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<li><a class="reference internal" href="#">mlab</a><ul>
<li><a class="reference internal" href="#module-matplotlib.mlab"><code class="docutils literal notranslate"><span class="pre">matplotlib.mlab</span></code></a><ul>
<li><a class="reference internal" href="#matlab-compatible-functions">MATLAB compatible functions</a></li>
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<div class="section" id="mlab">
<h1>mlab<a class="headerlink" href="#mlab" title="Permalink to this headline">¶</a></h1>
<div class="section" id="module-matplotlib.mlab">
<span id="matplotlib-mlab"></span><h2><a class="reference internal" href="#module-matplotlib.mlab" title="matplotlib.mlab"><code class="xref py py-mod docutils literal notranslate"><span class="pre">matplotlib.mlab</span></code></a><a class="headerlink" href="#module-matplotlib.mlab" title="Permalink to this headline">¶</a></h2>
<p>Numerical python functions written for compatibility with MATLAB
commands with the same names.</p>
<div class="section" id="matlab-compatible-functions">
<h3>MATLAB compatible functions<a class="headerlink" href="#matlab-compatible-functions" title="Permalink to this headline">¶</a></h3>
<dl class="docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal notranslate"><span class="pre">cohere()</span></code></a></dt>
<dd>Coherence (normalized cross spectral density)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><code class="xref py py-func docutils literal notranslate"><span class="pre">csd()</span></code></a></dt>
<dd>Cross spectral density using Welch’s average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><code class="xref py py-func docutils literal notranslate"><span class="pre">detrend()</span></code></a></dt>
<dd>Remove the mean or best fit line from an array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.find" title="matplotlib.mlab.find"><code class="xref py py-func docutils literal notranslate"><span class="pre">find()</span></code></a></dt>
<dd>Return the indices where some condition is true;
numpy.nonzero is similar but more general.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.griddata" title="matplotlib.mlab.griddata"><code class="xref py py-func docutils literal notranslate"><span class="pre">griddata()</span></code></a></dt>
<dd>Interpolate irregularly distributed data to a
regular grid.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.prctile" title="matplotlib.mlab.prctile"><code class="xref py py-func docutils literal notranslate"><span class="pre">prctile()</span></code></a></dt>
<dd>Find the percentiles of a sequence</dd>
<dt><code class="xref py py-func docutils literal notranslate"><span class="pre">prepca()</span></code></dt>
<dd>Principal Component Analysis</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-func docutils literal notranslate"><span class="pre">psd()</span></code></a></dt>
<dd>Power spectral density using Welch’s average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rk4" title="matplotlib.mlab.rk4"><code class="xref py py-func docutils literal notranslate"><span class="pre">rk4()</span></code></a></dt>
<dd>A 4th order runge kutta integrator for 1D or ND systems</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-func docutils literal notranslate"><span class="pre">specgram()</span></code></a></dt>
<dd>Spectrogram (spectrum over segments of time)</dd>
</dl>
</div>
<div class="section" id="miscellaneous-functions">
<h3>Miscellaneous functions<a class="headerlink" href="#miscellaneous-functions" title="Permalink to this headline">¶</a></h3>
<p>Functions that don’t exist in MATLAB, but are useful anyway:</p>
<dl class="docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><code class="xref py py-func docutils literal notranslate"><span class="pre">cohere_pairs()</span></code></a></dt>
<dd>Coherence over all pairs. This is not a MATLAB function, but we
compute coherence a lot in my lab, and we compute it for a lot of
pairs. This function is optimized to do this efficiently by
caching the direct FFTs.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rk4" title="matplotlib.mlab.rk4"><code class="xref py py-func docutils literal notranslate"><span class="pre">rk4()</span></code></a></dt>
<dd>A 4th order Runge-Kutta ODE integrator in case you ever find
yourself stranded without scipy (and the far superior
scipy.integrate tools)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.contiguous_regions" title="matplotlib.mlab.contiguous_regions"><code class="xref py py-func docutils literal notranslate"><span class="pre">contiguous_regions()</span></code></a></dt>
<dd>Return the indices of the regions spanned by some logical mask</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.cross_from_below" title="matplotlib.mlab.cross_from_below"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_from_below()</span></code></a></dt>
<dd>Return the indices where a 1D array crosses a threshold from below</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.cross_from_above" title="matplotlib.mlab.cross_from_above"><code class="xref py py-func docutils literal notranslate"><span class="pre">cross_from_above()</span></code></a></dt>
<dd>Return the indices where a 1D array crosses a threshold from above</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">complex_spectrum()</span></code></a></dt>
<dd>Return the complex-valued frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">magnitude_spectrum()</span></code></a></dt>
<dd>Return the magnitude of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_spectrum()</span></code></a></dt>
<dd>Return the angle (wrapped phase) of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">phase_spectrum()</span></code></a></dt>
<dd>Return the phase (unwrapped angle) of the frequency spectrum of a signal</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_mean()</span></code></a></dt>
<dd>Remove the mean from a line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.demean" title="matplotlib.mlab.demean"><code class="xref py py-func docutils literal notranslate"><span class="pre">demean()</span></code></a></dt>
