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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"><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 compatability 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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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="../examples/misc/index.html#misc-examples-index"><span class="std std-ref">misc Examples</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"><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"><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"><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"><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"><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"><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"><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"><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"><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"><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><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"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></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>fmt</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"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></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>fmt='%Y-%m-%d %H:%M:%S'</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"><span class="pre">matplotlib.mlab.FormatDate</span></code></a></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>precision=4</em>, <em>scale=1.0</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"><span class="pre">matplotlib.mlab.FormatFormatStr</span></code></a></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>fmt</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"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></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><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"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></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>precision=4</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"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></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><a class="headerlink" href="#matplotlib.mlab.FormatObj" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">object</span></code></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>precision=4</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"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></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><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"><span class="pre">matplotlib.mlab.FormatObj</span></code></a></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>precision=4</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"><span class="pre">matplotlib.mlab.FormatFloat</span></code></a></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: <code class="xref py py-class docutils literal"><span class="pre">object</span></code></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"><p class="first"><strong>dataset</strong> : array_like</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>bw_method</strong> : str, scalar or callable, optional</p>
<blockquote class="last">
<div><p>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"><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"><span class="pre">GaussianKDE</span></code></a> instance as only
parameter and return a scalar. If None (default), ‘scott’ is used.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Attributes</p>
<table border="1" class="docutils">
<colgroup>
<col width="8%" />
<col width="92%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>dataset</td>
<td>(ndarray) The dataset with which <code class="xref py py-obj docutils literal"><span class="pre">gaussian_kde</span></code> was initialized.</td>
</tr>
<tr class="row-even"><td>dim</td>
<td>(int) Number of dimensions.</td>
</tr>
<tr class="row-odd"><td>num_dp</td>
<td>(int) Number of datapoints.</td>
</tr>
<tr class="row-even"><td>factor</td>
<td>(float) The bandwidth factor, obtained from <code class="xref py py-obj docutils literal"><span class="pre">kde.covariance_factor</span></code>, with which the covariance matrix is multiplied.</td>
</tr>
<tr class="row-odd"><td>covariance</td>
<td>(ndarray) The covariance matrix of <code class="xref py py-obj docutils literal"><span class="pre">dataset</span></code>, scaled by the calculated bandwidth (<code class="xref py py-obj docutils literal"><span class="pre">kde.factor</span></code>).</td>
</tr>
<tr class="row-even"><td>inv_cov</td>
<td>(ndarray) The inverse of <code class="xref py py-obj docutils literal"><span class="pre">covariance</span></code>.</td>
</tr>
</tbody>
</table>
<p class="rubric">Methods</p>
<table border="1" class="docutils">
<colgroup>
<col width="24%" />
<col width="76%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>kde.evaluate(points)</td>
<td>(ndarray) Evaluate the estimated pdf on a provided set of points.</td>
</tr>
<tr class="row-even"><td>kde(points)</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"><p class="first"><strong>points</strong> : (# of dimensions, # of points)-array</p>
<blockquote>
<div><p>Alternatively, a (# of dimensions,) vector can be passed in and
treated as a single point.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>values</strong> : (# of points,)-array</p>
<blockquote>
<div><p>The values at each point.</p>
</div></blockquote>
</td>
</tr>
<tr class="field-odd field"><th class="field-name">Raises:</th><td class="field-body"><p class="first"><strong>ValueError</strong> : if the dimensionality of the input points is different</p>
<blockquote class="last">
<div><p>than the dimensionality of the KDE.</p>
</div></blockquote>
</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>a</em>, <em>standardize=True</em><span class="sig-paren">)</span><a class="headerlink" href="#matplotlib.mlab.PCA" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal"><span class="pre">object</span></code></p>
<p>compute the SVD of a and store data for PCA. Use project to
project the data onto a reduced set of dimensions</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"><p class="first"><strong>a</strong> : np.ndarray</p>
<blockquote>
<div><p>A numobservations x numdims array</p>
</div></blockquote>
<p><strong>standardize</strong> : bool</p>
<blockquote class="last">
<div><p>True if input data are to be standardized. If False, only centering
will be carried out.</p>
</div></blockquote>
</td>
</tr>
</tbody>
</table>
<p class="rubric">Notes</p>
<p>The factor loadings are in the <code class="docutils literal"><span class="pre">Wt</span></code> factor, i.e., the factor loadings
