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<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"

"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">

<head>

<title>mlab — Matplotlib 1.3.1 documentation</title>

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<div id="unreleased-message"> You are reading an old version of the documentation (v1.3.1). For the latest version see <a href="https://matplotlib.org/stable/api/mlab_api.html">https://matplotlib.org/stable/api/mlab_api.html</a></div>

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<h3><a href="../contents.html">Table Of Contents</a></h3>

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<li><a class="reference internal" href="#module-matplotlib.mlab"><tt class="docutils literal">matplotlib.mlab</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>

<li><a class="reference internal" href="#deprecated-functions">Deprecated functions</a></li>

</ul>

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<h2><a class="reference internal" href="#module-matplotlib.mlab" title="matplotlib.mlab"><tt class="xref py py-mod docutils literal">matplotlib.mlab</tt></a><a class="headerlink" href="#module-matplotlib.mlab" title="Permalink to this headline">¶</a></h2>

Numerical python functions written for compatability with MATLAB

commands with the same names.

<h3>MATLAB compatible functions<a class="headerlink" href="#matlab-compatible-functions" title="Permalink to this headline">¶</a></h3>

<dt><a class="reference internal" href="#matplotlib.mlab.cohere" title="matplotlib.mlab.cohere"><tt class="xref py py-func docutils literal">cohere()</tt></a></dt>

<dd>Coherence (normalized cross spectral density)</dd>

<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">detrend()</tt></a></dt>

<dd>Remove the mean or best fit line from an array</dd>

<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">griddata()</tt></a></dt>

<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">prctile()</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">prepca()</tt></a></dt>

<dd>Principal Component Analysis</dd>

<dd>Power spectral density uing Welch’s average periodogram</dd>

<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">specgram()</tt></a></dt>

<dd>Spectrogram (power spectral density over segments of time)</dd>

</dl>

</div>

<h3>Miscellaneous functions<a class="headerlink" href="#miscellaneous-functions" title="Permalink to this headline">¶</a></h3>

Functions that don’t exist in MATLAB, but are useful anyway:

<dt><a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><tt class="xref py py-meth docutils literal">cohere_pairs()</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>

<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">contiguous_regions()</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">cross_from_below()</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">cross_from_above()</tt></a></dt>

<dd>return the indices where a 1D array crosses a threshold from above</dd>

</dl>

</div>

<h3>record array helper functions<a class="headerlink" href="#record-array-helper-functions" title="Permalink to this headline">¶</a></h3>

A collection of helper methods for numpyrecord arrays

<div>See <a class="reference internal" href="../examples/misc/index.html#misc-examples-index">misc Examples</a></div></blockquote>

<dd>pretty print a record array</dd>

<dd>store record array in CSV file</dd>

<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">rec_append_fields()</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">rec_drop_fields()</tt></a></dt>

<dd>drop fields from record array</dd>

<dd>join two record arrays on sequence of fields</dd>

<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">rec_groupby()</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">rec_summarize()</tt></a></dt>

<dd>helper code to filter rec array fields into new fields</dd>

</dl>

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.

Example usage:

<div class="highlight-python"><div class="highlight"><pre>r = csv2rec('somefile.csv', checkrows=0)

formatd = dict(

weight = FormatFloat(2),

change = FormatPercent(2),

cost = FormatThousands(2),

)

rec2excel(r, 'test.xls', formatd=formatd)

rec2csv(r, 'test.csv', formatd=formatd)

scroll = rec2gtk(r, formatd=formatd)

win = gtk.Window()

win.set_size_request(600,800)

win.add(scroll)

win.show_all()

gtk.main()

</pre></div>

</div>

<h3>Deprecated functions<a class="headerlink" href="#deprecated-functions" title="Permalink to this headline">¶</a></h3>

The following are deprecated; please import directly from numpy (with

care–function signatures may differ):

<dd>load ASCII file - use numpy.loadtxt</dd>

<dd>save ASCII file - use numpy.savetxt</dd>

</dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FIFOBuffer</tt><big>(</big>*args, **kwargs<big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer" title="Permalink to this definition">¶</a></dt>

<dd>A FIFO queue to hold incoming x, y 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.