<dd>Remove the mean from a line. This function is the same as
<a class="reference internal" href="#matplotlib.mlab.detrend_mean" title="matplotlib.mlab.detrend_mean"><code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_mean()</span></code></a> except for the default <em>axis</em>.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_linear" title="matplotlib.mlab.detrend_linear"><code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_linear()</span></code></a></dt>
<dd>Remove the best fit line from a line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend_none" title="matplotlib.mlab.detrend_none"><code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_none()</span></code></a></dt>
<dd>Return the original line.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.stride_windows" title="matplotlib.mlab.stride_windows"><code class="xref py py-func docutils literal notranslate"><span class="pre">stride_windows()</span></code></a></dt>
<dd>Get all windows in an array in a memory-efficient manner</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.stride_repeat" title="matplotlib.mlab.stride_repeat"><code class="xref py py-func docutils literal notranslate"><span class="pre">stride_repeat()</span></code></a></dt>
<dd>Repeat an array in a memory-efficient manner</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.apply_window" title="matplotlib.mlab.apply_window"><code class="xref py py-func docutils literal notranslate"><span class="pre">apply_window()</span></code></a></dt>
<dd>Apply a window along a given axis</dd>
</dl>
</div>
<div class="section" id="record-array-helper-functions">
<h3>record array helper functions<a class="headerlink" href="#record-array-helper-functions" title="Permalink to this headline">¶</a></h3>
<p>A collection of helper methods for numpyrecord arrays</p>
<blockquote id="htmlonly">
<div>See <a class="reference internal" href="../gallery/index.html#misc-examples-index"><span class="std std-ref">Miscellaneous</span></a></div></blockquote>
<dl class="docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.rec2txt" title="matplotlib.mlab.rec2txt"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec2txt()</span></code></a></dt>
<dd>Pretty print a record array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec2csv" title="matplotlib.mlab.rec2csv"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec2csv()</span></code></a></dt>
<dd>Store record array in CSV file</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.csv2rec" title="matplotlib.mlab.csv2rec"><code class="xref py py-func docutils literal notranslate"><span class="pre">csv2rec()</span></code></a></dt>
<dd>Import record array from CSV file with type inspection</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_append_fields" title="matplotlib.mlab.rec_append_fields"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec_append_fields()</span></code></a></dt>
<dd>Adds field(s)/array(s) to record array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_drop_fields" title="matplotlib.mlab.rec_drop_fields"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec_drop_fields()</span></code></a></dt>
<dd>Drop fields from record array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_join" title="matplotlib.mlab.rec_join"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec_join()</span></code></a></dt>
<dd>Join two record arrays on sequence of fields</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.recs_join" title="matplotlib.mlab.recs_join"><code class="xref py py-func docutils literal notranslate"><span class="pre">recs_join()</span></code></a></dt>
<dd>A simple join of multiple recarrays using a single column as a key</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_groupby" title="matplotlib.mlab.rec_groupby"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec_groupby()</span></code></a></dt>
<dd>Summarize data by groups (similar to SQL GROUP BY)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_summarize" title="matplotlib.mlab.rec_summarize"><code class="xref py py-func docutils literal notranslate"><span class="pre">rec_summarize()</span></code></a></dt>
<dd>Helper code to filter rec array fields into new fields</dd>
</dl>
<p>For the rec viewer functions(e rec2csv), there are a bunch of Format
objects you can pass into the functions that will do things like color
negative values red, set percent formatting and scaling, etc.</p>
<p>Example usage:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">r</span> <span class="o">=</span> <span class="n">csv2rec</span><span class="p">(</span><span class="s1">'somefile.csv'</span><span class="p">,</span> <span class="n">checkrows</span><span class="o">=</span><span class="mi">0</span><span class="p">)</span>
<span class="n">formatd</span> <span class="o">=</span> <span class="nb">dict</span><span class="p">(</span>
<span class="n">weight</span> <span class="o">=</span> <span class="n">FormatFloat</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span>
<span class="n">change</span> <span class="o">=</span> <span class="n">FormatPercent</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span>
<span class="n">cost</span> <span class="o">=</span> <span class="n">FormatThousands</span><span class="p">(</span><span class="mi">2</span><span class="p">),</span>
<span class="p">)</span>
<span class="n">rec2excel</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="s1">'test.xls'</span><span class="p">,</span> <span class="n">formatd</span><span class="o">=</span><span class="n">formatd</span><span class="p">)</span>
<span class="n">rec2csv</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="s1">'test.csv'</span><span class="p">,</span> <span class="n">formatd</span><span class="o">=</span><span class="n">formatd</span><span class="p">)</span>
