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  <section id="scipy-routines">
<h1><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> Routines<a class="headerlink" href="#scipy-routines" title="Permalink to this heading">¶</a></h1>
<section id="fitter">
<h2>Fitter<a class="headerlink" href="#fitter" title="Permalink to this heading">¶</a></h2>
<p><a class="reference internal" href="lsqfit.html#module-lsqfit" title="lsqfit: Nonlinear least squares fitting."><code class="xref py py-mod docutils literal notranslate"><span class="pre">lsqfit</span></code></a> uses routines from the open-source <code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> Python module
provided it is installed. These routines are used in place of GSL routines
if the latter are not installed. There is one fitter available for use by
<a class="reference internal" href="lsqfit.html#lsqfit.nonlinear_fit" title="lsqfit.nonlinear_fit"><code class="xref py py-class docutils literal notranslate"><span class="pre">lsqfit.nonlinear_fit</span></code></a>.</p>
<dl class="py class">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">lsqfit.</span></span><span class="sig-name descname"><span class="pre">scipy_least_squares</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">n</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">(1e-08,</span> <span class="pre">1e-08,</span> <span class="pre">1e-08)</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">maxit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000</span></span></em>, <em class="sig-param"><span class="o"><span class="pre">**</span></span><span class="n"><span class="pre">extra_args</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#lsqfit.scipy_least_squares" title="Permalink to this definition">¶</a></dt>
<dd><p><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> fitter for nonlinear least-squares multidimensional fits.</p>
<p><a class="reference internal" href="#lsqfit.scipy_least_squares" title="lsqfit.scipy_least_squares"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy_least_squares</span></code></a> is a function-class whose constructor does a
least-squares fit by minimizing <code class="docutils literal notranslate"><span class="pre">sum_i</span> <span class="pre">f_i(x)**2</span></code> as a function of
vector <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p>
<p><a class="reference internal" href="#lsqfit.scipy_least_squares" title="lsqfit.scipy_least_squares"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy_least_squares</span></code></a> is a wrapper for the <code class="docutils literal notranslate"><span class="pre">scipy.optimize.least_squares</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x0</strong> (<em>array of floats</em>) – Starting point for minimization.</p></li>
<li><p><strong>n</strong> (<em>positive int</em>) – Length of vector returned by the fit function <code class="docutils literal notranslate"><span class="pre">f(x)</span></code>.</p></li>
<li><p><strong>f</strong> (<em>array-valued function</em>) – <code class="docutils literal notranslate"><span class="pre">sum_i</span> <span class="pre">f_i(x)**2</span></code> is minimized
by varying parameters <code class="docutils literal notranslate"><span class="pre">x</span></code>. The parameters are a 1-d
<code class="xref py py-class docutils literal notranslate"><span class="pre">numpy</span></code> array of either numbers or <code class="xref py py-class docutils literal notranslate"><span class="pre">gvar.GVar</span></code>s.</p></li>
<li><p><strong>tol</strong> (<em>float</em><em> or </em><em>tuple</em>) – <p>Assigning <code class="docutils literal notranslate"><span class="pre">tol=(xtol,</span> <span class="pre">gtol,</span> <span class="pre">ftol)</span></code> causes the
fit to stop searching for a minimum when any of</p>
<blockquote>
<div><p><code class="docutils literal notranslate"><span class="pre">xtol</span> <span class="pre">&gt;=</span></code> relative change in parameters between iterations</p>
<p><code class="docutils literal notranslate"><span class="pre">gtol</span> <span class="pre">&gt;=</span></code> relative size of gradient of <code class="docutils literal notranslate"><span class="pre">chi**2</span></code></p>
<p><code class="docutils literal notranslate"><span class="pre">ftol</span> <span class="pre">&gt;=</span></code> relative change in <code class="docutils literal notranslate"><span class="pre">chi**2</span></code> between iterations</p>
</div></blockquote>
<p>is statisfied. See the <code class="docutils literal notranslate"><span class="pre">scipy.optimize.least_squares</span></code>
documentation detailed definitions of the stopping conditions.
Typically one sets <code class="docutils literal notranslate"><span class="pre">xtol=1/10**d</span></code> where <code class="docutils literal notranslate"><span class="pre">d</span></code> is the number of
digits of precision desired in the result, while <code class="docutils literal notranslate"><span class="pre">gtol&lt;&lt;1</span></code> and
<code class="docutils literal notranslate"><span class="pre">ftol&lt;&lt;1</span></code>. Setting <code class="docutils literal notranslate"><span class="pre">tol=eps</span></code> where <code class="docutils literal notranslate"><span class="pre">eps</span></code> is a number is
equivalent to setting <code class="docutils literal notranslate"><span class="pre">tol=(eps,1e-10,1e-10)</span></code>. Setting
<code class="docutils literal notranslate"><span class="pre">tol=(eps1,eps2)</span></code> is equivlent to setting
<code class="docutils literal notranslate"><span class="pre">tol=(eps1,eps2,1e-10)</span></code>. Default is <code class="docutils literal notranslate"><span class="pre">tol=1e-5</span></code>.</p>
</p></li>