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.

If you set the dataLim attr to

<tt class="xref py py-class docutils literal">BBox</tt> (eg

<tt class="xref py py-attr docutils literal">matplotlib.Axes.dataLim</tt>), the dataLim will be updated as

new data come in.

TODO: add a grow method that will extend nmax

Note

mlab seems like the wrong place for this class.

</div>

Deprecated since version 1.3: The FIFOBuffer class was deprecated in version 1.3.

</div>

Buffer up to nmax points.

<dd>Add scalar x and y to the queue.

</dd></dl>

<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>Return x and y as arrays; their length will be the len of

data added or nmax.

</dd></dl>

<dd>Get the last x, y or None. None if no data set.

</dd></dl>

<tt class="descname">register</tt><big>(</big>func, N<big>)</big><a class="headerlink" href="#matplotlib.mlab.FIFOBuffer.register" title="Permalink to this definition">¶</a></dt>

<dd>Call func every time N events are passed; func signature

is <tt class="docutils literal">func(fifo)</tt>.

</dd></dl>

<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>Update the datalim in the current data in the fifo.

</dd></dl>

class <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>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatObj" title="matplotlib.mlab.FormatObj"><tt class="xref py py-class docutils literal">matplotlib.mlab.FormatObj</tt></a>

<tt class="descname">fromstr</tt><big>(</big>s<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatBool.fromstr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">toval</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatBool.toval" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatDate</tt><big>(</big>fmt<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatDate" title="Permalink to this definition">¶</a></dt>

<tt class="descname">fromstr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatDate.fromstr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">toval</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatDate.toval" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatDatetime</tt><big>(</big>fmt='%Y-%m-%d %H:%M:%S'<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatDatetime" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatDate" title="matplotlib.mlab.FormatDate"><tt class="xref py py-class docutils literal">matplotlib.mlab.FormatDate</tt></a>

<tt class="descname">fromstr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatDatetime.fromstr" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatFloat</tt><big>(</big>precision=4, scale=1.0<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatFloat" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFormatStr" title="matplotlib.mlab.FormatFormatStr"><tt class="xref py py-class docutils literal">matplotlib.mlab.FormatFormatStr</tt></a>

<tt class="descname">fromstr</tt><big>(</big>s<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatFloat.fromstr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">toval</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatFloat.toval" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatFormatStr</tt><big>(</big>fmt<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatFormatStr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">tostr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatFormatStr.tostr" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <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>

<tt class="descname">fromstr</tt><big>(</big>s<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatInt.fromstr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">tostr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatInt.tostr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">toval</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatInt.toval" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatMillions</tt><big>(</big>precision=4<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatMillions" title="Permalink to this definition">¶</a></dt>

<dd>Bases: <a class="reference internal" href="#matplotlib.mlab.FormatFloat" title="matplotlib.mlab.FormatFloat"><tt class="xref py py-class docutils literal">matplotlib.mlab.FormatFloat</tt></a>

</dd></dl>

class <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>

<tt class="descname">fromstr</tt><big>(</big>s<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatObj.fromstr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">tostr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatObj.tostr" title="Permalink to this definition">¶</a></dt>

<tt class="descname">toval</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatObj.toval" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatPercent</tt><big>(</big>precision=4<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatPercent" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <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>

<tt class="descname">tostr</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatString.tostr" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">FormatThousands</tt><big>(</big>precision=4<big>)</big><a class="headerlink" href="#matplotlib.mlab.FormatThousands" title="Permalink to this definition">¶</a></dt>

</dd></dl>

class <tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">PCA</tt><big>(</big>a<big>)</big><a class="headerlink" href="#matplotlib.mlab.PCA" title="Permalink to this definition">¶</a></dt>

<dd>compute the SVD of a and store data for PCA. Use project to

project the data onto a reduced set of dimensions

Inputs:

<div>a: a numobservations x numdims array</div></blockquote>

Attrs:

<div>a a centered unit sigma version of input a

numrows, numcols: the dimensions of a

mu : a numdims array of means of a

sigma : a numdims array of atandard deviation of a

fracs : the proportion of variance of each of the principal components

Wt : the weight vector for projecting a numdims point or array into PCA space

Y : a projected into PCA space

</div></blockquote>

The factor loadings are in the Wt factor, ie the factor

loadings for the 1st principal component are given by Wt[0]

<tt class="descname">center</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.PCA.center" title="Permalink to this definition">¶</a></dt>

<dd>center the data using the mean and sigma from training set a

</dd></dl>

<tt class="descname">project</tt><big>(</big>x, minfrac=0.0<big>)</big><a class="headerlink" href="#matplotlib.mlab.PCA.project" title="Permalink to this definition">¶</a></dt>

<dd>project x onto the principle axes, dropping any axes where fraction of variance<minfrac

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">amap</tt><big>(</big>function, sequence[, sequence, ...]<big>)</big> → array.<a class="headerlink" href="#matplotlib.mlab.amap" title="Permalink to this definition">¶</a></dt>

<dd>Works like <tt class="xref py py-func docutils literal">map()</tt>, but it returns an array. This is just a

convenient shorthand for <tt class="docutils literal">numpy.array(map(...))</tt>.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">base_repr</tt><big>(</big>number, base=2, padding=0<big>)</big><a class="headerlink" href="#matplotlib.mlab.base_repr" title="Permalink to this definition">¶</a></dt>

<dd>Return the representation of a number in any given base.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">binary_repr</tt><big>(</big>number, max_length=1025<big>)</big><a class="headerlink" href="#matplotlib.mlab.binary_repr" title="Permalink to this definition">¶</a></dt>

<dd>Return the binary representation of the input number as a

string.

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">base_repr()</tt></a> with base 2.

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.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">bivariate_normal</tt><big>(</big>X, Y, sigmax=1.0, sigmay=1.0, mux=0.0, muy=0.0, sigmaxy=0.0<big>)</big><a class="headerlink" href="#matplotlib.mlab.bivariate_normal" title="Permalink to this definition">¶</a></dt>

<dd>Bivariate Gaussian distribution for equal shape X, Y.

See <a class="reference external" href="http://mathworld.wolfram.com/BivariateNormalDistribution.html">bivariate normal</a>

at mathworld.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">center_matrix</tt><big>(</big>M, dim=0<big>)</big><a class="headerlink" href="#matplotlib.mlab.center_matrix" title="Permalink to this definition">¶</a></dt>

<dd>Return the matrix M with each row having zero mean and unit std.

If dim = 1 operate on columns instead of rows. (dim is

opposite to the numpy axis kwarg.)

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cohere</tt><big>(</big>x, y, NFFT=256, Fs=2, detrend=<function detrend_none at 0x2635de8>, window=<function window_hanning at 0x2635b90>, noverlap=0, pad_to=None, sides='default', scale_by_freq=None<big>)</big><a class="headerlink" href="#matplotlib.mlab.cohere" title="Permalink to this definition">¶</a></dt>

<dd>The coherence between x and y. Coherence is the normalized

cross spectral density:

<dd>Array or sequence containing the data</dd>

</dl>

Keyword arguments:

<dt>NFFT: 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 NOT be used to get zero padding, or the scaling of the

result will be incorrect. Use pad_to for this instead.</dd>

<dt>Fs: 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>detrend: 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 detrend parameter is a vector, in

matplotlib is it a function. The <tt class="xref py py-mod docutils literal">pylab</tt>

module defines <tt class="xref py py-func docutils literal">detrend_none()</tt>,

<tt class="xref py py-func docutils literal">detrend_mean()</tt>, and

<tt class="xref py py-func docutils literal">detrend_linear()</tt>, but you can use

a custom function as well.</dd>

<dt>window: callable or ndarray</dt>

<dd>A function or a vector of length NFFT. 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">window_hanning()</tt></a>, <a class="reference internal" href="#matplotlib.mlab.window_none" title="matplotlib.mlab.window_none"><tt class="xref py py-func docutils literal">window_none()</tt></a>,