<span class="n">scroll</span> <span class="o">=</span> <span class="n">rec2gtk</span><span class="p">(</span><span class="n">r</span><span class="p">,</span> <span class="n">formatd</span><span class="o">=</span><span class="n">formatd</span><span class="p">)</span>
<span class="n">win</span> <span class="o">=</span> <span class="n">gtk</span><span class="o">.</span><span class="n">Window</span><span class="p">()</span>
<span class="n">win</span><span class="o">.</span><span class="n">set_size_request</span><span class="p">(</span><span class="mi">600</span><span class="p">,</span><span class="mi">800</span><span class="p">)</span>
<span class="n">win</span><span class="o">.</span><span class="n">add</span><span class="p">(</span><span class="n">scroll</span><span class="p">)</span>
<span class="n">win</span><span class="o">.</span><span class="n">show_all</span><span class="p">()</span>
<span class="n">gtk</span><span class="o">.</span><span class="n">main</span><span class="p">()</span>
</pre></div>
</div>
<dl class="class">
<dt id="matplotlib.mlab.FormatBool">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatBool</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatBool" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatBool class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatBool.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>s</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatBool.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatBool.toval">
<code class="descname">toval</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatBool.toval" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatDate">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatDate</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatDate" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatDate class was deprecated in version 2.2. Use date.strftime instead.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatDate.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatDate.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatDate.toval">
<code class="descname">toval</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatDate.toval" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatDatetime">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatDatetime</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatDatetime" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatDate" title="matplotlib.mlab.FormatDate"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatDate</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatDatetime class was deprecated in version 2.2. Use datetime.strftime instead.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatDatetime.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatDatetime.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatFloat">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatFloat</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatFloat" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFormatStr" title="matplotlib.mlab.FormatFormatStr"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatFormatStr</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatFloat class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatFloat.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>s</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatFloat.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatFloat.toval">
<code class="descname">toval</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatFloat.toval" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatFormatStr">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatFormatStr</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatFormatStr" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatFormatStr class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatFormatStr.tostr">
<code class="descname">tostr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatFormatStr.tostr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatInt">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatInt</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatInt" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatInt class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatInt.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>s</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatInt.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatInt.tostr">
<code class="descname">tostr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatInt.tostr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatInt.toval">
<code class="descname">toval</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatInt.toval" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatMillions">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatMillions</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatMillions" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFloat" title="matplotlib.mlab.FormatFloat"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatMillions class was deprecated in version 2.2.</p>
</div>
<p></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatObj">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatObj</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatObj" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.6)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatObj class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatObj.fromstr">
<code class="descname">fromstr</code><span class="sig-paren">(</span><em>s</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatObj.fromstr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatObj.tostr">
<code class="descname">tostr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatObj.tostr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FormatObj.toval">
<code class="descname">toval</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatObj.toval" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatPercent">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatPercent</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatPercent" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFloat" title="matplotlib.mlab.FormatFloat"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatPercent class was deprecated in version 2.2.</p>
