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<li><a class="reference internal" href="#">mlab</a><ul>
<li><a class="reference internal" href="#module-matplotlib.mlab"><tt class="docutils literal"><span class="pre">matplotlib.mlab</span></tt></a><ul>
<li><a class="reference internal" href="#matlab-compatible-functions">MATLAB compatible functions</a></li>
<li><a class="reference internal" href="#miscellaneous-functions">Miscellaneous functions</a></li>
<li><a class="reference internal" href="#record-array-helper-functions">record array helper 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"><tt class="xref py py-mod docutils literal"><span class="pre">matplotlib.mlab</span></tt></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"><tt class="xref py py-func docutils literal"><span class="pre">cohere()</span></tt></a></dt>
<dd>Coherence (normalized cross spectral density)</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><tt class="xref py py-func docutils literal"><span class="pre">csd()</span></tt></a></dt>
<dd>Cross spectral density uing Welch’s average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.detrend" title="matplotlib.mlab.detrend"><tt class="xref py py-func docutils literal"><span class="pre">detrend()</span></tt></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"><tt class="xref py py-func docutils literal"><span class="pre">find()</span></tt></a></dt>
<dd><dl class="first last docutils">
<dt>Return the indices where some condition is true;</dt>
<dd>numpy.nonzero is similar but more general.</dd>
</dl>
</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.griddata" title="matplotlib.mlab.griddata"><tt class="xref py py-func docutils literal"><span class="pre">griddata()</span></tt></a></dt>
<dd><dl class="first last docutils">
<dt>interpolate irregularly distributed data to a</dt>
<dd>regular grid.</dd>
</dl>
</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.prctile" title="matplotlib.mlab.prctile"><tt class="xref py py-func docutils literal"><span class="pre">prctile()</span></tt></a></dt>
<dd>find the percentiles of a sequence</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.prepca" title="matplotlib.mlab.prepca"><tt class="xref py py-func docutils literal"><span class="pre">prepca()</span></tt></a></dt>
<dd>Principal Component Analysis</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.psd" title="matplotlib.mlab.psd"><tt class="xref py py-func docutils literal"><span class="pre">psd()</span></tt></a></dt>
<dd>Power spectral density uing Welch’s average periodogram</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rk4" title="matplotlib.mlab.rk4"><tt class="xref py py-func docutils literal"><span class="pre">rk4()</span></tt></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"><tt class="xref py py-func docutils literal"><span class="pre">specgram()</span></tt></a></dt>
<dd>Spectrogram (power spectral density 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"><tt class="xref py py-meth docutils literal"><span class="pre">cohere_pairs()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">rk4()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">contiguous_regions()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">cross_from_below()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">cross_from_above()</span></tt></a></dt>
<dd>return the indices where a 1D array crosses a threshold from above</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"><em>misc Examples</em></a></div></blockquote>
<dl class="docutils">
<dt><a class="reference internal" href="#matplotlib.mlab.rec2txt" title="matplotlib.mlab.rec2txt"><tt class="xref py py-meth docutils literal"><span class="pre">rec2txt()</span></tt></a></dt>
<dd>pretty print a record array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec2csv" title="matplotlib.mlab.rec2csv"><tt class="xref py py-meth docutils literal"><span class="pre">rec2csv()</span></tt></a></dt>
<dd>store record array in CSV file</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.csv2rec" title="matplotlib.mlab.csv2rec"><tt class="xref py py-meth docutils literal"><span class="pre">csv2rec()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">rec_append_fields()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">rec_drop_fields()</span></tt></a></dt>
<dd>drop fields from record array</dd>
<dt><a class="reference internal" href="#matplotlib.mlab.rec_join" title="matplotlib.mlab.rec_join"><tt class="xref py py-meth docutils literal"><span class="pre">rec_join()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">recs_join()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">rec_groupby()</span></tt></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"><tt class="xref py py-meth docutils literal"><span class="pre">rec_summarize()</span></tt></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-python"><div class="highlight"><pre><span class="n">r</span> <span class="o">=</span> <span class="n">csv2rec</span><span class="p">(</span><span class="s">'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="s">'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="s">'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>
</div>
<div class="section" id="deprecated-functions">
<h3>Deprecated functions<a class="headerlink" href="#deprecated-functions" title="Permalink to this headline">¶</a></h3>
<p>The following are deprecated; please import directly from numpy (with
care–function signatures may differ):</p>
<dl class="docutils">