<li><p><strong>method</strong> (<em>str</em><em> or </em><em>None</em>) – <p>Minimization algorithm. Options
include:</p>
<blockquote>
<div><dl class="simple">
<dt><code class="docutils literal notranslate"><span class="pre">'trf'</span></code></dt><dd><p>Trusted Region Reflective algorithm (default). Best
choice with bounded parameters.</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">'dogbox'</span></code></dt><dd><p>dogleg algorithm adapted for bounded parameters.</p>
</dd>
<dt><code class="docutils literal notranslate"><span class="pre">'lm'</span></code></dt><dd><p>Levenberg-Marquardt algorithm as implemented in MINPACK.
Best for smaller problems. Does not work with bounded
parameters (bounds are ignored).</p>
</dd>
</dl>
</div></blockquote>
<p>Setting <code class="docutils literal notranslate"><span class="pre">method=None</span></code> implies the default <code class="docutils literal notranslate"><span class="pre">'trf'</span></code>.</p>
</p></li>
<li><p><strong>maxit</strong> (<em>int</em>) – Maximum number of function evaluations in search
for minimum; default is 1000.</p></li>
</ul>
</dd>
</dl>
<p>Other arguments include: <code class="docutils literal notranslate"><span class="pre">x_jac</span></code>, <code class="docutils literal notranslate"><span class="pre">loss</span></code>, <code class="docutils literal notranslate"><span class="pre">tr_solver</span></code>,
<code class="docutils literal notranslate"><span class="pre">f_scale</span></code>, <code class="docutils literal notranslate"><span class="pre">tr_options</span></code>, <code class="docutils literal notranslate"><span class="pre">bounds</span></code>. See the documentation for
<code class="docutils literal notranslate"><span class="pre">scipy.optimize.least_squares</span></code> for information about these and other
options.</p>
<p><a class="reference internal" href="#lsqfit.scipy_least_squares" title="lsqfit.scipy_least_squares"><code class="xref py py-class docutils literal notranslate"><span class="pre">lsqfit.scipy_least_squares</span></code></a> objects have the following
attributes.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.x">
<span class="sig-name descname"><span class="pre">x</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Location of the most recently computed (best) fit point.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.cov">
<span class="sig-name descname"><span class="pre">cov</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.cov" title="Permalink to this definition">¶</a></dt>
<dd><p>Covariance matrix at the minimum point.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.description">
<span class="sig-name descname"><span class="pre">description</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.description" title="Permalink to this definition">¶</a></dt>
<dd><p>Short description of internal fitter settings.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.f">
<span class="sig-name descname"><span class="pre">f</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.f" title="Permalink to this definition">¶</a></dt>
<dd><p>Fit function value <code class="docutils literal notranslate"><span class="pre">f(x)</span></code> at the minimum in
the most recent fit.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.J">
<span class="sig-name descname"><span class="pre">J</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.J" title="Permalink to this definition">¶</a></dt>
<dd><p>Gradient <code class="docutils literal notranslate"><span class="pre">J_ij</span> <span class="pre">=</span> <span class="pre">df_i/dx[j]</span></code> for most recent fit.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.nit">
<span class="sig-name descname"><span class="pre">nit</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.nit" title="Permalink to this definition">¶</a></dt>
<dd><p>Number of function evaluations used in last fit to find
the minimum.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.stopping_criterion">
<span class="sig-name descname"><span class="pre">stopping_criterion</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.stopping_criterion" title="Permalink to this definition">¶</a></dt>
<dd><p>Criterion used to
stop fit:</p>
<blockquote>
<div><ol class="arabic simple" start="0">
<li><p>didn’t converge</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">xtol</span> <span class="pre">&gt;=</span></code> relative change in parameters between iterations</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">gtol</span> <span class="pre">&gt;=</span></code> relative size of gradient of <code class="docutils literal notranslate"><span class="pre">chi**2</span></code></p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">ftol</span> <span class="pre">&gt;=</span></code> relative change in <code class="docutils literal notranslate"><span class="pre">chi**2</span></code> between iterations</p></li>
</ol>
</div></blockquote>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.error">
<span class="sig-name descname"><span class="pre">error</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.error" title="Permalink to this definition">¶</a></dt>
<dd><p><code class="docutils literal notranslate"><span class="pre">None</span></code> if fit successful; an error
message otherwise.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>str or None</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_least_squares.results">
<span class="sig-name descname"><span class="pre">results</span></span><a class="headerlink" href="#lsqfit.scipy_least_squares.results" title="Permalink to this definition">¶</a></dt>
<dd><p>Results returned by <code class="docutils literal notranslate"><span class="pre">scipy.optimize.least_squares</span></code>.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>dict</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