</div>
<p></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatString">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatString</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatString" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatString class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatString.tostr">
<code class="descname">tostr</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatString.tostr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatThousands">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">FormatThousands</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.FormatThousands" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFloat" title="matplotlib.mlab.FormatFloat"><code class="xref py py-class docutils literal notranslate"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The FormatThousands class was deprecated in version 2.2.</p>
</div>
<p></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.GaussianKDE">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">GaussianKDE</code><span class="sig-paren">(</span><em>dataset</em>, <em>bw_method=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.6)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<p>Representation of a kernel-density estimate using Gaussian kernels.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>dataset</strong> <span class="classifier-delimiter">:</span> <span class="classifier">array_like</span></dt>
<dd><p class="first last">Datapoints to estimate from. In case of univariate data this is a 1-D
array, otherwise a 2-D array with shape (# of dims, # of data).</p>
</dd>
<dt><strong>bw_method</strong> <span class="classifier-delimiter">:</span> <span class="classifier">str, scalar or callable, optional</span></dt>
<dd><p class="first last">The method used to calculate the estimator bandwidth. This can be
‘scott’, ‘silverman’, a scalar constant or a callable. If a
scalar, this will be used directly as <code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.factor</span></code>. If a
callable, it should take a <a class="reference internal" href="#matplotlib.mlab.GaussianKDE" title="matplotlib.mlab.GaussianKDE"><code class="xref py py-obj docutils literal notranslate"><span class="pre">GaussianKDE</span></code></a> instance as only
parameter and return a scalar. If None (default), ‘scott’ is used.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Attributes:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>dataset</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The dataset with which <code class="xref py py-obj docutils literal notranslate"><span class="pre">gaussian_kde</span></code> was initialized.</p>
</dd>
<dt><strong>dim</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">Number of dimensions.</p>
</dd>
<dt><strong>num_dp</strong> <span class="classifier-delimiter">:</span> <span class="classifier">int</span></dt>
<dd><p class="first last">Number of datapoints.</p>
</dd>
<dt><strong>factor</strong> <span class="classifier-delimiter">:</span> <span class="classifier">float</span></dt>
<dd><p class="first last">The bandwidth factor, obtained from <code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.covariance_factor</span></code>, with which
the covariance matrix is multiplied.</p>
</dd>
<dt><strong>covariance</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The covariance matrix of <code class="xref py py-obj docutils literal notranslate"><span class="pre">dataset</span></code>, scaled by the calculated bandwidth
(<code class="xref py py-obj docutils literal notranslate"><span class="pre">kde.factor</span></code>).</p>
</dd>
<dt><strong>inv_cov</strong> <span class="classifier-delimiter">:</span> <span class="classifier">ndarray</span></dt>
<dd><p class="first last">The inverse of <code class="xref py py-obj docutils literal notranslate"><span class="pre">covariance</span></code>.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="27%" />
<col width="73%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td><strong>kde.evaluate(points)</strong></td>
<td>(ndarray) Evaluate the estimated pdf on a provided set of points.</td>
</tr>
<tr class="row-even"><td><strong>kde(points)</strong></td>
<td>(ndarray) Same as kde.evaluate(points)</td>
</tr>
</tbody>
</table>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.covariance_factor">
<code class="descname">covariance_factor</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.covariance_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.evaluate">
<code class="descname">evaluate</code><span class="sig-paren">(</span><em>points</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.evaluate" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluate the estimated pdf on a set of points.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>points</strong> <span class="classifier-delimiter">:</span> <span class="classifier">(# of dimensions, # of points)-array</span></dt>
<dd><p class="first last">Alternatively, a (# of dimensions,) vector can be passed in and
treated as a single point.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first docutils">
<dt><strong>values</strong> <span class="classifier-delimiter">:</span> <span class="classifier">(# of points,)-array</span></dt>
<dd><p class="first last">The values at each point.</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>ValueError</strong> <span class="classifier-delimiter">:</span> <span class="classifier">if the dimensionality of the input points is different</span></dt>
<dd><p class="first last">than the dimensionality of the KDE.</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.scotts_factor">
<code class="descname">scotts_factor</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.scotts_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.GaussianKDE.silverman_factor">