<tt class="xref py py-func docutils literal">numpy.blackman()</tt>, <tt class="xref py py-func docutils literal">numpy.hamming()</tt>,

<tt class="xref py py-func docutils literal">numpy.bartlett()</tt>, <tt class="xref py py-func docutils literal">scipy.signal()</tt>,

<tt class="xref py py-func docutils literal">scipy.signal.get_window()</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">window_hanning()</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>pad_to: integer</dt>

<dd>The number of points to which the data segment is padded when

performing the FFT. This can be different from NFFT, 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 n parameter

in the call to fft(). The default is None, which sets pad_to

equal to NFFT</dd>

<dt>sides: [ ‘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>scale_by_freq: 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>noverlap: integer</dt>

<dd>The number of points of overlap between blocks. The default value

is 0 (no overlap).</dd>

</dl>

</div></blockquote>

The return value is the tuple (Cxy, f), where f 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.

See also

<dd>For information about the methods used to compute

</dl>

</div>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cohere_pairs</tt><big>(</big>X, ij, NFFT=256, Fs=2, detrend=<function detrend_none at 0x2635de8>, window=<function window_hanning at 0x2635b90>, noverlap=0, preferSpeedOverMemory=True, progressCallback=<function donothing_callback at 0x263b398>, returnPxx=False<big>)</big><a class="headerlink" href="#matplotlib.mlab.cohere_pairs" title="Permalink to this definition">¶</a></dt>

<dd>Call signature:

<div class="highlight-python"><div class="highlight"><pre>Cxy, Phase, freqs = cohere_pairs( X, ij, ...)

</pre></div>

</div>

Compute the coherence and phase for all pairs ij, in X.

X is a numSamples * numCols array

ij 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 X has 64 columns, and you want to compute all

nonredundant pairs, define ij as:

<div class="highlight-python"><div class="highlight"><pre>ij = []

for i in range(64):

for j in range(i+1,64):

ij.append( (i,j) )

</pre></div>

</div>

preferSpeedOverMemory 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 preferSpeedOverMemory is False, <a class="reference internal" href="#matplotlib.mlab.cohere_pairs" title="matplotlib.mlab.cohere_pairs"><tt class="xref py py-func docutils literal">cohere_pairs()</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">cohere()</tt></a> for each pair, and will use subtantially less

memory than if preferSpeedOverMemory is True. In my tests with

a 43000,64 array over all nonredundant pairs,

preferSpeedOverMemory = True delivered a 33% performance boost

on a 1.7GHZ Athlon with 512MB RAM compared with

preferSpeedOverMemory = 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">cohere()</tt></a>.

Returns:

<div class="highlight-python"><div class="highlight"><pre>(Cxy, Phase, freqs)

</pre></div>

</div>

where:

<li>Cxy: dictionary of (i, j) tuples -> coherence vector for

that pair. I.e., <tt class="docutils literal">Cxy[(i,j) = cohere(X[:,i], X[:,j])</tt>.

Number of dictionary keys is <tt class="docutils literal">len(ij)</tt>.

</li>

<li>Phase: dictionary of phases of the cross spectral density at

each frequency for each pair. Keys are (i, j).

</li>

<dt>freqs: vector of frequencies, equal in length to either the</dt>

<dd>coherence or phase vectors for any (i, j) key.

</dd>

</dl>

</li>

</ul>

</div></blockquote>

e.g., to make a coherence Bode plot:

<div class="highlight-python"><div class="highlight"><pre>subplot(211)

plot( freqs, Cxy[(12,19)])

subplot(212)

plot( freqs, Phase[(12,19)])

</pre></div>

</div>

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">cohere_pairs()</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">cohere()</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 X.

