webkit-text-decoration-skip-ink:none;text-decoration-skip-ink:none}address{margin-bottom:1rem;font-style:normal;line-height:inherit}ol,ul{padding-left:2rem}dl,ol,ul{margin-top:0;margin-bottom:1rem}ol ol,ol ul,ul ol,ul ul{margin-bottom:0}dt{font-weight:700}dd{margin-bottom:.5rem;margin-left:0}blockquote{margin:0 0 1rem}b,strong{font-weight:bolder}small{font-size:.875em}mark{padding:.2em;background-color:#fcf8e3}sub,sup{position:relative;font-size:.75em;line-height:0;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:#0d6efd;text-decoration:underline}a:hover{color:#0a58ca}a:not([href]):not([class]),a:not([href]):not([class]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace;font-size:1em;direction:ltr;unicode-bidi:bidi-override}pre{display:block;margin-top:0;margin-bottom:1rem;overflow:auto;font-size:.875em}pre code{font-size:inherit;color:inherit;word-break:normal}code{font-size:.875em;color:#d63384;word-wrap:break-word}a>code{color:inherit}kbd{padding:.2rem .4rem;font-size:.875em;color:#fff;background-color:#212529;border-radius:.2rem}kbd kbd{padding:0;font-size:1em;font-weight:700}figure{margin:0 0 1rem}img,svg{vertical-align:middle}table{caption-side:bottom;border-collapse:collapse}caption{padding-top:.5rem;padding-bottom:.5rem;color:#6c757d;text-align:left}th{text-align:inherit;text-align:-webkit-match-parent}tbody,td,tfoot,th,thead,tr{border-color:inherit;border-style:solid;border-width:0}label{display:inline-block}button{border-radius:0}button:focus:not(:focus-visible){outline:0}button,input,optgroup,select,textarea{margin:0;font-family:inherit;font-size:inherit;line-height:inherit}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}select:disabled{opacity:1}[list]::-webkit-calendar-picker-indicator{display:none}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}::-moz-focus-inner{padding:0;border-style:none}textarea{resize:vertical}fieldset{min-width:0;padding:0;margin:0;border:0}legend{float:left;width:100%;padding:0;margin-bottom:.5rem;font-size:calc(1.275rem + .3vw);line-height:inherit}@media (min-width:1200px){legend{font-size:1.5rem}}legend+*{clear:left}::-webkit-datetime-edit-day-field,::-webkit-datetime-edit-fields-wrapper,::-webkit-datetime-edit-hour-field,::-webkit-datetime-edit-minute,::-webkit-datetime-edit-month-field,::-webkit-datetime-edit-text,::-webkit-datetime-edit-year-field{padding:0}::-webkit-inner-spin-button{height:auto}[type=search]{outline-offset:-2px;-webkit-appearance:textfield}::-webkit-search-decoration{-webkit-appearance:none}::-webkit-color-swatch-wrapper{padding:0}::file-selector-button{font:inherit}::-webkit-file-upload-button{font:inherit;-webkit-appearance:button}output{display:inline-block}iframe{border:0}summary{display:list-item;cursor:pointer}progress{vertical-align:baseline}[hidden]{display:none!important}</style>
|
||||
|
|
@ -74,11 +74,11 @@
|
|||
<h1 class="modulename">
|
||||
<a href="./../pyerrors.html">pyerrors</a><wbr>.input </h1>
|
||||
|
||||
<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>
|
||||
<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>
|
||||
|
||||
<h1 id="jackknife-samples">Jackknife samples</h1>
|
||||
|
||||
<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.
|
||||
<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.
|
||||
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>
|
||||
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@
|
|||
<head>
|
||||
<meta charset="utf-8">
|
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|
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<meta name="generator" content="pdoc 10.0.2"/>
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||||
<title>pyerrors.input.bdio API documentation</title>
|
||||
|
||||
<style>/*! * Bootstrap Reboot v5.0.0 (https://getbootstrap.com/) * Copyright 2011-2021 The Bootstrap Authors * Copyright 2011-2021 Twitter, Inc. * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE) * Forked from Normalize.css, licensed MIT (https://github.com/necolas/normalize.css/blob/master/LICENSE.md) */*,::after,::before{box-sizing:border-box}@media (prefers-reduced-motion:no-preference){:root{scroll-behavior:smooth}}body{margin:0;font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans","Liberation Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;-webkit-text-size-adjust:100%;-webkit-tap-highlight-color:transparent}hr{margin:1rem 0;color:inherit;background-color:currentColor;border:0;opacity:.25}hr:not([size]){height:1px}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}h1{font-size:calc(1.375rem + 1.5vw)}@media (min-width:1200px){h1{font-size:2.5rem}}h2{font-size:calc(1.325rem + .9vw)}@media (min-width:1200px){h2{font-size:2rem}}h3{font-size:calc(1.3rem + .6vw)}@media (min-width:1200px){h3{font-size:1.75rem}}h4{font-size:calc(1.275rem + .3vw)}@media (min-width:1200px){h4{font-size:1.5rem}}h5{font-size:1.25rem}h6{font-size:1rem}p{margin-top:0;margin-bottom:1rem}abbr[data-bs-original-title],abbr[title]{-webkit-text-decoration:underline dotted;text-decoration:underline dotted;cursor:help;-webkit-text-decoration-skip-ink:none;text-decoration-skip-ink:none}address{margin-bottom:1rem;font-style:normal;line-height:inherit}ol,ul{padding-left:2rem}dl,ol,ul{margin-top:0;margin-bottom:1rem}ol ol,ol ul,ul ol,ul ul{margin-bottom:0}dt{font-weight:700}dd{margin-bottom:.5rem;margin-left:0}blockquote{margin:0 0 1rem}b,strong{font-weight:bolder}small{font-size:.875em}mark{padding:.2em;background-color:#fcf8e3}sub,sup{position:relative;font-size:.75em;line-height:0;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:#0d6efd;text-decoration:underline}a:hover{color:#0a58ca}a:not([href]):not([class]),a:not([href]):not([class]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace;font-size:1em;direction:ltr;unicode-bidi:bidi-override}pre{display:block;margin-top:0;margin-bottom:1rem;overflow:auto;font-size:.875em}pre code{font-size:inherit;color:inherit;word-break:normal}code{font-size:.875em;color:#d63384;word-wrap:break-word}a>code{color:inherit}kbd{padding:.2rem .4rem;font-size:.875em;color:#fff;background-color:#212529;border-radius:.2rem}kbd kbd{padding:0;font-size:1em;font-weight:700}figure{margin:0 0 