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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>matplotlib.mlab — Matplotlib 3.4.1 documentation</title>

title="Search within Matplotlib 3.4.1 documentation"

href="../../_static/opensearch.xml"/>

</head><body>

<div id="unreleased-message"> You are reading an old version of the documentation (v3.4.1). For the latest version see <a href="/stable/">https://matplotlib.org/stable/</a> </div>

<!--

</div>

-->

<div style="float: left; position: absolute; width: 496px; bottom: 0; padding-bottom: 24px">Version 3.4.1</div>

<div id="forkongithub"><a href="https://github.com/matplotlib/matplotlib">Fork me on GitHub</a></div>

</div>

<ul>

<li><a href="../../users/installing.html">Installation</a></li>

<li><a href="../../contents.html">Documentation</a></li>

<li><a href="../../gallery/index.html">Examples</a></li>

<li><a href="../../tutorials/index.html">Tutorials</a></li>

<li><a href="../../devel/index.html">Contributing</a></li>

</form>

</li>

</ul>

</nav>

<h3>Navigation</h3>

<ul>

<a href="../../genindex.html" title="General Index"

accesskey="I">index</a></li>

<a href="../../py-modindex.html" title="Python Module Index"

>modules</a> |</li>

<li><a href="../../contents.html">contents</a> »</li>

<li class="nav-item nav-item-1"><a href="../index.html" >Module code</a> »</li>

<li class="nav-item nav-item-2"><a href="../matplotlib.html" accesskey="U">matplotlib</a> »</li>

<li class="nav-item nav-item-this"><a href="">matplotlib.mlab</a></li>

</ul>

</div>

</div>

<h1>Source code for matplotlib.mlab</h1><div class="highlight"><pre>

"""

Numerical python functions written for compatibility with MATLAB

commands with the same names. Most numerical python functions can be found in

the `numpy` and `scipy` libraries. What remains here is code for performing

spectral computations.

Spectral functions

------------------

`cohere`

Coherence (normalized cross spectral density)

`csd`

Cross spectral density using Welch's average periodogram

`detrend`

Remove the mean or best fit line from an array

`psd`

Power spectral density using Welch's average periodogram

`specgram`

Spectrogram (spectrum over segments of time)

`complex_spectrum`

Return the complex-valued frequency spectrum of a signal

`magnitude_spectrum`

Return the magnitude of the frequency spectrum of a signal

`angle_spectrum`

Return the angle (wrapped phase) of the frequency spectrum of a signal

`phase_spectrum`

Return the phase (unwrapped angle) of the frequency spectrum of a signal

`detrend_mean`

Remove the mean from a line.

`detrend_linear`

Remove the best fit line from a line.

`detrend_none`

Return the original line.

`stride_windows`

Get all windows in an array in a memory-efficient manner

"""

import functools

from numbers import Number

import numpy as np

from matplotlib import _api

import matplotlib.cbook as cbook

from matplotlib import docstring

<div class="viewcode-block" id="window_hanning"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.window_hanning">[docs]</a>def window_hanning(x):

"""

Return x times the hanning window of len(x).

See Also

--------

window_none : Another window algorithm.

"""

return np.hanning(len(x))*x</div>

<div class="viewcode-block" id="window_none"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.window_none">[docs]</a>def window_none(x):

"""

No window function; simply return x.

See Also

--------

window_hanning : Another window algorithm.

"""

return x</div>

<div class="viewcode-block" id="detrend"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend">[docs]</a>def detrend(x, key=None, axis=None):

"""

Return x with its trend removed.

Parameters

----------

x : array or sequence

Array or sequence containing the data.

key : {'default', 'constant', 'mean', 'linear', 'none'} or function

The detrending algorithm to use. 'default', 'mean', and 'constant' are

the same as `detrend_mean`. 'linear' is the same as `detrend_linear`.

'none' is the same as `detrend_none`. The default is 'mean'. See the

corresponding functions for more details regarding the algorithms. Can

also be a function that carries out the detrend operation.

axis : int

The axis along which to do the detrending.

See Also

--------

detrend_mean : Implementation of the 'mean' algorithm.

detrend_linear : Implementation of the 'linear' algorithm.

detrend_none : Implementation of the 'none' algorithm.