<dt><tt class="xref py py-meth docutils literal"><span class="pre">load()</span></tt></dt>
<dd>load ASCII file - use numpy.loadtxt</dd>
<dt><tt class="xref py py-meth docutils literal"><span class="pre">save()</span></tt></dt>
<dd>save ASCII file - use numpy.savetxt</dd>
</dl>
<dl class="class">
<dt id="matplotlib.mlab.FIFOBuffer">
<em class="property">class </em><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FIFOBuffer</tt><big>(</big><em>*args</em>, <em>**kwargs</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer" title="Permalink to this definition">¶</a></dt>
<dd><p>A FIFO queue to hold incoming <em>x</em>, <em>y</em> data in a rotating buffer
using numpy arrays under the hood. It is assumed that you will
call asarrays much less frequently than you add data to the queue
– otherwise another data structure will be faster.</p>
<p>This can be used to support plots where data is added from a real
time feed and the plot object wants to grab data from the buffer
and plot it to screen less freqeuently than the incoming.</p>
<p>If you set the <em>dataLim</em> attr to
<tt class="xref py py-class docutils literal"><span class="pre">BBox</span></tt> (eg
<tt class="xref py py-attr docutils literal"><span class="pre">matplotlib.Axes.dataLim</span></tt>), the <em>dataLim</em> will be updated as
new data come in.</p>
<p>TODO: add a grow method that will extend nmax</p>
<div class="admonition note">
<p class="first admonition-title">Note</p>
<p class="last">mlab seems like the wrong place for this class.</p>
</div>
<div class="deprecated">
<p><span>Deprecated since version 1.3: </span>The FIFOBuffer class was deprecated in version 1.3.</p>
</div>
<p>Buffer up to <em>nmax</em> points.</p>
<dl class="method">
<dt id="matplotlib.mlab.FIFOBuffer.add">
<tt class="descname">add</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.add" title="Permalink to this definition">¶</a></dt>
<dd><p>Add scalar <em>x</em> and <em>y</em> to the queue.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FIFOBuffer.asarrays">
<tt class="descname">asarrays</tt><big>(</big><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.asarrays" title="Permalink to this definition">¶</a></dt>
<dd><p>Return <em>x</em> and <em>y</em> as arrays; their length will be the len of
data added or <em>nmax</em>.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FIFOBuffer.last">
<tt class="descname">last</tt><big>(</big><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.last" title="Permalink to this definition">¶</a></dt>
<dd><p>Get the last <em>x</em>, <em>y</em> or <em>None</em>. <em>None</em> if no data set.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FIFOBuffer.register">
<tt class="descname">register</tt><big>(</big><em>func</em>, <em>N</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.register" title="Permalink to this definition">¶</a></dt>
<dd><p>Call <em>func</em> every time <em>N</em> events are passed; <em>func</em> signature
is <tt class="docutils literal"><span class="pre">func(fifo)</span></tt>.</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.FIFOBuffer.update_datalim_to_current">
<tt class="descname">update_datalim_to_current</tt><big>(</big><big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.update_datalim_to_current" title="Permalink to this definition">¶</a></dt>
<dd><p>Update the <em>datalim</em> in the current data in the fifo.</p>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatBool">
<em class="property">class </em><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatBool</tt><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatObj</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatBool.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>s</em><big>)</big><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">
<tt class="descname">toval</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatDate</tt><big>(</big><em>fmt</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatObj</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatDate.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>x</em><big>)</big><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">
<tt class="descname">toval</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatDatetime</tt><big>(</big><em>fmt='%Y-%m-%d %H:%M:%S'</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatDate</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatDatetime.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatFloat</tt><big>(</big><em>precision=4</em>, <em>scale=1.0</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatFormatStr</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatFloat.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>s</em><big>)</big><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">
<tt class="descname">toval</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatFormatStr</tt><big>(</big><em>fmt</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatObj</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatFormatStr.tostr">
<tt class="descname">tostr</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatInt</tt><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatObj</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatInt.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>s</em><big>)</big><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">
<tt class="descname">tostr</tt><big>(</big><em>x</em><big>)</big><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">