1rem}img,svg{vertical-align:middle}table{caption-side:bottom;border-collapse:collapse}caption{padding-top:.5rem;padding-bottom:.5rem;color:#6c757d;text-align:left}th{text-align:inherit;text-align:-webkit-match-parent}tbody,td,tfoot,th,thead,tr{border-color:inherit;border-style:solid;border-width:0}label{display:inline-block}button{border-radius:0}button:focus:not(:focus-visible){outline:0}button,input,optgroup,select,textarea{margin:0;font-family:inherit;font-size:inherit;line-height:inherit}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}select:disabled{opacity:1}[list]::-webkit-calendar-picker-indicator{display:none}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}::-moz-focus-inner{padding:0;border-style:none}textarea{resize:vertical}fieldset{min-width:0;padding:0;margin:0;border:0}legend{float:left;width:100%;padding:0;margin-bottom:.5rem;font-size:calc(1.275rem + .3vw);line-height:inherit}@media (min-width:1200px){legend{font-size:1.5rem}}legend+*{clear:left}::-webkit-datetime-edit-day-field,::-webkit-datetime-edit-fields-wrapper,::-webkit-datetime-edit-hour-field,::-webkit-datetime-edit-minute,::-webkit-datetime-edit-month-field,::-webkit-datetime-edit-text,::-webkit-datetime-edit-year-field{padding:0}::-webkit-inner-spin-button{height:auto}[type=search]{outline-offset:-2px;-webkit-appearance:textfield}::-webkit-search-decoration{-webkit-appearance:none}::-webkit-color-swatch-wrapper{padding:0}::file-selector-button{font:inherit}::-webkit-file-upload-button{font:inherit;-webkit-appearance:button}output{display:inline-block}iframe{border:0}summary{display:list-item;cursor:pointer}progress{vertical-align:baseline}[hidden]{display:none!important}</style>
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<style>/*! * Bootstrap Reboot v5.0.0 (https://getbootstrap.com/) * Copyright 2011-2021 The Bootstrap Authors * Copyright 2011-2021 Twitter, Inc. * Licensed under MIT (https://github.com/twbs/bootstrap/blob/main/LICENSE) * Forked from Normalize.css, licensed MIT (https://github.com/necolas/normalize.css/blob/master/LICENSE.md) */*,::after,::before{box-sizing:border-box}@media (prefers-reduced-motion:no-preference){:root{scroll-behavior:smooth}}body{margin:0;font-family:system-ui,-apple-system,"Segoe UI",Roboto,"Helvetica Neue",Arial,"Noto Sans","Liberation Sans",sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol","Noto Color Emoji";font-size:1rem;font-weight:400;line-height:1.5;color:#212529;background-color:#fff;-webkit-text-size-adjust:100%;-webkit-tap-highlight-color:transparent}hr{margin:1rem 0;color:inherit;background-color:currentColor;border:0;opacity:.25}hr:not([size]){height:1px}h1,h2,h3,h4,h5,h6{margin-top:0;margin-bottom:.5rem;font-weight:500;line-height:1.2}h1{font-size:calc(1.375rem + 1.5vw)}@media (min-width:1200px){h1{font-size:2.5rem}}h2{font-size:calc(1.325rem + .9vw)}@media (min-width:1200px){h2{font-size:2rem}}h3{font-size:calc(1.3rem + .6vw)}@media (min-width:1200px){h3{font-size:1.75rem}}h4{font-size:calc(1.275rem + .3vw)}@media (min-width:1200px){h4{font-size:1.5rem}}h5{font-size:1.25rem}h6{font-size:1rem}p{margin-top:0;margin-bottom:1rem}abbr[data-bs-original-title],abbr[title]{-webkit-text-decoration:underline dotted;text-decoration:underline dotted;cursor:help;-webkit-text-decoration-skip-ink:none;text-decoration-skip-ink:none}address{margin-bottom:1rem;font-style:normal;line-height:inherit}ol,ul{padding-left:2rem}dl,ol,ul{margin-top:0;margin-bottom:1rem}ol ol,ol ul,ul ol,ul ul{margin-bottom:0}dt{font-weight:700}dd{margin-bottom:.5rem;margin-left:0}blockquote{margin:0 0 1rem}b,strong{font-weight:bolder}small{font-size:.875em}mark{padding:.2em;background-color:#fcf8e3}sub,sup{position:relative;font-size:.75em;line-height:0;vertical-align:baseline}sub{bottom:-.25em}sup{top:-.5em}a{color:#0d6efd;text-decoration:underline}a:hover{color:#0a58ca}a:not([href]):not([class]),a:not([href]):not([class]):hover{color:inherit;text-decoration:none}code,kbd,pre,samp{font-family:SFMono-Regular,Menlo,Monaco,Consolas,"Liberation Mono","Courier New",monospace;font-size:1em;direction:ltr;unicode-bidi:bidi-override}pre{display:block;margin-top:0;margin-bottom:1rem;overflow:auto;font-size:.875em}pre code{font-size:inherit;color:inherit;word-break:normal}code{font-size:.875em;color:#d63384;word-wrap:break-word}a>code{color:inherit}kbd{padding:.2rem .4rem;font-size:.875em;color:#fff;background-color:#212529;border-radius:.2rem}kbd kbd{padding:0;font-size:1em;font-weight:700}figure{margin:0 0 1rem}img,svg{vertical-align:middle}table{caption-side:bottom;border-collapse:collapse}caption{padding-top:.5rem;padding-bottom:.5rem;color:#6c757d;text-align:left}th{text-align:inherit;text-align:-webkit-match-parent}tbody,td,tfoot,th,thead,tr{border-color:inherit;border-style:solid;border-width:0}label{display:inline-block}button{border-radius:0}button:focus:not(:focus-visible){outline:0}button,input,optgroup,select,textarea{margin:0;font-family:inherit;font-size:inherit;line-height:inherit}button,select{text-transform:none}[role=button]{cursor:pointer}select{word-wrap:normal}select:disabled{opacity:1}[list]::-webkit-calendar-picker-indicator{display:none}[type=button],[type=reset],[type=submit],button{-webkit-appearance:button}[type=button]:not(:disabled),[type=reset]:not(:disabled),[type=submit]:not(:disabled),button:not(:disabled){cursor:pointer}::-moz-focus-inner{padding:0;border-style:none}textarea{resize:vertical}fieldset{min-width:0;padding:0;margin:0;border:0}legend{float:left;width:100%;padding:0;margin-bottom:.5rem;font-size:calc(1.275rem + .3vw);line-height:inherit}@media (min-width:1200px){legend{font-size:1.5rem}}legend+*{clear:left}::-webkit-datetime-edit-day-field,::-webkit-datetime-edit-fields-wrapper,::-webkit-datetime-edit-hour-field,::-webkit-datetime-edit-minute,::-webkit-datetime-edit-month-field,::-webkit-datetime-edit-text,::-webkit-datetime-edit-year-field{padding:0}::-webkit-inner-spin-button{height:auto}[type=search]{outline-offset:-2px;-webkit-appearance:textfield}::-webkit-search-decoration{-webkit-appearance:none}::-webkit-color-swatch-wrapper{padding:0}::file-selector-button{font:inherit}::-webkit-file-upload-button{font:inherit;-webkit-appearance:button}output{display:inline-block}iframe{border:0}summary{display:list-item;cursor:pointer}progress{vertical-align:baseline}[hidden]{display:none!important}</style>
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|
||||
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|
||||
|
|
@ -1643,21 +1643,60 @@
|
|||
<span class="k">return</span> <span class="n">o</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">covariance</span><span class="p">(</span><span class="n">obs1</span><span class="p">,</span> <span class="n">obs2</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||
<span class="sd">"""Calculates the covariance of two observables.</span>
|
||||
<span class="k">def</span> <span class="nf">covariance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">visualize</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||