</section>
<section id="minimizer">
<h2>Minimizer<a class="headerlink" href="#minimizer" title="Permalink to this heading">¶</a></h2>
<p>The <a class="reference internal" href="lsqfit.html#lsqfit.empbayes_fit" title="lsqfit.empbayes_fit"><code class="xref py py-func docutils literal notranslate"><span class="pre">lsqfit.empbayes_fit()</span></code></a> uses a minimizer from the <code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code>
module to minimize <code class="docutils literal notranslate"><span class="pre">logGBF</span></code>.</p>
<dl class="py class">
<dt class="sig sig-object py" id="lsqfit.scipy_multiminex">
<em class="property"><span class="pre">class</span><span class="w"> </span></em><span class="sig-prename descclassname"><span class="pre">lsqfit.</span></span><span class="sig-name descname"><span class="pre">scipy_multiminex</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x0</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">f</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">tol</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1e-4</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">maxit</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1000</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">step</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">1</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">alg</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">'nmsimplex2'</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">analyzer</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="headerlink" href="#lsqfit.scipy_multiminex" title="Permalink to this definition">¶</a></dt>
<dd><p><code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> minimizer for multidimensional functions.</p>
<p><a class="reference internal" href="#lsqfit.scipy_multiminex" title="lsqfit.scipy_multiminex"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy_multiminex</span></code></a> is a function-class whose constructor minimizes a
multidimensional function <code class="docutils literal notranslate"><span class="pre">f(x)</span></code> by varying vector <code class="docutils literal notranslate"><span class="pre">x</span></code>. This routine
does <em>not</em> use user-supplied information about the gradient of <code class="docutils literal notranslate"><span class="pre">f(x)</span></code>.</p>
<p><a class="reference internal" href="#lsqfit.scipy_multiminex" title="lsqfit.scipy_multiminex"><code class="xref py py-class docutils literal notranslate"><span class="pre">scipy_multiminex</span></code></a> is a wrapper for the <code class="docutils literal notranslate"><span class="pre">minimize</span></code>
<code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> function. It gives access to only part of that
function.</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>x0</strong> (<em>array of floats</em>) – Starting point for minimization search.</p></li>
<li><p><strong>f</strong> – Function <code class="docutils literal notranslate"><span class="pre">f(x)</span></code> to be minimized by varying vector <code class="docutils literal notranslate"><span class="pre">x</span></code>.</p></li>
<li><p><strong>tol</strong> (<em>float</em>) – Minimization stops when <code class="docutils literal notranslate"><span class="pre">x</span></code> has converged to with
tolerance <code class="docutils literal notranslate"><span class="pre">tol</span></code>; default is <code class="docutils literal notranslate"><span class="pre">1e-4</span></code>.</p></li>
<li><p><strong>maxit</strong> (<em>positive int</em>) – Maximum number of iterations in search for minimum;
default is 1000.</p></li>
<li><p><strong>analyzer</strong> (<em>function</em>) – Optional function of the current <code class="docutils literal notranslate"><span class="pre">x</span></code>.
This can be used to inspect intermediate steps in the
minimization, if needed.</p></li>
<li><p><strong>step</strong> (<em>bool</em>) – Included for consistency with GSL routines but ignored
in <code class="xref py py-mod docutils literal notranslate"><span class="pre">scipy</span></code> routine.</p></li>
</ul>
</dd>
</dl>
<p><a class="reference internal" href="#lsqfit.scipy_multiminex" title="lsqfit.scipy_multiminex"><code class="xref py py-class docutils literal notranslate"><span class="pre">lsqfit.scipy_multiminex</span></code></a> objects have the following attributes.</p>
<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_multiminex.x">
<span class="sig-name descname"><span class="pre">x</span></span><a class="headerlink" href="#lsqfit.scipy_multiminex.x" title="Permalink to this definition">¶</a></dt>
<dd><p>Location of the minimum.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>array</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_multiminex.f">
<span class="sig-name descname"><span class="pre">f</span></span><a class="headerlink" href="#lsqfit.scipy_multiminex.f" title="Permalink to this definition">¶</a></dt>
<dd><p>Value of function <code class="docutils literal notranslate"><span class="pre">f(x)</span></code> at the minimum.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_multiminex.nit">
<span class="sig-name descname"><span class="pre">nit</span></span><a class="headerlink" href="#lsqfit.scipy_multiminex.nit" title="Permalink to this definition">¶</a></dt>
<dd><p>Number of iterations required to find the minimum.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>int</p>
</dd>
</dl>
</dd></dl>

<dl class="py attribute">
<dt class="sig sig-object py" id="lsqfit.scipy_multiminex.error">
<span class="sig-name descname"><span class="pre">error</span></span><a class="headerlink" href="#lsqfit.scipy_multiminex.error" title="Permalink to this definition">¶</a></dt>
<dd><p><code class="docutils literal notranslate"><span class="pre">None</span></code> if fit successful; an error
message otherwise.</p>
<dl class="field-list simple">
<dt class="field-odd">Type<span class="colon">:</span></dt>
<dd class="field-odd"><p>Noe or str</p>
</dd>
</dl>
</dd></dl>

</dd></dl>

</section>
</section>


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