See <tt class="file docutils literal">test/cohere_pairs_test.py</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">cohere_pairs()</tt></a> and

See also

<dd>For information about the methods used to compute

</dl>

</div>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">contiguous_regions</tt><big>(</big>mask<big>)</big><a class="headerlink" href="#matplotlib.mlab.contiguous_regions" title="Permalink to this definition">¶</a></dt>

<dd>return a list of (ind0, ind1) such that mask[ind0:ind1].all() is

True and we cover all such regions

TODO: this is a pure python implementation which probably has a much faster numpy impl

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cross_from_above</tt><big>(</big>x, threshold<big>)</big><a class="headerlink" href="#matplotlib.mlab.cross_from_above" title="Permalink to this definition">¶</a></dt>

<dd>return the indices into x where x crosses some threshold from

below, eg the i’s where:

<div class="highlight-python"><div class="highlight"><pre>x[i-1]>threshold and x[i]<=threshold

</pre></div>

</div>

See also

<a class="reference internal" href="#matplotlib.mlab.cross_from_below" title="matplotlib.mlab.cross_from_below"><tt class="xref py py-func docutils literal">cross_from_below()</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">contiguous_regions()</tt></a>

</div>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">cross_from_below</tt><big>(</big>x, threshold<big>)</big><a class="headerlink" href="#matplotlib.mlab.cross_from_below" title="Permalink to this definition">¶</a></dt>

<dd>return the indices into x where x crosses some threshold from

below, eg the i’s where:

<div class="highlight-python"><div class="highlight"><pre>x[i-1]<threshold and x[i]>=threshold

</pre></div>

</div>

Example code:

<div class="highlight-python"><div class="highlight"><pre>import matplotlib.pyplot as plt

t = np.arange(0.0, 2.0, 0.1)

s = np.sin(2*np.pi*t)

fig = plt.figure()

ax = fig.add_subplot(111)

ax.plot(t, s, '-o')

ax.axhline(0.5)

ax.axhline(-0.5)

ind = cross_from_below(s, 0.5)

ax.vlines(t[ind], -1, 1)

ind = cross_from_above(s, -0.5)

plt.show()

</pre></div>

</div>

See also

<a class="reference internal" href="#matplotlib.mlab.cross_from_above" title="matplotlib.mlab.cross_from_above"><tt class="xref py py-func docutils literal">cross_from_above()</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">contiguous_regions()</tt></a>

</div>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csd</tt><big>(</big>x, y, NFFT=256, Fs=2, detrend=<function detrend_none at 0x2635de8>, window=<function window_hanning at 0x2635b90>, noverlap=0, pad_to=None, sides='default', scale_by_freq=None<big>)</big><a class="headerlink" href="#matplotlib.mlab.csd" title="Permalink to this definition">¶</a></dt>

<dd>The cross power spectral density by Welch’s average periodogram

method. The vectors x and y are divided into NFFT length

blocks. Each block is detrended by the function detrend and

windowed by the function window. noverlap gives the length

of the overlap between blocks. The product of the direct FFTs

of x and y are averaged over each segment to compute Pxy,

with a scaling to correct for power loss due to windowing.

If len(x) < NFFT or len(y) < NFFT, they will be zero

padded to NFFT.

<dd>Array or sequence containing the data</dd>

</dl>

Keyword arguments:

<dt>NFFT: 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 NOT be used to get zero padding, or the scaling of the

result will be incorrect. Use pad_to for this instead.</dd>

<dt>Fs: 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>detrend: 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 detrend parameter is a vector, in

matplotlib is it a function. The <tt class="xref py py-mod docutils literal">pylab</tt>

module defines <tt class="xref py py-func docutils literal">detrend_none()</tt>,

<tt class="xref py py-func docutils literal">detrend_mean()</tt>, and

<tt class="xref py py-func docutils literal">detrend_linear()</tt>, but you can use

a custom function as well.</dd>

<dt>window: callable or ndarray</dt>

<dd>A function or a vector of length NFFT. To create window

<tt class="xref py py-func docutils literal">numpy.blackman()</tt>, <tt class="xref py py-func docutils literal">numpy.hamming()</tt>,

<tt class="xref py py-func docutils literal">numpy.bartlett()</tt>, <tt class="xref py py-func docutils literal">scipy.signal()</tt>,