<span class="sd">"""Calculates the covariance matrix of a set of observables.</span>
|
||||
|
||||
<span class="sd"> covariance(obs, obs) is equal to obs.dvalue ** 2</span>
|
||||
<span class="sd"> The gamma method has to be applied first to both observables.</span>
|
||||
|
||||
<span class="sd"> If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance</span>
|
||||
<span class="sd"> is constrained to the maximum value.</span>
|
||||
<span class="sd"> The gamma method has to be applied first to all observables.</span>
|
||||
|
||||
<span class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
<span class="sd"> obs : list or numpy.ndarray</span>
|
||||
<span class="sd"> List or one dimensional array of Obs</span>
|
||||
<span class="sd"> visualize : bool</span>
|
||||
<span class="sd"> If True plots the corresponding normalized correlation matrix (default False).</span>
|
||||
<span class="sd"> correlation : bool</span>
|
||||
<span class="sd"> if true the correlation instead of the covariance is returned (default False)</span>
|
||||
<span class="sd"> If True the correlation instead of the covariance is returned (default False).</span>
|
||||
|
||||
<span class="sd"> Notes</span>
|
||||
<span class="sd"> -----</span>
|
||||
<span class="sd"> The 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. For observables defined on a single ensemble this 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.</span>
|
||||
<span class="sd"> $$</span>
|
||||
<span class="sd"> \tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}</span>
|
||||
<span class="sd"> $$</span>
|
||||
<span class="sd"> This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</span>
|
||||
<span class="sd"> """</span>
|
||||
|
||||
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">obs</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">length</span><span class="p">):</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">_covariance_element</span><span class="p">(</span><span class="n">obs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">cov</span> <span class="o">+</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</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="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
||||
|
||||
<span class="n">corr</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">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span> <span class="o">@</span> <span class="n">cov</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">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span>
|
||||
|
||||
<span class="n">errors</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">obs</span><span class="p">]</span>
|
||||
<span class="n">cov</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="n">errors</span><span class="p">)</span> <span class="o">@</span> <span class="n">corr</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="n">errors</span><span class="p">)</span>
|
||||
|
||||
<span class="n">eigenvalues</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">eigh</span><span class="p">(</span><span class="n">cov</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">eigenvalues</span> <span class="o">>=</span> <span class="mi">0</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">"Covariance matrix is not positive semi-definite (Eigenvalues: "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">eigenvalues</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">visualize</span><span class="p">:</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">matshow</span><span class="p">(</span><span class="n">corr</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">set_cmap</span><span class="p">(</span><span class="s1">'RdBu'</span><span class="p">)</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">correlation</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">corr</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">cov</span>
|
||||
|
||||
|
||||
<span class="k">def</span> <span class="nf">_covariance_element</span><span class="p">(</span><span class="n">obs1</span><span class="p">,</span> <span class="n">obs2</span><span class="p">):</span>
|
||||
<span class="sd">"""Estimates the covariance of two Obs objects, neglecting autocorrelations."""</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">expand_deltas</span><span class="p">(</span><span class="n">deltas</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">new_idx</span><span class="p">):</span>
|
||||
<span class="sd">"""Expand deltas defined on idx to a contiguous range [new_idx[0], new_idx[-1]].</span>
|
||||
<span class="sd"> New, empy entries are filled by 0. If idx and new_idx are of type range, the smallest</span>
|
||||
|
|
@ -1680,29 +1719,18 @@
|
|||
<span class="n">ret</span><span class="p">[</span><span class="n">idx</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">new_idx</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> <span class="o">=</span> <span class="n">deltas</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
||||
<span class="k">return</span> <span class="n">ret</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">calc_gamma</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">deltas2</span><span class="p">,</span> <span class="n">idx1</span><span class="p">,</span> <span class="n">idx2</span><span class="p">,</span> <span class="n">new_idx</span><span class="p">,</span> <span class="n">w_max</span><span class="p">):</span>
|
||||
<span class="n">gamma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="k">def</span> <span class="nf">calc_gamma</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">deltas2</span><span class="p">,</span> <span class="n">idx1</span><span class="p">,</span> <span class="n">idx2</span><span class="p">,</span> <span class="n">new_idx</span><span class="p">):</span>
|
||||
<span class="n">deltas1</span> <span class="o">=</span> <span class="n">expand_deltas</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">idx1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx1</span><span class="p">),</span> <span class="n">new_idx</span><span class="p">)</span>
|
||||
<span class="n">deltas2</span> <span class="o">=</span> <span class="n">expand_deltas</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">idx2</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx2</span><span class="p">),</span> <span class="n">new_idx</span><span class="p">)</span>
|
||||