<tt class="descname">toval</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatMillions</tt><big>(</big><em>precision=4</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatFloat</span></tt></a></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatObj">
<em class="property">class </em><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatObj</tt><a class="headerlink" href="#matplotlib.mlab.FormatObj" title="Permalink to this definition">¶</a></dt>
<dd><dl class="method">
<dt id="matplotlib.mlab.FormatObj.fromstr">
<tt class="descname">fromstr</tt><big>(</big><em>s</em><big>)</big><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">
<tt class="descname">tostr</tt><big>(</big><em>x</em><big>)</big><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">
<tt class="descname">toval</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatPercent</tt><big>(</big><em>precision=4</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatFloat</span></tt></a></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.FormatString">
<em class="property">class </em><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatString</tt><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatObj</span></tt></a></p>
<dl class="method">
<dt id="matplotlib.mlab.FormatString.tostr">
<tt class="descname">tostr</tt><big>(</big><em>x</em><big>)</big><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><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatThousands</tt><big>(</big><em>precision=4</em><big>)</big><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"><tt class="xref py py-class docutils literal"><span class="pre">matplotlib.mlab.FormatFloat</span></tt></a></p>
</dd></dl>
<dl class="class">
<dt id="matplotlib.mlab.PCA">
<em class="property">class </em><tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">PCA</tt><big>(</big><em>a</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.PCA" title="Permalink to this definition">¶</a></dt>
<dd><p>compute the SVD of a and store data for PCA. Use project to
project the data onto a reduced set of dimensions</p>
<p>Inputs:</p>
<blockquote>
<div><em>a</em>: a numobservations x numdims array</div></blockquote>
<p>Attrs:</p>
<blockquote>
<div><p><em>a</em> a centered unit sigma version of input a</p>
<p><em>numrows</em>, <em>numcols</em>: the dimensions of a</p>
<p><em>mu</em> : a numdims array of means of a</p>
<p><em>sigma</em> : a numdims array of atandard deviation of a</p>
<p><em>fracs</em> : the proportion of variance of each of the principal components</p>
<p><em>Wt</em> : the weight vector for projecting a numdims point or array into PCA space</p>
<p><em>Y</em> : a projected into PCA space</p>
</div></blockquote>
<p>The factor loadings are in the Wt factor, ie the factor
loadings for the 1st principal component are given by Wt[0]</p>
<dl class="method">
<dt id="matplotlib.mlab.PCA.center">
<tt class="descname">center</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.PCA.center" title="Permalink to this definition">¶</a></dt>
<dd><p>center the data using the mean and sigma from training set a</p>
</dd></dl>
<dl class="method">
<dt id="matplotlib.mlab.PCA.project">
<tt class="descname">project</tt><big>(</big><em>x</em>, <em>minfrac=0.0</em><big>)</big><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">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">amap</tt><big>(</big><em>function</em>, <em>sequence</em><span class="optional">[</span>, <em>sequence</em>, <em>...</em><span class="optional">]</span><big>)</big> → array.<a class="headerlink" href="#matplotlib.mlab.amap" title="Permalink to this definition">¶</a></dt>
<dd><p>Works like <tt class="xref py py-func docutils literal"><span class="pre">map()</span></tt>, but it returns an array. This is just a
convenient shorthand for <tt class="docutils literal"><span class="pre">numpy.array(map(...))</span></tt>.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.base_repr">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">base_repr</tt><big>(</big><em>number</em>, <em>base=2</em>, <em>padding=0</em><big>)</big><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">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">binary_repr</tt><big>(</big><em>number</em>, <em>max_length=1025</em><big>)</big><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"><tt class="xref py py-func docutils literal"><span class="pre">base_repr()</span></tt></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">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">bivariate_normal</tt><big>(</big><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><big>)</big><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">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">center_matrix</tt><big>(</big><em>M</em>, <em>dim=0</em><big>)</big><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">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cohere</tt><big>(</big><em>x</em>, <em>y</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none at 0x2635de8></em>, <em>window=<function window_hanning at 0x2635b90></em>, <em>noverlap=0</em>, <em>pad_to=None</em>, <em>sides='default'</em>, <em>scale_by_freq=None</em><big>)</big><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" /><dl class="docutils">
<dt><em>x</em>, <em>y</em></dt>
<dd>Array or sequence containing the data</dd>
</dl>
<p>Keyword arguments:</p>
<blockquote>
<div><dl class="docutils">
<dt><em>NFFT</em>: integer</dt>
<dd>The number of data points used in each block for the FFT.