"""

if key is None or key in ['constant', 'mean', 'default']:

return detrend(x, key=detrend_mean, axis=axis)

elif key == 'linear':

return detrend(x, key=detrend_linear, axis=axis)

elif key == 'none':

return detrend(x, key=detrend_none, axis=axis)

elif callable(key):

x = np.asarray(x)

if axis is not None and axis + 1 > x.ndim:

raise ValueError(f'axis(={axis}) out of bounds')

if (axis is None and x.ndim == 0) or (not axis and x.ndim == 1):

return key(x)

# try to use the 'axis' argument if the function supports it,

# otherwise use apply_along_axis to do it

try:

return key(x, axis=axis)

except TypeError:

return np.apply_along_axis(key, axis=axis, arr=x)

else:

raise ValueError(

f"Unknown value for key: {key!r}, must be one of: 'default', "

f"'constant', 'mean', 'linear', or a function")</div>

<div class="viewcode-block" id="detrend_mean"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_mean">[docs]</a>def detrend_mean(x, axis=None):

"""

Return x minus the mean(x).

Parameters

----------

x : array or sequence

Array or sequence containing the data

Can have any dimensionality

axis : int

The axis along which to take the mean. See numpy.mean for a

description of this argument.

See Also

--------

detrend_linear : Another detrend algorithm.

detrend_none : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

"""

if axis is not None and axis+1 > x.ndim:

raise ValueError('axis(=%s) out of bounds' % axis)

return x - x.mean(axis, keepdims=True)</div>

<div class="viewcode-block" id="detrend_none"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_none">[docs]</a>def detrend_none(x, axis=None):

"""

Return x: no detrending.

Parameters

----------

x : any object

An object containing the data

axis : int

This parameter is ignored.

It is included for compatibility with detrend_mean

See Also

--------

detrend_mean : Another detrend algorithm.

detrend_linear : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

"""

return x</div>

<div class="viewcode-block" id="detrend_linear"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.detrend_linear">[docs]</a>def detrend_linear(y):

"""

Return x minus best fit line; 'linear' detrending.

Parameters

----------

y : 0-D or 1-D array or sequence

Array or sequence containing the data

axis : int

The axis along which to take the mean. See numpy.mean for a

description of this argument.

See Also

--------

detrend_mean : Another detrend algorithm.

detrend_none : Another detrend algorithm.

detrend : A wrapper around all the detrend algorithms.

"""

# This is faster than an algorithm based on linalg.lstsq.

y = np.asarray(y)

if y.ndim > 1:

raise ValueError('y cannot have ndim > 1')

# short-circuit 0-D array.

if not y.ndim:

return np.array(0., dtype=y.dtype)

x = np.arange(y.size, dtype=float)

C = np.cov(x, y, bias=1)

b = C[0, 1]/C[0, 0]

a = y.mean() - b*x.mean()

return y - (b*x + a)</div>

<div class="viewcode-block" id="stride_windows"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.stride_windows">[docs]</a>def stride_windows(x, n, noverlap=None, axis=0):

"""

Get all windows of x with length n as a single array,

using strides to avoid data duplication.

.. warning::

It is not safe to write to the output array. Multiple

elements may point to the same piece of memory,

so modifying one value may change others.

Parameters

----------

x : 1D array or sequence

Array or sequence containing the data.

n : int

The number of data points in each window.

noverlap : int, default: 0 (no overlap)

The overlap between adjacent windows.

axis : int

The axis along which the windows will run.

References

----------

`stackoverflow: Rolling window for 1D arrays in Numpy?

<http://stackoverflow.com/a/6811241>`_

`stackoverflow: Using strides for an efficient moving average filter

<http://stackoverflow.com/a/4947453>`_

"""

if noverlap is None:

noverlap = 0

if noverlap >= n:

raise ValueError('noverlap must be less than n')

if n < 1:

raise ValueError('n cannot be less than 1')

if x.ndim != 1:

raise ValueError('only 1-dimensional arrays can be used')

if n == 1 and noverlap == 0:

if axis == 0:

return x[np.newaxis]

else:

return x[np.newaxis].transpose()

if n > x.size:

raise ValueError('n cannot be greater than the length of x')

# np.lib.stride_tricks.as_strided easily leads to memory corruption for

# non integer shape and strides, i.e. noverlap or n. See #3845.

noverlap = int(noverlap)

n = int(n)

step = n - noverlap

if axis == 0:

shape = (n, (x.shape[-1]-noverlap)//step)

strides = (x.strides[0], step*x.strides[0])

else:

shape = ((x.shape[-1]-noverlap)//step, n)

strides = (step*x.strides[0], x.strides[0])

return np.lib.stride_tricks.as_strided(x, shape=shape, strides=strides)</div>

def _spectral_helper(x, y=None, NFFT=None, Fs=None, detrend_func=None,

window=None, noverlap=None, pad_to=None,

sides=None, scale_by_freq=None, mode=None):

"""

Private helper implementing the common parts between the psd, csd,

spectrogram and complex, magnitude, angle, and phase spectrums.