<span class="n">new_shape</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deltas1</span><span class="p">)</span>
|
||||
<span class="n">max_gamma</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">new_shape</span><span class="p">,</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="c1"># The padding for the fft has to be even</span>
|
||||
<span class="n">padding</span> <span class="o">=</span> <span class="n">new_shape</span> <span class="o">+</span> <span class="n">max_gamma</span> <span class="o">+</span> <span class="p">(</span><span class="n">new_shape</span> <span class="o">+</span> <span class="n">max_gamma</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span>
|
||||
<span class="n">gamma</span><span class="p">[:</span><span class="n">max_gamma</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">padding</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">padding</span><span class="p">)))[:</span><span class="n">max_gamma</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">padding</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">padding</span><span class="p">)))[:</span><span class="n">max_gamma</span><span class="p">])</span> <span class="o">/</span> <span class="mf">2.0</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">gamma</span>
|
||||
<span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">deltas1</span> <span class="o">*</span> <span class="n">deltas2</span><span class="p">)</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">set</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">names</span><span class="p">)</span><span class="o">.</span><span class="n">isdisjoint</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">obs2</span><span class="o">.</span><span class="n">names</span><span class="p">)):</span>
|
||||
<span class="k">return</span> <span class="mf">0.</span>
|
||||
<span class="k">return</span> <span class="mf">0.0</span>
|
||||
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obs1</span><span class="p">,</span> <span class="s1">'e_dvalue'</span><span class="p">)</span> <span class="ow">or</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obs2</span><span class="p">,</span> <span class="s1">'e_dvalue'</span><span class="p">):</span>
|
||||
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The gamma method has to be applied to both Obs first.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="n">e_gamma</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_dvalue</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_n_tauint</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_rho</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="mf">0.0</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">e_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">mc_names</span><span class="p">:</span>
|
||||
|
||||
|
|
@ -1710,52 +1738,32 @@
|
|||
<span class="k">continue</span>
|
||||
|
||||
<span class="n">idl_d</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">r_length</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_merge_idx</span><span class="p">([</span><span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">]])</span>
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="nb">range</span><span class="p">):</span>
|
||||
<span class="n">r_length</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]))</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">r_length</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
|
||||
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">r_length</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="mf">0.</span>
|
||||
|
||||
<span class="n">w_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">r_length</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">gamma</span> <span class="o">=</span> <span class="mf">0.0</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">gamma</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">])</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.0</span><span class="p">):</span>
|
||||
<span class="k">if</span> <span class="n">gamma</span> <span class="o">==</span> <span class="mf">0.0</span><span class="p">:</span>
|
||||
<span class="k">continue</span>
|
||||
|
||||
<span class="n">e_shapes</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="n">e_shapes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">])</span>
|
||||
<span class="n">gamma_div</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">gamma_div</span> <span class="o">=</span> <span class="mf">0.0</span>
|
||||
<span class="n">e_N</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">gamma_div</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs2</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">gamma_div</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs2</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">])</span>
|
||||
<span class="n">e_N</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]))</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">/=</span> <span class="n">gamma_div</span><span class="p">[:</span><span class="n">w_max</span><span class="p">]</span>
|
||||
<span class="n">gamma</span> <span class="o">/=</span> <span class="n">gamma_div</span>
|
||||
|
||||
<span class="n">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][:</span><span class="n">w_max</span><span class="p">]</span> <span class="o">/</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(([</span><span class="mf">0.5</span><span class="p">],</span> <span class="n">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">1</span><span class="p">:])))</span>
|
||||
<span class="c1"># Make sure no entry of tauint is smaller than 0.5</span>
|
||||
<span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o"><</span> <span class="mf">0.5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.500000000001</span>
|
||||
|
||||
<span class="n">window</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">e_windowsize</span><span class="p">[</span><span class="n">e_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_windowsize</span><span class="p">[</span><span class="n">e_name</span><span class="p">])</span>
|
||||
<span class="c1"># Bias correction hep-lat/0306017 eq. (49)</span>
|
||||