Must be even; 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.</dd>
<dt><em>Fs</em>: scalar</dt>
<dd>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.</dd>
<dt><em>detrend</em>: callable</dt>
<dd>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 <tt class="xref py py-mod docutils literal"><span class="pre">pylab</span></tt>
module defines <tt class="xref py py-func docutils literal"><span class="pre">detrend_none()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">detrend_mean()</span></tt>, and
<tt class="xref py py-func docutils literal"><span class="pre">detrend_linear()</span></tt>, but you can use
a custom function as well.</dd>
<dt><em>window</em>: callable or ndarray</dt>
<dd>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"><tt class="xref py py-func docutils literal"><span class="pre">window_hanning()</span></tt></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><tt class="xref py py-func docutils literal"><span class="pre">window_none()</span></tt></a>,
<tt class="xref py py-func docutils literal"><span class="pre">numpy.blackman()</span></tt>, <tt class="xref py py-func docutils literal"><span class="pre">numpy.hamming()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">numpy.bartlett()</span></tt>, <tt class="xref py py-func docutils literal"><span class="pre">scipy.signal()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">scipy.signal.get_window()</span></tt>, etc. The default is
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><tt class="xref py py-func docutils literal"><span class="pre">window_hanning()</span></tt></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.</dd>
<dt><em>pad_to</em>: integer</dt>
<dd>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 psd (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></dd>
<dt><em>sides</em>: [ ‘default’ | ‘onesided’ | ‘twosided’ ]</dt>
<dd>Specifies which sides of the PSD 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 PSD,
while ‘twosided’ forces two-sided.</dd>
<dt><em>scale_by_freq</em>: boolean</dt>
<dd>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.</dd>
<dt><em>noverlap</em>: integer</dt>
<dd>The number of points of overlap between blocks. The default value
is 0 (no overlap).</dd>
</dl>
</div></blockquote>
<p>The return value is the tuple (<em>Cxy</em>, <em>f</em>), where <em>f</em> are the
frequencies of the coherence vector. For cohere, scaling the
individual densities by the sampling frequency has no effect,
since the factors cancel out.</p>
<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"><tt class="xref py py-func docutils literal"><span class="pre">psd()</span></tt></a> and <a class="reference internal" href="#matplotlib.mlab.csd" title="matplotlib.mlab.csd"><tt class="xref py py-func docutils literal"><span class="pre">csd()</span></tt></a></dt>
<dd>For information about the methods used to compute
<img src="../_images/mathmpl/math-0005c3a5e5.png" style="position: relative; bottom: -10px"/>, <img src="../_images/mathmpl/math-f6d65b7f49.png" style="position: relative; bottom: -7px"/> and <img src="../_images/mathmpl/math-0938c51d1a.png" style="position: relative; bottom: -10px"/>.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cohere_pairs">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cohere_pairs</tt><big>(</big><em>X</em>, <em>ij</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none at 0x2635de8></em>, <em>window=<function window_hanning at 0x2635b90></em>, <em>noverlap=0</em>, <em>preferSpeedOverMemory=True</em>, <em>progressCallback=<function donothing_callback at 0x263b398></em>, <em>returnPxx=False</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.cohere_pairs" title="Permalink to this definition">¶</a></dt>
<dd><p>Call signature:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">Cxy</span><span class="p">,</span> <span class="n">Phase</span><span class="p">,</span> <span class="n">freqs</span> <span class="o">=</span> <span class="n">cohere_pairs</span><span class="p">(</span> <span class="n">X</span><span class="p">,</span> <span class="n">ij</span><span class="p">,</span> <span class="o">...</span><span class="p">)</span>
</pre></div>
</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-python"><div class="highlight"><pre><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"><tt class="xref py py-func docutils literal"><span class="pre">cohere_pairs()</span></tt></a>
will still give significant performace gains over calling
<a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><tt class="xref py py-func docutils literal"><span class="pre">cohere()</span></tt></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"><tt class="xref py py-func docutils literal"><span class="pre">cohere()</span></tt></a>.</p>
<p>Returns:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="p">(</span><span class="n">Cxy</span><span class="p">,</span> <span class="n">Phase</span><span class="p">,</span> <span class="n">freqs</span><span class="p">)</span>
</pre></div>
</div>
<p>where:</p>
<blockquote>
<div><ul>
<li><p class="first"><em>Cxy</em>: dictionary of (<em>i</em>, <em>j</em>) tuples -> coherence vector for
that pair. I.e., <tt 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></tt>.
Number of dictionary keys is <tt class="docutils literal"><span class="pre">len(ij)</span></tt>.</p>
</li>
<li><p class="first"><em>Phase</em>: dictionary of phases of the cross spectral density at
each frequency for each pair. Keys are (<em>i</em>, <em>j</em>).</p>
</li>
<li><dl class="first docutils">
<dt><em>freqs</em>: vector of frequencies, equal in length to either the</dt>
<dd><p class="first last">coherence or phase vectors for any (<em>i</em>, <em>j</em>) key.</p>
</dd>
</dl>
</li>
</ul>
</div></blockquote>
<p>e.g., to make a coherence Bode plot:</p>