<tt class="xref py py-func docutils literal">scipy.signal.get_window()</tt>, etc. The default is

argument, it must take a data segment as an argument and

return the windowed version of the segment.</dd>

<dt>pad_to: integer</dt>

<dd>The number of points to which the data segment is padded when

performing the FFT. This can be different from NFFT, 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 n parameter

in the call to fft(). The default is None, which sets pad_to

equal to NFFT</dd>

<dt>sides: [ ‘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>scale_by_freq: 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>noverlap: integer</dt>

<dd>The number of points of overlap between blocks. The default value

is 0 (no overlap).</dd>

</dl>

</div></blockquote>

Returns the tuple (Pxy, freqs).

<dd>Bendat & Piersol – Random Data: Analysis and Measurement

Procedures, John Wiley & Sons (1986)</dd>

</dl>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csv2rec</tt><big>(</big>fname, comments='#', skiprows=0, checkrows=0, delimiter=', ', converterd=None, names=None, missing='', missingd=None, use_mrecords=False, dayfirst=False, yearfirst=False<big>)</big><a class="headerlink" href="#matplotlib.mlab.csv2rec" title="Permalink to this definition">¶</a></dt>

<dd>Load data from comma/space/tab delimited file in fname into a

numpy record array and return the record array.

If names is None, 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 names is not None, it is a

sequence of names to use for the column names. In this case, it

is assumed there is no header row.

<ul>

<li>fname: can be a filename or a file handle. Support for gzipped

files is automatic, if the filename ends in ‘.gz’

</li>

<li>comments: the character used to indicate the start of a comment

in the file, or None to switch off the removal of comments

</li>

<li>skiprows: is the number of rows from the top to skip

</li>

<li>checkrows: is the number of rows to check to validate the column

data type. When set to zero all rows are validated.

</li>

<li>converterd: if not None, is a dictionary mapping column number or

munged column name to a converter function.

</li>

<li>names: if not None, is a list of header names. In this case, no

header will be read from the file

</li>

<li>missingd 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’

</li>

<li>missing: a string whose value signals a missing field regardless of

the column it appears in

</li>

<li>use_mrecords: if True, return an mrecords.fromrecords record array if any of the data are missing

</li>

<li>dayfirst: 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.

</li>

<li>yearfirst: 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.

If no rows are found, None is returned – see <tt class="file docutils literal">examples/loadrec.py</tt>

</li>

</ul>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">csvformat_factory</tt><big>(</big>format<big>)</big><a class="headerlink" href="#matplotlib.mlab.csvformat_factory" title="Permalink to this definition">¶</a></dt>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">demean</tt><big>(</big>x, axis=0<big>)</big><a class="headerlink" href="#matplotlib.mlab.demean" title="Permalink to this definition">¶</a></dt>

<dd>Return x minus its mean along the specified axis

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend</tt><big>(</big>x, key=None<big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend" title="Permalink to this definition">¶</a></dt>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_linear</tt><big>(</big>y<big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_linear" title="Permalink to this definition">¶</a></dt>

<dd>Return y minus best fit line; ‘linear’ detrending

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_mean</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_mean" title="Permalink to this definition">¶</a></dt>

<dd>Return x minus the mean(x)

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">detrend_none</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.detrend_none" title="Permalink to this definition">¶</a></dt>

<dd>Return x: no detrending

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">dist</tt><big>(</big>x, y<big>)</big><a class="headerlink" href="#matplotlib.mlab.dist" title="Permalink to this definition">¶</a></dt>

<dd>Return the distance between two points.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">dist_point_to_segment</tt><big>(</big>p, s0, s1<big>)</big><a class="headerlink" href="#matplotlib.mlab.dist_point_to_segment" title="Permalink to this definition">¶</a></dt>

<dd>Get the distance of a point to a segment.

<div>p, s0, s1 are xy sequences</div></blockquote>

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>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">distances_along_curve</tt><big>(</big>X<big>)</big><a class="headerlink" href="#matplotlib.mlab.distances_along_curve" title="Permalink to this definition">¶</a></dt>

<dd>Computes the distance between a set of successive points in N dimensions.