<span class="n">e_dvalue</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">window</span><span class="p">]</span> <span class="o">+</span> <span class="n">obs1</span><span class="o">.</span><span class="n">tau_exp</span><span class="p">[</span><span class="n">e_name</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">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">window</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">window</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">e_N</span><span class="p">)</span> <span class="o">*</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">e_N</span>
|
||||
|
||||
<span class="n">dvalue</span> <span class="o">+=</span> <span class="n">e_dvalue</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span>
|
||||
<span class="n">dvalue</span> <span class="o">+=</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="mi">1</span> <span class="o">/</span> <span class="n">e_N</span><span class="p">)</span> <span class="o">*</span> <span class="n">gamma</span> <span class="o">/</span> <span class="n">e_N</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">e_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
|
||||
|
||||
|
|
@ -1764,12 +1772,6 @@
|
|||
|
||||
<span class="n">dvalue</span> <span class="o">+=</span> <span class="nb">float</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">cov</span><span class="p">,</span> <span class="n">obs2</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span><span class="p">)))</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)</span> <span class="o">></span> <span class="mf">1.0</span><span class="p">:</span>
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">dvalue</span><span class="p">)</span> <span class="o">*</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">*</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">correlation</span><span class="p">:</span>
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">dvalue</span>
|
||||
|
||||
|
||||
|
|
@ -4827,157 +4829,86 @@ Second observable</li>
|
|||
|
||||
|
||||
<span class="def">def</span>
|
||||
<span class="name">covariance</span><span class="signature">(obs1, obs2, correlation=False, **kwargs)</span>:
|
||||
<span class="name">covariance</span><span class="signature">(obs, visualize=False, correlation=False, **kwargs)</span>:
|
||||
</div>
|
||||
|
||||
<details>
|
||||
<summary>View Source</summary>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span class="k">def</span> <span class="nf">covariance</span><span class="p">(</span><span class="n">obs1</span><span class="p">,</span> <span class="n">obs2</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||
<span class="sd">"""Calculates the covariance of two observables.</span>
|
||||
<div class="pdoc-code codehilite"><pre><span></span><span class="k">def</span> <span class="nf">covariance</span><span class="p">(</span><span class="n">obs</span><span class="p">,</span> <span class="n">visualize</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="n">correlation</span><span class="o">=</span><span class="kc">False</span><span class="p">,</span> <span class="o">**</span><span class="n">kwargs</span><span class="p">):</span>
|
||||
<span class="sd">"""Calculates the covariance matrix of a set of observables.</span>
|
||||
|
||||
<span class="sd"> covariance(obs, obs) is equal to obs.dvalue ** 2</span>
|
||||
<span class="sd"> The gamma method has to be applied first to both observables.</span>
|
||||
|
||||
<span class="sd"> If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance</span>
|
||||
<span class="sd"> is constrained to the maximum value.</span>
|
||||
<span class="sd"> The gamma method has to be applied first to all observables.</span>
|
||||
|
||||
<span class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
<span class="sd"> obs : list or numpy.ndarray</span>
|
||||
<span class="sd"> List or one dimensional array of Obs</span>
|
||||
<span class="sd"> visualize : bool</span>
|
||||
<span class="sd"> If True plots the corresponding normalized correlation matrix (default False).</span>
|
||||
<span class="sd"> correlation : bool</span>
|
||||
<span class="sd"> if true the correlation instead of the covariance is returned (default False)</span>
|
||||
<span class="sd"> If True the correlation instead of the covariance is returned (default False).</span>
|
||||
|
||||
<span class="sd"> Notes</span>
|
||||
<span class="sd"> -----</span>
|
||||
<span class="sd"> The 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. For observables defined on a single ensemble this 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.</span>
|
||||
<span class="sd"> $$</span>
|
||||
<span class="sd"> \tau_{\mathrm{int}, ij}=\sqrt{\tau_{\mathrm{int}, i}\times \tau_{\mathrm{int}, j}}</span>
|
||||
<span class="sd"> $$</span>
|
||||
<span class="sd"> This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</span>
|
||||
<span class="sd"> """</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">expand_deltas</span><span class="p">(</span><span class="n">deltas</span><span class="p">,</span> <span class="n">idx</span><span class="p">,</span> <span class="n">shape</span><span class="p">,</span> <span class="n">new_idx</span><span class="p">):</span>
|
||||
<span class="sd">"""Expand deltas defined on idx to a contiguous range [new_idx[0], new_idx[-1]].</span>
|
||||
<span class="sd"> New, empy entries are filled by 0. If idx and new_idx are of type range, the smallest</span>
|
||||
<span class="sd"> common divisor of the step sizes is used as new step size.</span>
|
||||
<span class="n">length</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">obs</span><span class="p">)</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">((</span><span class="n">length</span><span class="p">,</span> <span class="n">length</span><span class="p">))</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">length</span><span class="p">):</span>
|
||||
<span class="k">for</span> <span class="n">j</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">i</span><span class="p">,</span> <span class="n">length</span><span class="p">):</span>
|
||||
<span class="n">cov</span><span class="p">[</span><span class="n">i</span><span class="p">,</span> <span class="n">j</span><span class="p">]</span> <span class="o">=</span> <span class="n">_covariance_element</span><span class="p">(</span><span class="n">obs</span><span class="p">[</span><span class="n">i</span><span class="p">],</span> <span class="n">obs</span><span class="p">[</span><span class="n">j</span><span class="p">])</span>
|
||||
<span class="n">cov</span> <span class="o">=</span> <span class="n">cov</span> <span class="o">+</span> <span class="n">cov</span><span class="o">.</span><span class="n">T</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="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">))</span>