<code class="descname">silverman_factor</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.GaussianKDE.silverman_factor" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.PCA">
<em class="property">class </em><code class="descclassname">matplotlib.mlab.</code><code class="descname">PCA</code><span class="sig-paren">(</span><em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.PCA" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <a class="reference external" href="https://docs.python.org/3/library/functions.html#object" title="(in Python v3.6)"><code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></a></p>
<div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The PCA class was deprecated in version 2.2.</p>
</div>
<p></p>
<dl class="method">
<dt id="matplotlib.mlab.PCA.center">
<code class="descname">center</code><span class="sig-paren">(</span><em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.PCA.center" title="Permalink to this definition">¶</a></dt>
<dd><p>center and optionally standardize the data using the mean and sigma
from training set a</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.PCA.project">
<code class="descname">project</code><span class="sig-paren">(</span><em>x</em>, <em>minfrac=0.0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.PCA.project" title="Permalink to this definition">¶</a></dt>
<dd><p>project x onto the principle axes, dropping any axes where fraction
of variance<minfrac</p>
</dd></dl>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.amap">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">amap</code><span class="sig-paren">(</span><em>fn</em>, <em>*args</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.amap" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The amap function was deprecated in version 2.2. Use numpy.array(list(map(…))) instead.</p>
</div>
<p>amap(function, sequence[, sequence, …]) -> array.</p>
<p>Works like <a class="reference external" href="https://docs.python.org/3/library/functions.html#map" title="(in Python v3.6)"><code class="xref py py-func docutils literal notranslate"><span class="pre">map()</span></code></a>, but it returns an array. This is just a
convenient shorthand for <code class="docutils literal notranslate"><span class="pre">numpy.array(map(...))</span></code>.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.angle_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">angle_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.angle_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the angle of the frequency spectrum (wrapped phase spectrum) of
<em>x</em>. Data is padded to a length of <em>pad_to</em> and the windowing function
<em>window</em> is applied to the signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window
vectors see <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_none()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.blackman()</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.hamming()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.bartlett()</span></code></a>, <code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal()</span></code>,
<a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.0.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal.get_window()</span></code></a>, etc. The default is
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>. If a function is passed as the
argument, it must take a data segment as an argument and
return the windowed version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">[ ‘default’ | ‘onesided’ | ‘twosided’ ]</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. ‘onesided’ forces the return of a one-sided
spectrum, while ‘twosided’ forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the angle spectrum in radians (real valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">complex_spectrum()</span></code></a></dt>
<dd>This function returns the angle value of <a class="reference internal" href="#matplotlib.mlab.complex_spectrum" title="matplotlib.mlab.complex_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">complex_spectrum()</span></code></a>.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">magnitude_spectrum()</span></code></a></dt>
<dd><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">angle_spectrum()</span></code></a> returns the magnitudes of the corresponding frequencies.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">phase_spectrum()</span></code></a></dt>
<dd><a class="reference internal" href="#matplotlib.mlab.phase_spectrum" title="matplotlib.mlab.phase_spectrum"><code class="xref py py-func docutils literal notranslate"><span class="pre">phase_spectrum()</span></code></a> returns the unwrapped version of this function.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-func docutils literal notranslate"><span class="pre">specgram()</span></code></a></dt>
<dd><a class="reference internal" href="#matplotlib.mlab.specgram" title="matplotlib.mlab.specgram"><code class="xref py py-func docutils literal notranslate"><span class="pre">specgram()</span></code></a> can return the angle spectrum of segments within the signal.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.apply_window">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">apply_window</code><span class="sig-paren">(</span><em>x</em>, <em>window</em>, <em>axis=0</em>, <em>return_window=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.apply_window" title="Permalink to this definition">¶</a></dt>
<dd><p>Apply the given window to the given 1D or 2D array along the given axis.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1D or 2D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">function or array.</span></dt>
<dd><p class="first last">Either a function to generate a window or an array with length
<em>x</em>.shape[<em>axis</em>]</p>
</dd>
<dt><strong>axis</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The axis over which to do the repetition.