"""

if y is None:

# if y is None use x for y

same_data = True

else:

# The checks for if y is x are so that we can use the same function to

# implement the core of psd(), csd(), and spectrogram() without doing

# extra calculations. We return the unaveraged Pxy, freqs, and t.

same_data = y is x

if Fs is None:

Fs = 2

if noverlap is None:

noverlap = 0

if detrend_func is None:

detrend_func = detrend_none

if window is None:

window = window_hanning

# if NFFT is set to None use the whole signal

if NFFT is None:

NFFT = 256

if mode is None or mode == 'default':

mode = 'psd'

_api.check_in_list(

['default', 'psd', 'complex', 'magnitude', 'angle', 'phase'],

mode=mode)

if not same_data and mode != 'psd':

raise ValueError("x and y must be equal if mode is not 'psd'")

# Make sure we're dealing with a numpy array. If y and x were the same

# object to start with, keep them that way

if not same_data:

if sides is None or sides == 'default':

if np.iscomplexobj(x):

sides = 'twosided'

else:

sides = 'onesided'

_api.check_in_list(['default', 'onesided', 'twosided'], sides=sides)

# zero pad x and y up to NFFT if they are shorter than NFFT

if len(x) < NFFT:

n = len(x)

x = np.resize(x, NFFT)

x[n:] = 0

if not same_data and len(y) < NFFT:

n = len(y)

y = np.resize(y, NFFT)

y[n:] = 0

if pad_to is None:

pad_to = NFFT

if mode != 'psd':

scale_by_freq = False

elif scale_by_freq is None:

scale_by_freq = True

# For real x, ignore the negative frequencies unless told otherwise

if sides == 'twosided':

numFreqs = pad_to

if pad_to % 2:

freqcenter = (pad_to - 1)//2 + 1

else:

freqcenter = pad_to//2

scaling_factor = 1.

elif sides == 'onesided':

if pad_to % 2:

numFreqs = (pad_to + 1)//2

else:

numFreqs = pad_to//2 + 1

scaling_factor = 2.

if not np.iterable(window):

window = window(np.ones(NFFT, x.dtype))

if len(window) != NFFT:

raise ValueError(

"The window length must match the data's first dimension")

result = stride_windows(x, NFFT, noverlap, axis=0)

result = detrend(result, detrend_func, axis=0)

result = result * window.reshape((-1, 1))

result = np.fft.fft(result, n=pad_to, axis=0)[:numFreqs, :]

freqs = np.fft.fftfreq(pad_to, 1/Fs)[:numFreqs]

if not same_data:

# if same_data is False, mode must be 'psd'

resultY = stride_windows(y, NFFT, noverlap)

resultY = detrend(resultY, detrend_func, axis=0)

resultY = resultY * window.reshape((-1, 1))

resultY = np.fft.fft(resultY, n=pad_to, axis=0)[:numFreqs, :]

result = np.conj(result) * resultY

elif mode == 'psd':

elif mode == 'magnitude':

result = np.abs(result) / np.abs(window).sum()

elif mode == 'angle' or mode == 'phase':

# we unwrap the phase later to handle the onesided vs. twosided case

result = np.angle(result)

elif mode == 'complex':

result /= np.abs(window).sum()

if mode == 'psd':

# Also include scaling factors for one-sided densities and dividing by

# the sampling frequency, if desired. Scale everything, except the DC

# component and the NFFT/2 component:

# if we have a even number of frequencies, don't scale NFFT/2

if not NFFT % 2:

slc = slice(1, -1, None)

# if we have an odd number, just don't scale DC

else:

slc = slice(1, None, None)

result[slc] *= scaling_factor

# MATLAB divides by the sampling frequency so that density function

# has units of dB/Hz and can be integrated by the plotted frequency

# values. Perform the same scaling here.

if scale_by_freq:

result /= Fs

# Scale the spectrum by the norm of the window to compensate for

# windowing loss; see Bendat & Piersol Sec 11.5.2.

result /= (np.abs(window)**2).sum()

else:

# In this case, preserve power in the segment, not amplitude

t = np.arange(NFFT/2, len(x) - NFFT/2 + 1, NFFT - noverlap)/Fs

if sides == 'twosided':

# center the frequency range at zero

freqs = np.roll(freqs, -freqcenter, axis=0)

result = np.roll(result, -freqcenter, axis=0)

elif not pad_to % 2:

# get the last value correctly, it is negative otherwise

freqs[-1] *= -1

# we unwrap the phase here to handle the onesided vs. twosided case

if mode == 'phase':

result = np.unwrap(result, axis=0)

return result, freqs, t

def _single_spectrum_helper(

mode, x, Fs=None, window=None, pad_to=None, sides=None):

"""

Private helper implementing the commonality between the complex, magnitude,

angle, and phase spectrums.