|
||||
|
||||
<span class="sd"> Parameters</span>
|
||||
<span class="sd"> ----------</span>
|
||||
<span class="sd"> deltas -- List of fluctuations</span>
|
||||
<span class="sd"> idx -- List or range of configs on which the deltas are defined.</span>
|
||||
<span class="sd"> Has to be a subset of new_idx.</span>
|
||||
<span class="sd"> shape -- Number of configs in idx.</span>
|
||||
<span class="sd"> new_idx -- List of configs that defines the new range.</span>
|
||||
<span class="sd"> """</span>
|
||||
<span class="n">corr</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">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span> <span class="o">@</span> <span class="n">cov</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">sqrt</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">diag</span><span class="p">(</span><span class="n">cov</span><span class="p">)))</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">type</span><span class="p">(</span><span class="n">idx</span><span class="p">)</span> <span class="ow">is</span> <span class="nb">range</span> <span class="ow">and</span> <span class="nb">type</span><span class="p">(</span><span class="n">new_idx</span><span class="p">)</span> <span class="ow">is</span> <span class="nb">range</span><span class="p">:</span>
|
||||
<span class="k">if</span> <span class="n">idx</span> <span class="o">==</span> <span class="n">new_idx</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">deltas</span>
|
||||
<span class="n">ret</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">new_idx</span><span class="p">[</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">new_idx</span><span class="p">[</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span>
|
||||
<span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">range</span><span class="p">(</span><span class="n">shape</span><span class="p">):</span>
|
||||
<span class="n">ret</span><span class="p">[</span><span class="n">idx</span><span class="p">[</span><span class="n">i</span><span class="p">]</span> <span class="o">-</span> <span class="n">new_idx</span><span class="p">[</span><span class="mi">0</span><span class="p">]]</span> <span class="o">=</span> <span class="n">deltas</span><span class="p">[</span><span class="n">i</span><span class="p">]</span>
|
||||
<span class="k">return</span> <span class="n">ret</span>
|
||||
<span class="n">errors</span> <span class="o">=</span> <span class="p">[</span><span class="n">o</span><span class="o">.</span><span class="n">dvalue</span> <span class="k">for</span> <span class="n">o</span> <span class="ow">in</span> <span class="n">obs</span><span class="p">]</span>
|
||||
<span class="n">cov</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="n">errors</span><span class="p">)</span> <span class="o">@</span> <span class="n">corr</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="n">errors</span><span class="p">)</span>
|
||||
|
||||
<span class="k">def</span> <span class="nf">calc_gamma</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">deltas2</span><span class="p">,</span> <span class="n">idx1</span><span class="p">,</span> <span class="n">idx2</span><span class="p">,</span> <span class="n">new_idx</span><span class="p">,</span> <span class="n">w_max</span><span class="p">):</span>
|
||||
<span class="n">gamma</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">deltas1</span> <span class="o">=</span> <span class="n">expand_deltas</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">idx1</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx1</span><span class="p">),</span> <span class="n">new_idx</span><span class="p">)</span>
|
||||
<span class="n">deltas2</span> <span class="o">=</span> <span class="n">expand_deltas</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">idx2</span><span class="p">,</span> <span class="nb">len</span><span class="p">(</span><span class="n">idx2</span><span class="p">),</span> <span class="n">new_idx</span><span class="p">)</span>
|
||||
<span class="n">new_shape</span> <span class="o">=</span> <span class="nb">len</span><span class="p">(</span><span class="n">deltas1</span><span class="p">)</span>
|
||||
<span class="n">max_gamma</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">new_shape</span><span class="p">,</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="c1"># The padding for the fft has to be even</span>
|
||||
<span class="n">padding</span> <span class="o">=</span> <span class="n">new_shape</span> <span class="o">+</span> <span class="n">max_gamma</span> <span class="o">+</span> <span class="p">(</span><span class="n">new_shape</span> <span class="o">+</span> <span class="n">max_gamma</span><span class="p">)</span> <span class="o">%</span> <span class="mi">2</span>
|
||||
<span class="n">gamma</span><span class="p">[:</span><span class="n">max_gamma</span><span class="p">]</span> <span class="o">+=</span> <span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">padding</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">padding</span><span class="p">)))[:</span><span class="n">max_gamma</span><span class="p">]</span> <span class="o">+</span> <span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">irfft</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas2</span><span class="p">,</span> <span class="n">padding</span><span class="p">)</span> <span class="o">*</span> <span class="n">np</span><span class="o">.</span><span class="n">conjugate</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">fft</span><span class="o">.</span><span class="n">rfft</span><span class="p">(</span><span class="n">deltas1</span><span class="p">,</span> <span class="n">padding</span><span class="p">)))[:</span><span class="n">max_gamma</span><span class="p">])</span> <span class="o">/</span> <span class="mf">2.0</span>
|
||||
<span class="n">eigenvalues</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">eigh</span><span class="p">(</span><span class="n">cov</span><span class="p">)[</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">eigenvalues</span> <span class="o">>=</span> <span class="mi">0</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">"Covariance matrix is not positive semi-definite (Eigenvalues: "</span> <span class="o">+</span> <span class="nb">str</span><span class="p">(</span><span class="n">eigenvalues</span><span class="p">)</span> <span class="o">+</span> <span class="s2">")"</span><span class="p">,</span> <span class="ne">RuntimeWarning</span><span class="p">)</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">gamma</span>