Must be 0 or 1. The default is 0</p>
</dd>
<dt><strong>return_window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">bool</span></dt>
<dd><p class="first last">If true, also return the 1D values of the window that was applied</p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.base_repr">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">base_repr</code><span class="sig-paren">(</span><em>number</em>, <em>base=2</em>, <em>padding=0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.base_repr" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The base_repr function was deprecated in version 2.2.</p>
</div>
<p>Return the representation of a <em>number</em> in any given <em>base</em>.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.binary_repr">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">binary_repr</code><span class="sig-paren">(</span><em>number</em>, <em>max_length=1025</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.binary_repr" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The binary_repr function was deprecated in version 2.2.</p>
</div>
<p>Return the binary representation of the input <em>number</em> as a
string.</p>
<p>This is more efficient than using <a class="reference internal" href="#matplotlib.mlab.base_repr" title="matplotlib.mlab.base_repr"><code class="xref py py-func docutils literal notranslate"><span class="pre">base_repr()</span></code></a> with base 2.</p>
<p>Increase the value of max_length for very large numbers. Note that
on 32-bit machines, 2**1023 is the largest integer power of 2
which can be converted to a Python float.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.bivariate_normal">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">bivariate_normal</code><span class="sig-paren">(</span><em>X</em>, <em>Y</em>, <em>sigmax=1.0</em>, <em>sigmay=1.0</em>, <em>mux=0.0</em>, <em>muy=0.0</em>, <em>sigmaxy=0.0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.bivariate_normal" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The bivariate_normal function was deprecated in version 2.2.</p>
</div>
<p>Bivariate Gaussian distribution for equal shape <em>X</em>, <em>Y</em>.</p>
<p>See <a class="reference external" href="http://mathworld.wolfram.com/BivariateNormalDistribution.html">bivariate normal</a>
at mathworld.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.center_matrix">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">center_matrix</code><span class="sig-paren">(</span><em>M</em>, <em>dim=0</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.center_matrix" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>The center_matrix function was deprecated in version 2.2.</p>
</div>
<p>Return the matrix <em>M</em> with each row having zero mean and unit std.</p>
<p>If <em>dim</em> = 1 operate on columns instead of rows. (<em>dim</em> is
opposite to the numpy axis kwarg.)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cohere">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">cohere</code><span class="sig-paren">(</span><em>x</em>, <em>y</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none></em>, <em>window=<function window_hanning></em>, <em>noverlap=0</em>, <em>pad_to=None</em>, <em>sides='default'</em>, <em>scale_by_freq=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.cohere" title="Permalink to this definition">¶</a></dt>
<dd><p>The coherence between <em>x</em> and <em>y</em>. Coherence is the normalized
cross spectral density:</p>
<img src="../_images/mathmpl/math-58775d54bf.png" class="center" /><table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x, y</strong></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window
vectors see <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_none()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.blackman()</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.hamming()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.bartlett()</span></code></a>, <code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal()</span></code>,
<a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.0.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal.get_window()</span></code></a>, etc. The default is
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>. If a function is passed as the
argument, it must take a data segment as an argument and
return the windowed version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">[ ‘default’ | ‘onesided’ | ‘twosided’ ]</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. ‘onesided’ forces the return of a one-sided
spectrum, while ‘twosided’ forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. This can be different from <em>NFFT</em>, which
specifies the number of data points used. While not increasing
the actual resolution of the spectrum (the minimum distance between
resolvable peaks), this can give more points in the plot,
allowing for more detail. This corresponds to the <em>n</em> parameter
in the call to fft(). The default is None, which sets <em>pad_to</em>
equal to <em>NFFT</em></p>
</dd>
<dt><strong>NFFT</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of data points used in each block for the FFT.
A power 2 is most efficient. The default value is 256.
This should <em>NOT</em> be used to get zero padding, or the scaling of the
result will be incorrect. Use <em>pad_to</em> for this instead.</p>
</dd>
<dt><strong>detrend</strong> <span class="classifier-delimiter">:</span> <span class="classifier">{‘default’, ‘constant’, ‘mean’, ‘linear’, ‘none’} or callable</span></dt>
<dd><p class="first last">The function applied to each segment before fft-ing,
designed to remove the mean or linear trend. Unlike in
MATLAB, where the <em>detrend</em> parameter is a vector, in
matplotlib is it a function. The <code class="xref py py-mod docutils literal notranslate"><span class="pre">pylab</span></code>
module defines <code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_none()</span></code>,
<code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_mean()</span></code>, and
<code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_linear()</span></code>, but you can use
a custom function as well. You can also use a string to choose
one of the functions. ‘default’, ‘constant’, and ‘mean’ call
<code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_mean()</span></code>. ‘linear’ calls
<code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_linear()</span></code>. ‘none’ calls
<code class="xref py py-func docutils literal notranslate"><span class="pre">detrend_none()</span></code>.</p>
</dd>
<dt><strong>scale_by_freq</strong> <span class="classifier-delimiter">:</span> <span class="classifier">boolean, optional</span></dt>
<dd><p class="first last">Specifies whether the resulting density values should be scaled
by the scaling frequency, which gives density in units of Hz^-1.
This allows for integration over the returned frequency values.