for the first principal component are given by <code class="docutils literal"><span class="pre">Wt[0]</span></code>. This row is
also the first eigenvector.</p>
<p class="rubric">Attributes</p>
<table border="1" class="docutils">
<colgroup>
<col width="15%" />
<col width="85%" />
</colgroup>
<tbody valign="top">
<tr class="row-odd"><td>a</td>
<td>A centered unit sigma version of input <code class="docutils literal"><span class="pre">a</span></code>.</td>
</tr>
<tr class="row-even"><td>numrows, numcols</td>
<td>The dimensions of <code class="docutils literal"><span class="pre">a</span></code>.</td>
</tr>
<tr class="row-odd"><td>mu</td>
<td>A numdims array of means of <code class="docutils literal"><span class="pre">a</span></code>. This is the vector that points to the origin of PCA space.</td>
</tr>
<tr class="row-even"><td>sigma</td>
<td>A numdims array of standard deviation of <code class="docutils literal"><span class="pre">a</span></code>.</td>
</tr>
<tr class="row-odd"><td>fracs</td>
<td>The proportion of variance of each of the principal components.</td>
</tr>
<tr class="row-even"><td>s</td>
<td>The actual eigenvalues of the decomposition.</td>
</tr>
<tr class="row-odd"><td>Wt</td>
<td>The weight vector for projecting a numdims point or array into PCA space.</td>
</tr>
<tr class="row-even"><td>Y</td>
<td>A projected into PCA space.</td>
</tr>
</tbody>
</table>
<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>function</em>, <em>sequence</em><span class="optional">[</span>, <em>sequence</em>, <em>...</em><span class="optional">]</span><span class="sig-paren">)</span> → array.<a class="headerlink" href="#matplotlib.mlab.amap" title="Permalink to this definition">¶</a></dt>
<dd><p>Works like <code class="xref py py-func docutils literal"><span class="pre">map()</span></code>, but it returns an array. This is just a
convenient shorthand for <code class="docutils literal"><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"><p class="first"><strong>x</strong> : 1-D array or sequence</p>
<blockquote>
<div><p>Array or sequence containing the data</p>
</div></blockquote>
<p><strong>Fs</strong> : scalar</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>window</strong> : callable or ndarray</p>
<blockquote>
<div><p>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"><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"><span class="pre">window_none()</span></code></a>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.blackman()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">numpy.hamming()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.bartlett()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">scipy.signal()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">scipy.signal.get_window()</span></code>, 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"><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>
</div></blockquote>
<p><strong>sides</strong> : [ ‘default’ | ‘onesided’ | ‘twosided’ ]</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>pad_to</strong> : integer</p>
<blockquote>
<div><p>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>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>spectrum</strong> : 1-D array</p>
<blockquote>
<div><p>The values for the angle spectrum in radians (real valued)</p>
</div></blockquote>
<p><strong>freqs</strong> : 1-D array</p>
<blockquote class="last">
<div><p>The frequencies corresponding to the elements in <em>spectrum</em></p>
</div></blockquote>
</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"><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"><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"><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"><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"><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"><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"><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"><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"><p class="first"><strong>x</strong> : 1D or 2D array or sequence</p>
<blockquote>
<div><p>Array or sequence containing the data.</p>
</div></blockquote>
<p><strong>window</strong> : function or array.</p>
<blockquote>
<div><p>Either a function to generate a window or an array with length
<em>x</em>.shape[<em>axis</em>]</p>
</div></blockquote>
<p><strong>axis</strong> : integer</p>
<blockquote>
<div><p>The axis over which to do the repetition.
Must be 0 or 1. The default is 0</p>
</div></blockquote>
<p><strong>return_window</strong> : bool</p>
<blockquote class="last">
<div><p>If true, also return the 1D values of the window that was applied</p>
</div></blockquote>
</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><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><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"><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><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><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"><p class="first"><strong>x, y</strong></p>
<blockquote>
<div><p>Array or sequence containing the data</p>
</div></blockquote>
<p><strong>Fs</strong> : scalar</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>window</strong> : callable or ndarray</p>
<blockquote>
<div><p>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"><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"><span class="pre">window_none()</span></code></a>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.blackman()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">numpy.hamming()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.bartlett()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">scipy.signal()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">scipy.signal.get_window()</span></code>, 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"><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>
</div></blockquote>
<p><strong>sides</strong> : [ ‘default’ | ‘onesided’ | ‘twosided’ ]</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>pad_to</strong> : integer</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>NFFT</strong> : integer</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>detrend</strong> : {‘default’, ‘constant’, ‘mean’, ‘linear’, ‘none’} or callable</p>
<blockquote>
<div><p>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"><span class="pre">pylab</span></code>
module defines <code class="xref py py-func docutils literal"><span class="pre">detrend_none()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">detrend_mean()</span></code>, and
<code class="xref py py-func docutils literal"><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"><span class="pre">detrend_mean()</span></code>. ‘linear’ calls
<code class="xref py py-func docutils literal"><span class="pre">detrend_linear()</span></code>. ‘none’ calls
<code class="xref py py-func docutils literal"><span class="pre">detrend_none()</span></code>.</p>