|
||||
<span class="k">if</span> <span class="n">visualize</span><span class="p">:</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">matshow</span><span class="p">(</span><span class="n">corr</span><span class="p">,</span> <span class="n">vmin</span><span class="o">=-</span><span class="mi">1</span><span class="p">,</span> <span class="n">vmax</span><span class="o">=</span><span class="mi">1</span><span class="p">)</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">set_cmap</span><span class="p">(</span><span class="s1">'RdBu'</span><span class="p">)</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">colorbar</span><span class="p">()</span>
|
||||
<span class="n">plt</span><span class="o">.</span><span class="n">draw</span><span class="p">()</span>
|
||||
|
||||
<span class="k">if</span> <span class="nb">set</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">names</span><span class="p">)</span><span class="o">.</span><span class="n">isdisjoint</span><span class="p">(</span><span class="nb">set</span><span class="p">(</span><span class="n">obs2</span><span class="o">.</span><span class="n">names</span><span class="p">)):</span>
|
||||
<span class="k">return</span> <span class="mf">0.</span>
|
||||
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obs1</span><span class="p">,</span> <span class="s1">'e_dvalue'</span><span class="p">)</span> <span class="ow">or</span> <span class="ow">not</span> <span class="nb">hasattr</span><span class="p">(</span><span class="n">obs2</span><span class="p">,</span> <span class="s1">'e_dvalue'</span><span class="p">):</span>
|
||||
<span class="k">raise</span> <span class="ne">Exception</span><span class="p">(</span><span class="s1">'The gamma method has to be applied to both Obs first.'</span><span class="p">)</span>
|
||||
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="n">e_gamma</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_dvalue</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_n_tauint</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">e_rho</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">e_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">mc_names</span><span class="p">:</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">e_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">mc_names</span><span class="p">:</span>
|
||||
<span class="k">continue</span>
|
||||
|
||||
<span class="n">idl_d</span> <span class="o">=</span> <span class="p">{}</span>
|
||||
<span class="n">r_length</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">_merge_idx</span><span class="p">([</span><span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">]])</span>
|
||||
<span class="k">if</span> <span class="nb">isinstance</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="nb">range</span><span class="p">):</span>
|
||||
<span class="n">r_length</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="nb">len</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]))</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="n">r_length</span><span class="o">.</span><span class="n">append</span><span class="p">((</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">][</span><span class="o">-</span><span class="mi">1</span><span class="p">]</span> <span class="o">-</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">+</span> <span class="mi">1</span><span class="p">))</span>
|
||||
|
||||
<span class="k">if</span> <span class="ow">not</span> <span class="n">r_length</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="mf">0.</span>
|
||||
|
||||
<span class="n">w_max</span> <span class="o">=</span> <span class="nb">max</span><span class="p">(</span><span class="n">r_length</span><span class="p">)</span> <span class="o">//</span> <span class="mi">2</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">deltas</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">all</span><span class="p">(</span><span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">==</span> <span class="mf">0.0</span><span class="p">):</span>
|
||||
<span class="k">continue</span>
|
||||
|
||||
<span class="n">e_shapes</span> <span class="o">=</span> <span class="p">[]</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="n">e_shapes</span><span class="o">.</span><span class="n">append</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">])</span>
|
||||
<span class="n">gamma_div</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">zeros</span><span class="p">(</span><span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">e_N</span> <span class="o">=</span> <span class="mi">0</span>
|
||||
<span class="k">for</span> <span class="n">r_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">if</span> <span class="n">r_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_content</span><span class="p">[</span><span class="n">e_name</span><span class="p">]:</span>
|
||||
<span class="k">continue</span>
|
||||
<span class="n">gamma_div</span> <span class="o">+=</span> <span class="n">calc_gamma</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">np</span><span class="o">.</span><span class="n">ones</span><span class="p">(</span><span class="n">obs2</span><span class="o">.</span><span class="n">shape</span><span class="p">[</span><span class="n">r_name</span><span class="p">]),</span> <span class="n">obs1</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">idl</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">],</span> <span class="n">w_max</span><span class="p">)</span>
|
||||
<span class="n">e_N</span> <span class="o">+=</span> <span class="n">np</span><span class="o">.</span><span class="n">sum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">ones_like</span><span class="p">(</span><span class="n">idl_d</span><span class="p">[</span><span class="n">r_name</span><span class="p">]))</span>
|
||||
<span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">/=</span> <span class="n">gamma_div</span><span class="p">[:</span><span class="n">w_max</span><span class="p">]</span>
|
||||
|
||||
<span class="n">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][:</span><span class="n">w_max</span><span class="p">]</span> <span class="o">/</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span>
|
||||