<div class="highlight-python"><div class="highlight"><pre><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"><tt class="xref py py-func docutils literal"><span class="pre">cohere_pairs()</span></tt></a> can be much more
efficient than just calling <a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><tt class="xref py py-func docutils literal"><span class="pre">cohere()</span></tt></a> for each pair, because
it caches most of the intensive computations. If <img src="../_images/mathmpl/math-1922d1ceaa.png" style="position: relative; bottom: -3px"/> is the
number of pairs, this function is <img src="../_images/mathmpl/math-98c8089378.png" style="position: relative; bottom: -8px"/> for most of the
heavy lifting, whereas calling cohere for each pair is
<img src="../_images/mathmpl/math-83ff203e39.png" style="position: relative; bottom: -8px"/>. However, because of the caching, it is also more
memory intensive, making 2 additional complex arrays with
approximately the same number of elements as <em>X</em>.</p>
<p>See <tt class="file docutils literal"><span class="pre">test/cohere_pairs_test.py</span></tt> in the src tree for an
example script that shows that this <a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><tt class="xref py py-func docutils literal"><span class="pre">cohere_pairs()</span></tt></a> and
<a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><tt class="xref py py-func docutils literal"><span class="pre">cohere()</span></tt></a> give the same results for a given pair.</p>
<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"><tt class="xref py py-func docutils literal"><span class="pre">psd()</span></tt></a></dt>
<dd>For information about the methods used to compute
<img src="../_images/mathmpl/math-0005c3a5e5.png" style="position: relative; bottom: -10px"/>, <img src="../_images/mathmpl/math-f6d65b7f49.png" style="position: relative; bottom: -7px"/> and <img src="../_images/mathmpl/math-0938c51d1a.png" style="position: relative; bottom: -10px"/>.</dd>
</dl>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.contiguous_regions">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">contiguous_regions</tt><big>(</big><em>mask</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.contiguous_regions" title="Permalink to this definition">¶</a></dt>
<dd><p>return a list of (ind0, ind1) such that mask[ind0:ind1].all() is
True and we cover all such regions</p>
<p>TODO: this is a pure python implementation which probably has a much faster numpy impl</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cross_from_above">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cross_from_above</tt><big>(</big><em>x</em>, <em>threshold</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.cross_from_above" title="Permalink to this definition">¶</a></dt>
<dd><p>return the indices into <em>x</em> where <em>x</em> crosses some threshold from
below, eg the i’s where:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">x</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="o">></span><span class="n">threshold</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o"><=</span><span class="n">threshold</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="#matplotlib.mlab.cross_from_below" title="matplotlib.mlab.cross_from_below"><tt class="xref py py-func docutils literal"><span class="pre">cross_from_below()</span></tt></a> and <a class="reference internal" href="#matplotlib.mlab.contiguous_regions" title="matplotlib.mlab.contiguous_regions"><tt class="xref py py-func docutils literal"><span class="pre">contiguous_regions()</span></tt></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.cross_from_below">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cross_from_below</tt><big>(</big><em>x</em>, <em>threshold</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.cross_from_below" title="Permalink to this definition">¶</a></dt>
<dd><p>return the indices into <em>x</em> where <em>x</em> crosses some threshold from
below, eg the i’s where:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">x</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="o"><</span><span class="n">threshold</span> <span class="ow">and</span> <span class="n">x</span><span class="p">[</span><span class="n">i</span><span class="p">]</span><span class="o">>=</span><span class="n">threshold</span>
</pre></div>
</div>
<p>Example code:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="kn">import</span> <span class="nn">matplotlib.pyplot</span> <span class="kn">as</span> <span class="nn">plt</span>
<span class="n">t</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">arange</span><span class="p">(</span><span class="mf">0.0</span><span class="p">,</span> <span class="mf">2.0</span><span class="p">,</span> <span class="mf">0.1</span><span class="p">)</span>
<span class="n">s</span> <span class="o">=</span> <span class="n">np</span><span class="o">.</span><span class="n">sin</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">np</span><span class="o">.</span><span class="n">pi</span><span class="o">*</span><span class="n">t</span><span class="p">)</span>
<span class="n">fig</span> <span class="o">=</span> <span class="n">plt</span><span class="o">.</span><span class="n">figure</span><span class="p">()</span>
<span class="n">ax</span> <span class="o">=</span> <span class="n">fig</span><span class="o">.</span><span class="n">add_subplot</span><span class="p">(</span><span class="mi">111</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">plot</span><span class="p">(</span><span class="n">t</span><span class="p">,</span> <span class="n">s</span><span class="p">,</span> <span class="s">'-o'</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">axhline</span><span class="p">(</span><span class="o">-</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">cross_from_below</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">ind</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">ind</span> <span class="o">=</span> <span class="n">cross_from_above</span><span class="p">(</span><span class="n">s</span><span class="p">,</span> <span class="o">-</span><span class="mf">0.5</span><span class="p">)</span>