"""

_api.check_in_list(['complex', 'magnitude', 'angle', 'phase'], mode=mode)

if pad_to is None:

pad_to = len(x)

spec, freqs, _ = _spectral_helper(x=x, y=None, NFFT=len(x), Fs=Fs,

detrend_func=detrend_none, window=window,

sides=sides,

scale_by_freq=False,

mode=mode)

if mode != 'complex':

spec = spec.real

if spec.ndim == 2 and spec.shape[1] == 1:

spec = spec[:, 0]

return spec, freqs

# Split out these keyword docs so that they can be used elsewhere

docstring.interpd.update(

Spectral="""\

Fs : float, default: 2

The sampling frequency (samples per time unit). It is used to calculate

the Fourier frequencies, *freqs*, in cycles per time unit.

window : callable or ndarray, default: `.window_hanning`

A function or a vector of length *NFFT*. To create window vectors see

`.window_hanning`, `.window_none`, `numpy.blackman`, `numpy.hamming`,

`numpy.bartlett`, `scipy.signal`, `scipy.signal.get_window`, etc. 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.

sides : {'default', 'onesided', 'twosided'}, optional

Which sides of the spectrum to return. 'default' is one-sided for real

data and two-sided for complex data. 'onesided' forces the return of a

one-sided spectrum, while 'twosided' forces two-sided.""",

Single_Spectrum="""\

pad_to : int, optional

The number of points to which the data segment is padded when performing

the FFT. While not increasing the actual resolution of the spectrum (the

minimum distance between resolvable peaks), this can give more points in

the plot, allowing for more detail. This corresponds to the *n* parameter

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

the length of the input signal (i.e. no padding).""",

PSD="""\

pad_to : int, optional

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

spectrum (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*

NFFT : int, default: 256

The number of data points used in each block for the FFT. A power 2 is

most efficient. This should *NOT* be used to get zero padding, or the

scaling of the result will be incorrect; use *pad_to* for this instead.

detrend : {'none', 'mean', 'linear'} or callable, default: 'none'

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 :mod:`~matplotlib.mlab`

module defines `.detrend_none`, `.detrend_mean`, and `.detrend_linear`,

but you can use a custom function as well. You can also use a string to

choose one of the functions: 'none' calls `.detrend_none`. 'mean' calls

`.detrend_mean`. 'linear' calls `.detrend_linear`.

scale_by_freq : bool, default: True

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.""")

<div class="viewcode-block" id="psd"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.psd">[docs]</a>@docstring.dedent_interpd

def psd(x, NFFT=None, Fs=None, detrend=None, window=None,

noverlap=None, pad_to=None, sides=None, scale_by_freq=None):

r"""

Compute the power spectral density.

The power spectral density :math:`P_{xx}` by Welch's average

periodogram method. The vector *x* is divided into *NFFT* length

segments. Each segment is detrended by function *detrend* and

windowed by function *window*. *noverlap* gives the length of

the overlap between segments. The :math:`|\mathrm{fft}(i)|^2`

of each segment :math:`i` are averaged to compute :math:`P_{xx}`.

If len(*x*) < *NFFT*, it will be zero padded to *NFFT*.

Parameters

----------

x : 1-D array or sequence

Array or sequence containing the data

%(Spectral)s

%(PSD)s

noverlap : int, default: 0 (no overlap)

The number of points of overlap between segments.

Returns

-------

Pxx : 1-D array

The values for the power spectrum :math:`P_{xx}` (real valued)

freqs : 1-D array

The frequencies corresponding to the elements in *Pxx*

References

----------

Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John

Wiley & Sons (1986)

See Also

--------

specgram

`specgram` differs in the default overlap; in not returning the mean of

the segment periodograms; and in returning the times of the segments.

magnitude_spectrum : returns the magnitude spectrum.

csd : returns the spectral density between two signals.

"""

Pxx, freqs = csd(x=x, y=None, NFFT=NFFT, Fs=Fs, detrend=detrend,

window=window, noverlap=noverlap, pad_to=pad_to,

sides=sides, scale_by_freq=scale_by_freq)

return Pxx.real, freqs</div>

<div class="viewcode-block" id="csd"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.csd">[docs]</a>@docstring.dedent_interpd

def csd(x, y, NFFT=None, Fs=None, detrend=None, window=None,

"""

Compute the cross-spectral density.