The default is True for MATLAB compatibility.</p>
</dd>
<dt><strong>noverlap</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points of overlap between blocks. The default value
is 0 (no overlap).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>The return value is the tuple (*Cxy*, *f*), where *f* are the</strong></dt>
<dd></dd>
<dt><strong>frequencies of the coherence vector. For cohere, scaling the</strong></dt>
<dd></dd>
<dt><strong>individual densities by the sampling frequency has no effect,</strong></dt>
<dd></dd>
<dt><strong>since the factors cancel out.</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-func docutils literal notranslate"><span class="pre">psd()</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><code class="xref py py-func docutils literal notranslate"><span class="pre">csd()</span></code></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cohere_pairs">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">cohere_pairs</code><span class="sig-paren">(</span><em>X</em>, <em>ij</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none></em>, <em>window=<function window_hanning></em>, <em>noverlap=0</em>, <em>preferSpeedOverMemory=True</em>, <em>progressCallback=<function donothing_callback></em>, <em>returnPxx=False</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.cohere_pairs" title="Permalink to this definition">¶</a></dt>
<dd><div class="deprecated">
<p><span class="versionmodified">Deprecated since version 2.2: </span>scipy.signal.coherence</p>
</div>
<p>Compute the coherence and phase for all pairs <em>ij</em>, in <em>X</em>.</p>
<p><em>X</em> is a <em>numSamples</em> * <em>numCols</em> array</p>
<p><em>ij</em> is a list of tuples. Each tuple is a pair of indexes into
the columns of X for which you want to compute coherence. For
example, if <em>X</em> has 64 columns, and you want to compute all
nonredundant pairs, define <em>ij</em> as:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">ij</span> <span class="o">=</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="mi">64</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="o">+</span><span class="mi">1</span><span class="p">,</span><span class="mi">64</span><span class="p">):</span>
<span class="n">ij</span><span class="o">.</span><span class="n">append</span><span class="p">(</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="p">)</span>
</pre></div>
</div>
<p><em>preferSpeedOverMemory</em> is an optional bool. Defaults to true. If
False, limits the caching by only making one, rather than two,
complex cache arrays. This is useful if memory becomes critical.
Even when <em>preferSpeedOverMemory</em> is False, <a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><code class="xref py py-func docutils literal notranslate"><span class="pre">cohere_pairs()</span></code></a>
will still give significant performance gains over calling
<a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal notranslate"><span class="pre">cohere()</span></code></a> for each pair, and will use subtantially less
memory than if <em>preferSpeedOverMemory</em> is True. In my tests with
a 43000,64 array over all nonredundant pairs,
<em>preferSpeedOverMemory</em> = True delivered a 33% performance boost
on a 1.7GHZ Athlon with 512MB RAM compared with
<em>preferSpeedOverMemory</em> = False. But both solutions were more
than 10x faster than naively crunching all possible pairs through
<a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal notranslate"><span class="pre">cohere()</span></code></a>.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>Cxy</strong> <span class="classifier-delimiter">:</span> <span class="classifier">dictionary of (<em>i</em>, <em>j</em>) tuples -> coherence vector for</span></dt>
<dd><p class="first last">that pair. i.e., <code class="docutils literal notranslate"><span class="pre">Cxy[(i,j)</span> <span class="pre">=</span> <span class="pre">cohere(X[:,i],</span> <span class="pre">X[:,j])</span></code>.
Number of dictionary keys is <code class="docutils literal notranslate"><span class="pre">len(ij)</span></code>.</p>
</dd>
<dt><strong>Phase</strong> <span class="classifier-delimiter">:</span> <span class="classifier">dictionary of phases of the cross spectral density at</span></dt>
<dd><p class="first last">each frequency for each pair. Keys are (<em>i</em>, <em>j</em>).</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">vector of frequencies, equal in length to either the</span></dt>
<dd><p class="first last">coherence or phase vectors for any (<em>i</em>, <em>j</em>) key.</p>
</dd>
<dt><strong>e.g., to make a coherence Bode plot::</strong></dt>
<dd><p class="first last">subplot(211)
plot( freqs, Cxy[(12,19)])
subplot(212)
plot( freqs, Phase[(12,19)])</p>
</dd>
<dt><strong>For a large number of pairs, :func:`cohere_pairs` can be much more</strong></dt>
<dd></dd>
<dt><strong>efficient than just calling :func:`cohere` for each pair, because</strong></dt>
<dd></dd>
<dt><strong>it caches most of the intensive computations. If :math:`N` is the</strong></dt>
<dd></dd>
<dt><strong>number of pairs, this function is :math:`O(N)` for most of the</strong></dt>
<dd></dd>
<dt><strong>heavy lifting, whereas calling cohere for each pair is</strong></dt>
<dd></dd>