<span class="n">ax</span><span class="o">.</span><span class="n">vlines</span><span class="p">(</span><span class="n">t</span><span class="p">[</span><span class="n">ind</span><span class="p">],</span> <span class="o">-</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">)</span>
<span class="n">plt</span><span class="o">.</span><span class="n">show</span><span class="p">()</span>
</pre></div>
</div>
<div class="admonition seealso">
<p class="first admonition-title">See also</p>
<p class="last"><a class="reference internal" href="#matplotlib.mlab.cross_from_above" title="matplotlib.mlab.cross_from_above"><tt class="xref py py-func docutils literal"><span class="pre">cross_from_above()</span></tt></a> and <a class="reference internal" href="#matplotlib.mlab.contiguous_regions" title="matplotlib.mlab.contiguous_regions"><tt class="xref py py-func docutils literal"><span class="pre">contiguous_regions()</span></tt></a></p>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.csd">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csd</tt><big>(</big><em>x</em>, <em>y</em>, <em>NFFT=256</em>, <em>Fs=2</em>, <em>detrend=<function detrend_none at 0x2635de8></em>, <em>window=<function window_hanning at 0x2635b90></em>, <em>noverlap=0</em>, <em>pad_to=None</em>, <em>sides='default'</em>, <em>scale_by_freq=None</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.csd" title="Permalink to this definition">¶</a></dt>
<dd><p>The cross power spectral density by Welch’s average periodogram
method. The vectors <em>x</em> and <em>y</em> are divided into <em>NFFT</em> length
blocks. Each block is detrended by the function <em>detrend</em> and
windowed by the function <em>window</em>. <em>noverlap</em> gives the length
of the overlap between blocks. The product of the direct FFTs
of <em>x</em> and <em>y</em> are averaged over each segment to compute <em>Pxy</em>,
with a scaling to correct for power loss due to windowing.</p>
<p>If len(<em>x</em>) < <em>NFFT</em> or len(<em>y</em>) < <em>NFFT</em>, they will be zero
padded to <em>NFFT</em>.</p>
<dl class="docutils">
<dt><em>x</em>, <em>y</em></dt>
<dd>Array or sequence containing the data</dd>
</dl>
<p>Keyword arguments:</p>
<blockquote>
<div><dl class="docutils">
<dt><em>NFFT</em>: integer</dt>
<dd>The number of data points used in each block for the FFT.
Must be even; 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.</dd>
<dt><em>Fs</em>: scalar</dt>
<dd>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.</dd>
<dt><em>detrend</em>: callable</dt>
<dd>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 <tt class="xref py py-mod docutils literal"><span class="pre">pylab</span></tt>
module defines <tt class="xref py py-func docutils literal"><span class="pre">detrend_none()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">detrend_mean()</span></tt>, and
<tt class="xref py py-func docutils literal"><span class="pre">detrend_linear()</span></tt>, but you can use
a custom function as well.</dd>
<dt><em>window</em>: callable or ndarray</dt>
<dd>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"><tt class="xref py py-func docutils literal"><span class="pre">window_hanning()</span></tt></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><tt class="xref py py-func docutils literal"><span class="pre">window_none()</span></tt></a>,
<tt class="xref py py-func docutils literal"><span class="pre">numpy.blackman()</span></tt>, <tt class="xref py py-func docutils literal"><span class="pre">numpy.hamming()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">numpy.bartlett()</span></tt>, <tt class="xref py py-func docutils literal"><span class="pre">scipy.signal()</span></tt>,
<tt class="xref py py-func docutils literal"><span class="pre">scipy.signal.get_window()</span></tt>, etc. The default is
<a class="reference internal" href="#matplotlib.mlab.window_hanning" title="matplotlib.mlab.window_hanning"><tt class="xref py py-func docutils literal"><span class="pre">window_hanning()</span></tt></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.</dd>
<dt><em>pad_to</em>: integer</dt>
<dd>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 psd (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></dd>
<dt><em>sides</em>: [ ‘default’ | ‘onesided’ | ‘twosided’ ]</dt>
<dd>Specifies which sides of the PSD 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 PSD,
while ‘twosided’ forces two-sided.</dd>
<dt><em>scale_by_freq</em>: boolean</dt>
<dd>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.</dd>
<dt><em>noverlap</em>: integer</dt>
<dd>The number of points of overlap between blocks. The default value
is 0 (no overlap).</dd>
</dl>
</div></blockquote>
<p>Returns the tuple (<em>Pxy</em>, <em>freqs</em>).</p>
<dl class="docutils">
<dt>Refs:</dt>
<dd>Bendat & Piersol – Random Data: Analysis and Measurement
Procedures, John Wiley & Sons (1986)</dd>
</dl>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.csv2rec">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csv2rec</tt><big>(</big><em>fname</em>, <em>comments='#'</em>, <em>skiprows=0</em>, <em>checkrows=0</em>, <em>delimiter='</em>, <em>'</em>, <em>converterd=None</em>, <em>names=None</em>, <em>missing=''</em>, <em>missingd=None</em>, <em>use_mrecords=False</em>, <em>dayfirst=False</em>, <em>yearfirst=False</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.csv2rec" title="Permalink to this definition">¶</a></dt>
<dd><p>Load data from comma/space/tab delimited file in <em>fname</em> into a
numpy record array and return the record array.</p>