<span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">cumsum</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">concatenate</span><span class="p">(([</span><span class="mf">0.5</span><span class="p">],</span> <span class="n">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">1</span><span class="p">:])))</span>
|
||||
<span class="c1"># Make sure no entry of tauint is smaller than 0.5</span>
|
||||
<span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o"><</span> <span class="mf">0.5</span><span class="p">]</span> <span class="o">=</span> <span class="mf">0.500000000001</span>
|
||||
|
||||
<span class="n">window</span> <span class="o">=</span> <span class="nb">min</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">e_windowsize</span><span class="p">[</span><span class="n">e_name</span><span class="p">],</span> <span class="n">obs2</span><span class="o">.</span><span class="n">e_windowsize</span><span class="p">[</span><span class="n">e_name</span><span class="p">])</span>
|
||||
<span class="c1"># Bias correction hep-lat/0306017 eq. (49)</span>
|
||||
<span class="n">e_dvalue</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span> <span class="o">=</span> <span class="mi">2</span> <span class="o">*</span> <span class="p">(</span><span class="n">e_n_tauint</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">window</span><span class="p">]</span> <span class="o">+</span> <span class="n">obs1</span><span class="o">.</span><span class="n">tau_exp</span><span class="p">[</span><span class="n">e_name</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">e_rho</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="n">window</span> <span class="o">+</span> <span class="mi">1</span><span class="p">]))</span> <span class="o">*</span> <span class="p">(</span><span class="mi">1</span> <span class="o">+</span> <span class="p">(</span><span class="mi">2</span> <span class="o">*</span> <span class="n">window</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">/</span> <span class="n">e_N</span><span class="p">)</span> <span class="o">*</span> <span class="n">e_gamma</span><span class="p">[</span><span class="n">e_name</span><span class="p">][</span><span class="mi">0</span><span class="p">]</span> <span class="o">/</span> <span class="n">e_N</span>
|
||||
|
||||
<span class="n">dvalue</span> <span class="o">+=</span> <span class="n">e_dvalue</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span>
|
||||
|
||||
<span class="k">for</span> <span class="n">e_name</span> <span class="ow">in</span> <span class="n">obs1</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">e_name</span> <span class="ow">not</span> <span class="ow">in</span> <span class="n">obs2</span><span class="o">.</span><span class="n">cov_names</span><span class="p">:</span>
|
||||
<span class="k">continue</span>
|
||||
|
||||
<span class="n">dvalue</span> <span class="o">+=</span> <span class="nb">float</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">np</span><span class="o">.</span><span class="n">transpose</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span><span class="p">),</span> <span class="n">np</span><span class="o">.</span><span class="n">dot</span><span class="p">(</span><span class="n">obs1</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">cov</span><span class="p">,</span> <span class="n">obs2</span><span class="o">.</span><span class="n">covobs</span><span class="p">[</span><span class="n">e_name</span><span class="p">]</span><span class="o">.</span><span class="n">grad</span><span class="p">)))</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">np</span><span class="o">.</span><span class="n">abs</span><span class="p">(</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span><span class="p">)</span> <span class="o">></span> <span class="mf">1.0</span><span class="p">:</span>
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sign</span><span class="p">(</span><span class="n">dvalue</span><span class="p">)</span> <span class="o">*</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">*</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span>
|
||||
|
||||
<span class="k">if</span> <span class="n">correlation</span><span class="p">:</span>
|
||||
<span class="n">dvalue</span> <span class="o">=</span> <span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs1</span><span class="o">.</span><span class="n">dvalue</span> <span class="o">/</span> <span class="n">obs2</span><span class="o">.</span><span class="n">dvalue</span>
|
||||
|
||||
<span class="k">return</span> <span class="n">dvalue</span>
|
||||
<span class="k">if</span> <span class="n">correlation</span> <span class="ow">is</span> <span class="kc">True</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">corr</span>
|
||||
<span class="k">else</span><span class="p">:</span>
|
||||
<span class="k">return</span> <span class="n">cov</span>
|
||||
</pre></div>
|
||||
|
||||
</details>
|
||||
|
||||
<div class="docstring"><p>Calculates the covariance of two observables.</p>
|
||||
<div class="docstring"><p>Calculates the covariance matrix of a set of observables.</p>
|
||||
|
||||
<p>covariance(obs, obs) is equal to obs.dvalue ** 2
|
||||
The gamma method has to be applied first to both observables.</p>
|
||||
|
||||
<p>If abs(covariance(obs1, obs2)) > obs1.dvalue * obs2.dvalue, the covariance
|
||||
is constrained to the maximum value.</p>
|
||||
<p>The gamma method has to be applied first to all observables.</p>
|
||||
|
||||
<h6 id="parameters">Parameters</h6>
|
||||
|
||||
<ul>
|
||||
<li><strong>obs</strong> (list or numpy.ndarray):
|
||||
List or one dimensional array of Obs</li>
|
||||
<li><strong>visualize</strong> (bool):
|
||||
If True plots the corresponding normalized correlation matrix (default False).</li>
|
||||
<li><strong>correlation</strong> (bool):
|
||||
if true the correlation instead of the covariance is returned (default False)</li>
|
||||
If True the correlation instead of the covariance is returned (default False).</li>
|
||||
</ul>
|
||||
|
||||
<h6 id="notes">Notes</h6>
|
||||
|
||||
<p>The 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. For observables defined on a single ensemble this 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.
|
||||
$$
|
||||
au_{\mathrm{int}, ij}=\sqrt{ au_{\mathrm{int}, i} imes au_{\mathrm{int}, j}}
|
||||
$$
|
||||
This construction ensures that the estimated covariance matrix is positive semi-definite (up to numerical rounding errors).</p>
|
||||
</div>
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -3,7 +3,7 @@
|
|||
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Add table
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