<dt><strong>:math:`O(N^2)`. However, because of the caching, it is also more</strong></dt>
<dd></dd>
<dt><strong>memory intensive, making 2 additional complex arrays with</strong></dt>
<dd></dd>
<dt><strong>approximately the same number of elements as *X*.</strong></dt>
<dd></dd>
<dt><strong>See :file:`test/cohere_pairs_test.py` in the src tree for an</strong></dt>
<dd></dd>
<dt><strong>example script that shows that this :func:`cohere_pairs` and</strong></dt>
<dd></dd>
<dt><strong>:func:`cohere` give the same results for a given pair.</strong></dt>
<dd></dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><code class="xref py py-func docutils literal notranslate"><span class="pre">psd()</span></code></a></dt>
<dd>For information about the methods used to compute <img src="../_images/mathmpl/math-0005c3a5e5.png" style="position: relative; bottom: -9px"/>, <img src="../_images/mathmpl/math-f6d65b7f49.png" style="position: relative; bottom: -6px"/> and <img src="../_images/mathmpl/math-0938c51d1a.png" style="position: relative; bottom: -9px"/>.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.complex_spectrum">
<code class="descclassname">matplotlib.mlab.</code><code class="descname">complex_spectrum</code><span class="sig-paren">(</span><em>x</em>, <em>Fs=None</em>, <em>window=None</em>, <em>pad_to=None</em>, <em>sides=None</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.complex_spectrum" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute the complex-valued frequency spectrum of <em>x</em>. Data is padded to a
length of <em>pad_to</em> and the windowing function <em>window</em> is applied to the
signal.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><dl class="first docutils">
<dt><strong>x</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array or sequence</span></dt>
<dd><p class="first last">Array or sequence containing the data</p>
</dd>
<dt><strong>Fs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">scalar</span></dt>
<dd><p class="first last">The sampling frequency (samples per time unit). It is used
to calculate the Fourier frequencies, freqs, in cycles per time
unit. The default value is 2.</p>
</dd>
<dt><strong>window</strong> <span class="classifier-delimiter">:</span> <span class="classifier">callable or ndarray</span></dt>
<dd><p class="first last">A function or a vector of length <em>NFFT</em>. To create window
vectors see <a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_none()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.blackman.html#numpy.blackman" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.blackman()</span></code></a>, <a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.hamming.html#numpy.hamming" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.hamming()</span></code></a>,
<a class="reference external" href="https://docs.scipy.org/doc/numpy/reference/generated/numpy.bartlett.html#numpy.bartlett" title="(in NumPy v1.14)"><code class="xref py py-func docutils literal notranslate"><span class="pre">numpy.bartlett()</span></code></a>, <code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal()</span></code>,
<a class="reference external" href="https://docs.scipy.org/doc/scipy/reference/generated/scipy.signal.get_window.html#scipy.signal.get_window" title="(in SciPy v1.0.0)"><code class="xref py py-func docutils literal notranslate"><span class="pre">scipy.signal.get_window()</span></code></a>, etc. The default is
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><code class="xref py py-func docutils literal notranslate"><span class="pre">window_hanning()</span></code></a>. If a function is passed as the
argument, it must take a data segment as an argument and
return the windowed version of the segment.</p>
</dd>
<dt><strong>sides</strong> <span class="classifier-delimiter">:</span> <span class="classifier">[ ‘default’ | ‘onesided’ | ‘twosided’ ]</span></dt>
<dd><p class="first last">Specifies which sides of the spectrum to return. Default gives the
default behavior, which returns one-sided for real data and both
for complex data. ‘onesided’ forces the return of a one-sided
spectrum, while ‘twosided’ forces two-sided.</p>
</dd>
<dt><strong>pad_to</strong> <span class="classifier-delimiter">:</span> <span class="classifier">integer</span></dt>
<dd><p class="first last">The number of points to which the data segment is padded when
performing the FFT. While not increasing the actual resolution of
the spectrum (the minimum distance between resolvable peaks),
this can give more points in the plot, allowing for more
detail. This corresponds to the <em>n</em> parameter in the call to fft().
The default is None, which sets <em>pad_to</em> equal to the length of the
input signal (i.e. no padding).</p>
</dd>
</dl>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><dl class="first last docutils">
<dt><strong>spectrum</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The values for the complex spectrum (complex valued)</p>
</dd>
<dt><strong>freqs</strong> <span class="classifier-delimiter">:</span> <span class="classifier">1-D array</span></dt>
<dd><p class="first last">The frequencies corresponding to the elements in <em>spectrum</em></p>
</dd>
</dl>
</td>
</tr>
</tbody>
</table>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<dl class="last docutils">