Where X is an M x N array or matrix. The distances between

successive rows is computed. Distance is the standard Euclidean

distance.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">donothing_callback</tt><big>(</big>*args<big>)</big><a class="headerlink" href="#matplotlib.mlab.donothing_callback" title="Permalink to this definition">¶</a></dt>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">entropy</tt><big>(</big>y, bins<big>)</big><a class="headerlink" href="#matplotlib.mlab.entropy" title="Permalink to this definition">¶</a></dt>

<dd>Return the entropy of the data in y.

<img src="../_images/mathmpl/math-5c77f15b40.png" class="center" />where <img src="../_images/mathmpl/math-6700e99fd3.png" style="position: relative; bottom: -7px"/> is the probability of observing y in the

<img src="../_images/mathmpl/math-fce1799ac3.png" style="position: relative; bottom: -3px"/> bin of bins. bins can be a number of bins or a

range of bins; see <tt class="xref py py-func docutils literal">numpy.histogram()</tt>.

Compare S with analytic calculation for a Gaussian:

<div class="highlight-python"><div class="highlight"><pre>x = mu + sigma * randn(200000)

Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) )

</pre></div>

</div>

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">exp_safe</tt><big>(</big>x<big>)</big><a class="headerlink" href="#matplotlib.mlab.exp_safe" title="Permalink to this definition">¶</a></dt>

<dd>Compute exponentials which safely underflow to zero.

Slow, but convenient to use. Note that numpy provides proper

floating point exception handling with access to the underlying

hardware.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">fftsurr</tt><big>(</big>x, detrend=<function detrend_none at 0x2635de8>, window=<function window_none at 0x2635c08><big>)</big><a class="headerlink" href="#matplotlib.mlab.fftsurr" title="Permalink to this definition">¶</a></dt>

<dd>Compute an FFT phase randomized surrogate of x.

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">find</tt><big>(</big>condition<big>)</big><a class="headerlink" href="#matplotlib.mlab.find" title="Permalink to this definition">¶</a></dt>

<dd>Return the indices where ravel(condition) is true

</dd></dl>

<tt class="descclassname">matplotlib.mlab.</tt><tt class="descname">frange</tt><big>(</big>[start], stop[, step, keywords]<big>)</big> → array of floats<a class="headerlink" href="#matplotlib.mlab.frange" title="Permalink to this definition">¶</a></dt>

<dd>Return a numpy ndarray containing a progression of floats. Similar to

<tt class="xref py py-func docutils literal">numpy.arange()</tt>, but defaults to a closed interval.

<tt class="docutils literal">frange(x0, x1)</tt> returns <tt class="docutils literal">[x0, x0+1, x0+2, ..., x1]</tt>; start

defaults to 0, and the endpoint is included. This behavior is

different from that of <tt class="xref py py-func docutils literal">range()</tt> and

<tt class="xref py py-func docutils literal">numpy.arange()</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">frange()</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">range()</tt> can be obtained by

setting the keyword closed = 0, in this case, <a class="reference internal" href="#matplotlib.mlab.frange" title="matplotlib.mlab.frange"><tt class="xref py py-func docutils literal">frange()</tt></a>

basically becomes :func:numpy.arange`.

When step is given, it specifies the increment (or

decrement). All arguments can be floating point numbers.

<tt class="docutils literal">frange(x0,x1,d)</tt> returns <tt class="docutils literal">[x0,x0+d,x0+2d,...,xfin]</tt> where

xfin <= x1.

<a class="reference internal" href="#matplotlib.mlab.frange" title="matplotlib.mlab.frange"><tt class="xref py py-func docutils literal">frange()</tt></a> can also be called with the keyword npts. This

sets the number of points the list should contain (and overrides

the value step might have been given). <tt class="xref py py-func docutils literal">numpy.arange()</tt>

doesn’t offer this option.

Examples:

<div class="highlight-python"><div class="highlight"><pre>>>> frange(3)

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