<p>If <em>names</em> is <em>None</em>, a header row is required to automatically
assign the recarray names. The headers will be lower cased,
spaces will be converted to underscores, and illegal attribute
name characters removed. If <em>names</em> is not <em>None</em>, it is a
sequence of names to use for the column names. In this case, it
is assumed there is no header row.</p>
<ul>
<li><p class="first"><em>fname</em>: can be a filename or a file handle. Support for gzipped
files is automatic, if the filename ends in ‘.gz’</p>
</li>
<li><p class="first"><em>comments</em>: the character used to indicate the start of a comment
in the file, or <em>None</em> to switch off the removal of comments</p>
</li>
<li><p class="first"><em>skiprows</em>: is the number of rows from the top to skip</p>
</li>
<li><p class="first"><em>checkrows</em>: is the number of rows to check to validate the column
data type. When set to zero all rows are validated.</p>
</li>
<li><p class="first"><em>converterd</em>: if not <em>None</em>, is a dictionary mapping column number or
munged column name to a converter function.</p>
</li>
<li><p class="first"><em>names</em>: if not None, is a list of header names. In this case, no
header will be read from the file</p>
</li>
<li><p class="first"><em>missingd</em> is a dictionary mapping munged column names to field values
which signify that the field does not contain actual data and should
be masked, e.g., ‘0000-00-00’ or ‘unused’</p>
</li>
<li><p class="first"><em>missing</em>: a string whose value signals a missing field regardless of
the column it appears in</p>
</li>
<li><p class="first"><em>use_mrecords</em>: if True, return an mrecords.fromrecords record array if any of the data are missing</p>
</li>
<li><p class="first"><em>dayfirst</em>: default is False so that MM-DD-YY has precedence over
DD-MM-YY. See <a class="reference external" href="http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47">http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47</a>
for further information.</p>
</li>
<li><p class="first"><em>yearfirst</em>: default is False so that MM-DD-YY has precedence over
YY-MM-DD. See <a class="reference external" href="http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47">http://labix.org/python-dateutil#head-b95ce2094d189a89f80f5ae52a05b4ab7b41af47</a>
for further information.</p>
<p>If no rows are found, <em>None</em> is returned – see <tt class="file docutils literal"><span class="pre">examples/loadrec.py</span></tt></p>
</li>
</ul>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.csvformat_factory">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csvformat_factory</tt><big>(</big><em>format</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.csvformat_factory" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.demean">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">demean</tt><big>(</big><em>x</em>, <em>axis=0</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.demean" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x minus its mean along the specified axis</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend</tt><big>(</big><em>x</em>, <em>key=None</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_linear">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_linear</tt><big>(</big><em>y</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_linear" title="Permalink to this definition">¶</a></dt>
<dd><p>Return y minus best fit line; ‘linear’ detrending</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_mean">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_mean</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_mean" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x minus the mean(x)</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.detrend_none">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_none</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_none" title="Permalink to this definition">¶</a></dt>
<dd><p>Return x: no detrending</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.dist">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">dist</tt><big>(</big><em>x</em>, <em>y</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.dist" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the distance between two points.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.dist_point_to_segment">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">dist_point_to_segment</tt><big>(</big><em>p</em>, <em>s0</em>, <em>s1</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.dist_point_to_segment" title="Permalink to this definition">¶</a></dt>
<dd><p>Get the distance of a point to a segment.</p>
<blockquote>
<div><em>p</em>, <em>s0</em>, <em>s1</em> are <em>xy</em> sequences</div></blockquote>
<p>This algorithm from
<a class="reference external" href="http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm#Distance%20to%20Ray%20or%20Segment">http://softsurfer.com/Archive/algorithm_0102/algorithm_0102.htm#Distance%20to%20Ray%20or%20Segment</a></p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.distances_along_curve">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">distances_along_curve</tt><big>(</big><em>X</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.distances_along_curve" title="Permalink to this definition">¶</a></dt>
<dd><p>Computes the distance between a set of successive points in <em>N</em> dimensions.</p>
<p>Where <em>X</em> is an <em>M</em> x <em>N</em> array or matrix. The distances between
successive rows is computed. Distance is the standard Euclidean
distance.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.donothing_callback">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">donothing_callback</tt><big>(</big><em>*args</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.donothing_callback" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.entropy">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">entropy</tt><big>(</big><em>y</em>, <em>bins</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.entropy" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the entropy of the data in <em>y</em>.</p>