</div></blockquote>
<p><strong>scale_by_freq</strong> : boolean, optional</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>noverlap</strong> : integer</p>
<blockquote>
<div><p>The number of points of overlap between blocks. The default value
is 0 (no overlap).</p>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first">The return value is the tuple (<em>Cxy</em>, <em>f</em>), where <em>f</em> are the</p>
<p>frequencies of the coherence vector. For cohere, scaling the</p>
<p>individual densities by the sampling frequency has no effect,</p>
<p class="last">since the factors cancel out.</p>
</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"><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"><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><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"><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"><span class="pre">cohere_pairs()</span></code></a>
will still give significant performace gains over calling
<a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal"><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"><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"><p class="first"><strong>Cxy</strong> : dictionary of (<em>i</em>, <em>j</em>) tuples -> coherence vector for</p>
<blockquote>
<div><p>that pair. i.e., <code class="docutils literal"><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"><span class="pre">len(ij)</span></code>.</p>
</div></blockquote>
<p><strong>Phase</strong> : dictionary of phases of the cross spectral density at</p>
<blockquote>
<div><p>each frequency for each pair. Keys are (<em>i</em>, <em>j</em>).</p>
</div></blockquote>
<p><strong>freqs</strong> : vector of frequencies, equal in length to either the</p>
<blockquote>
<div><p>coherence or phase vectors for any (<em>i</em>, <em>j</em>) key.</p>
</div></blockquote>
<p>e.g., to make a coherence Bode plot:</p>
<div class="highlight-default"><div class="highlight"><pre><span></span><span class="n">subplot</span><span class="p">(</span><span class="mi">211</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span> <span class="n">freqs</span><span class="p">,</span> <span class="n">Cxy</span><span class="p">[(</span><span class="mi">12</span><span class="p">,</span><span class="mi">19</span><span class="p">)])</span>
<span class="n">subplot</span><span class="p">(</span><span class="mi">212</span><span class="p">)</span>
<span class="n">plot</span><span class="p">(</span> <span class="n">freqs</span><span class="p">,</span> <span class="n">Phase</span><span class="p">[(</span><span class="mi">12</span><span class="p">,</span><span class="mi">19</span><span class="p">)])</span>
</pre></div>
</div>
<p>For a large number of pairs, <a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><code class="xref py py-func docutils literal"><span class="pre">cohere_pairs()</span></code></a> can be much more</p>
<p>efficient than just calling <a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal"><span class="pre">cohere()</span></code></a> for each pair, because</p>
<p>it caches most of the intensive computations. If <img src="../_images/mathmpl/math-1922d1ceaa.png" style="position: relative; bottom: -3px"/> is the</p>
<p>number of pairs, this function is <img src="../_images/mathmpl/math-98c8089378.png" style="position: relative; bottom: -8px"/> for most of the</p>
<p>heavy lifting, whereas calling cohere for each pair is</p>
<p><img src="../_images/mathmpl/math-83ff203e39.png" style="position: relative; bottom: -8px"/>. However, because of the caching, it is also more</p>
<p>memory intensive, making 2 additional complex arrays with</p>
<p>approximately the same number of elements as <em>X</em>.</p>
<p>See <code class="file docutils literal"><span class="pre">test/cohere_pairs_test.py</span></code> in the src tree for an</p>
<p>example script that shows that this <a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><code class="xref py py-func docutils literal"><span class="pre">cohere_pairs()</span></code></a> and</p>
<p class="last"><a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><code class="xref py py-func docutils literal"><span class="pre">cohere()</span></code></a> give the same results for a given pair.</p>
</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"><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"><p class="first"><strong>x</strong> : 1-D array or sequence</p>
<blockquote>
<div><p>Array or sequence containing the data</p>
</div></blockquote>
<p><strong>Fs</strong> : scalar</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>window</strong> : callable or ndarray</p>
<blockquote>
<div><p>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"><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"><span class="pre">window_none()</span></code></a>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.blackman()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">numpy.hamming()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">numpy.bartlett()</span></code>, <code class="xref py py-func docutils literal"><span class="pre">scipy.signal()</span></code>,
<code class="xref py py-func docutils literal"><span class="pre">scipy.signal.get_window()</span></code>, 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"><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>
</div></blockquote>
<p><strong>sides</strong> : [ ‘default’ | ‘onesided’ | ‘twosided’ ]</p>
<blockquote>
<div><p>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>
</div></blockquote>
<p><strong>pad_to</strong> : integer</p>
<blockquote>
<div><p>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>
</div></blockquote>
</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body"><p class="first"><strong>spectrum</strong> : 1-D array</p>
<blockquote>
<div><p>The values for the complex spectrum (complex valued)</p>
</div></blockquote>
<p><strong>freqs</strong> : 1-D array</p>
<blockquote class="last">
<div><p>The frequencies corresponding to the elements in <em>spectrum</em></p>
</div></blockquote>
</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.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-func docutils literal"><span class="pre">magnitude_spectrum()</span></code></a></dt>
<dd><a class="reference internal" href="#matplotlib.mlab.magnitude_spectrum" title="matplotlib.mlab.magnitude_spectrum"><code class="xref py py-func docutils literal"><span class="pre">magnitude_spectrum()</span></code></a> returns the absolute value of this function.</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.angle_spectrum" title="matplotlib.mlab.angle_spectrum"><code class="xref py py-func docutils literal"><span class="pre">angle_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"><span class="pre">angle_spectrum()</span></code></a> returns the angle of this function.</dd>