<img src="../_images/mathmpl/math-5c77f15b40.png" class="center" /><p>where <img src="../_images/mathmpl/math-6700e99fd3.png" style="position: relative; bottom: -7px"/> is the probability of observing <em>y</em> in the
<img src="../_images/mathmpl/math-fce1799ac3.png" style="position: relative; bottom: -3px"/> bin of <em>bins</em>. <em>bins</em> can be a number of bins or a
range of bins; see <tt class="xref py py-func docutils literal"><span class="pre">numpy.histogram()</span></tt>.</p>
<p>Compare <em>S</em> with analytic calculation for a Gaussian:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="n">x</span> <span class="o">=</span> <span class="n">mu</span> <span class="o">+</span> <span class="n">sigma</span> <span class="o">*</span> <span class="n">randn</span><span class="p">(</span><span class="mi">200000</span><span class="p">)</span>
<span class="n">Sanalytic</span> <span class="o">=</span> <span class="mf">0.5</span> <span class="o">*</span> <span class="p">(</span> <span class="mf">1.0</span> <span class="o">+</span> <span class="n">log</span><span class="p">(</span><span class="mi">2</span><span class="o">*</span><span class="n">pi</span><span class="o">*</span><span class="n">sigma</span><span class="o">**</span><span class="mf">2.0</span><span class="p">)</span> <span class="p">)</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.exp_safe">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">exp_safe</tt><big>(</big><em>x</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.exp_safe" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute exponentials which safely underflow to zero.</p>
<p>Slow, but convenient to use. Note that numpy provides proper
floating point exception handling with access to the underlying
hardware.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.fftsurr">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">fftsurr</tt><big>(</big><em>x</em>, <em>detrend=<function detrend_none at 0x2635de8></em>, <em>window=<function window_none at 0x2635c08></em><big>)</big><a class="headerlink" href="#matplotlib.mlab.fftsurr" title="Permalink to this definition">¶</a></dt>
<dd><p>Compute an FFT phase randomized surrogate of <em>x</em>.</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.find">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">find</tt><big>(</big><em>condition</em><big>)</big><a class="headerlink" href="#matplotlib.mlab.find" title="Permalink to this definition">¶</a></dt>
<dd><p>Return the indices where ravel(condition) is true</p>
</dd></dl>
<dl class="function">
<dt id="matplotlib.mlab.frange">
<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">frange</tt><big>(</big><span class="optional">[</span><em>start</em><span class="optional">]</span>, <em>stop</em><span class="optional">[</span>, <em>step</em>, <em>keywords</em><span class="optional">]</span><big>)</big> → array of floats<a class="headerlink" href="#matplotlib.mlab.frange" title="Permalink to this definition">¶</a></dt>
<dd><p>Return a numpy ndarray containing a progression of floats. Similar to
<tt class="xref py py-func docutils literal"><span class="pre">numpy.arange()</span></tt>, but defaults to a closed interval.</p>
<p><tt class="docutils literal"><span class="pre">frange(x0,</span> <span class="pre">x1)</span></tt> returns <tt class="docutils literal"><span class="pre">[x0,</span> <span class="pre">x0+1,</span> <span class="pre">x0+2,</span> <span class="pre">...,</span> <span class="pre">x1]</span></tt>; <em>start</em>
defaults to 0, and the endpoint <em>is included</em>. This behavior is
different from that of <tt class="xref py py-func docutils literal"><span class="pre">range()</span></tt> and
<tt class="xref py py-func docutils literal"><span class="pre">numpy.arange()</span></tt>. This is deliberate, since <a class="reference internal" href="#matplotlib.mlab.frange" title="matplotlib.mlab.frange"><tt class="xref py py-func docutils literal"><span class="pre">frange()</span></tt></a>
will probably be more useful for generating lists of points for
function evaluation, and endpoints are often desired in this
use. The usual behavior of <tt class="xref py py-func docutils literal"><span class="pre">range()</span></tt> can be obtained by
setting the keyword <em>closed</em> = 0, in this case, <a class="reference internal" href="#matplotlib.mlab.frange" title="matplotlib.mlab.frange"><tt class="xref py py-func docutils literal"><span class="pre">frange()</span></tt></a>
basically becomes :func:numpy.arange`.</p>
<p>When <em>step</em> is given, it specifies the increment (or
decrement). All arguments can be floating point numbers.</p>
<p><tt class="docutils literal"><span class="pre">frange(x0,x1,d)</span></tt> returns <tt class="docutils literal"><span class="pre">[x0,x0+d,x0+2d,...,xfin]</span></tt> where
<em>xfin</em> <= <em>x1</em>.</p>
<p><a class="reference internal" href="#matplotlib.mlab.frange" title="matplotlib.mlab.frange"><tt class="xref py py-func docutils literal"><span class="pre">frange()</span></tt></a> can also be called with the keyword <em>npts</em>. This
sets the number of points the list should contain (and overrides
the value <em>step</em> might have been given). <tt class="xref py py-func docutils literal"><span class="pre">numpy.arange()</span></tt>
doesn’t offer this option.</p>
<p>Examples:</p>
<div class="highlight-python"><div class="highlight"><pre><span class="gp">>>> </span><span class="n">frange</span><span class="p">(</span><span class="mi">3</span><span class="p">)</span>
<span class="go">array([ 0., 1., 2., 3.])</span>