The cross spectral density :math:`P_{xy}` by Welch's average

periodogram method. The vectors *x* and *y* are divided into

*NFFT* length segments. Each segment is detrended by function

*detrend* and windowed by function *window*. *noverlap* gives

the length of the overlap between segments. The product of

the direct FFTs of *x* and *y* are averaged over each segment

to compute :math:`P_{xy}`, 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*.

Parameters

----------

x, y : 1-D arrays or sequences

Arrays or sequences containing the data

%(Spectral)s

%(PSD)s

noverlap : int, default: 0 (no overlap)

The number of points of overlap between segments.

Returns

-------

Pxy : 1-D array

The values for the cross spectrum :math:`P_{xy}` before scaling (real

valued)

freqs : 1-D array

The frequencies corresponding to the elements in *Pxy*

References

----------

Bendat & Piersol -- Random Data: Analysis and Measurement Procedures, John

Wiley & Sons (1986)

See Also

--------

psd : equivalent to setting ``y = x``.

"""

if NFFT is None:

NFFT = 256

Pxy, freqs, _ = _spectral_helper(x=x, y=y, NFFT=NFFT, Fs=Fs,

detrend_func=detrend, window=window,

noverlap=noverlap, pad_to=pad_to,

mode='psd')

if Pxy.ndim == 2:

if Pxy.shape[1] > 1:

Pxy = Pxy.mean(axis=1)

else:

Pxy = Pxy[:, 0]

return Pxy, freqs</div>

_single_spectrum_docs = """\

Compute the {quantity} of *x*.

Data is padded to a length of *pad_to* and the windowing function *window* is

applied to the signal.

Parameters

----------

x : 1-D array or sequence

Array or sequence containing the data

{Spectral}

{Single_Spectrum}

Returns

-------

spectrum : 1-D array

The {quantity}.

freqs : 1-D array

The frequencies corresponding to the elements in *spectrum*.

See Also

--------

psd

Returns the power spectral density.

complex_spectrum

Returns the complex-valued frequency spectrum.

magnitude_spectrum

Returns the absolute value of the `complex_spectrum`.

angle_spectrum

Returns the angle of the `complex_spectrum`.

phase_spectrum

Returns the phase (unwrapped angle) of the `complex_spectrum`.

specgram

Can return the complex spectrum of segments within the signal.

"""

complex_spectrum = functools.partial(_single_spectrum_helper, "complex")

complex_spectrum.__doc__ = _single_spectrum_docs.format(

quantity="complex-valued frequency spectrum",

**docstring.interpd.params)

magnitude_spectrum = functools.partial(_single_spectrum_helper, "magnitude")

magnitude_spectrum.__doc__ = _single_spectrum_docs.format(

quantity="magnitude (absolute value) of the frequency spectrum",

**docstring.interpd.params)

angle_spectrum = functools.partial(_single_spectrum_helper, "angle")

angle_spectrum.__doc__ = _single_spectrum_docs.format(

quantity="angle of the frequency spectrum (wrapped phase spectrum)",

**docstring.interpd.params)

phase_spectrum = functools.partial(_single_spectrum_helper, "phase")

phase_spectrum.__doc__ = _single_spectrum_docs.format(

quantity="phase of the frequency spectrum (unwrapped phase spectrum)",

**docstring.interpd.params)

<div class="viewcode-block" id="specgram"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.specgram">[docs]</a>@docstring.dedent_interpd

def specgram(x, NFFT=None, Fs=None, detrend=None, window=None,

mode=None):

"""

Compute a spectrogram.

Compute and plot a spectrogram of data in x. Data are split into

NFFT length segments and the spectrum of each section is

computed. The windowing function window is applied to each

segment, and the amount of overlap of each segment is

specified with noverlap.

Parameters

----------

x : array-like

1-D array or sequence.

%(Spectral)s

%(PSD)s

noverlap : int, default: 128

The number of points of overlap between blocks.

mode : str, default: 'psd'

What sort of spectrum to use:

'psd'

Returns the power spectral density.

'complex'

Returns the complex-valued frequency spectrum.

'magnitude'

Returns the magnitude spectrum.

'angle'

Returns the phase spectrum without unwrapping.

'phase'

Returns the phase spectrum with unwrapping.

Returns

-------

spectrum : array-like

2D array, columns are the periodograms of successive segments.

freqs : array-like

1-D array, frequencies corresponding to the rows in *spectrum*.

t : array-like

1-D array, the times corresponding to midpoints of segments

(i.e the columns in *spectrum*).

See Also

--------

psd : differs in the overlap and in the return values.

complex_spectrum : similar, but with complex valued frequencies.

magnitude_spectrum : similar single segment when mode is 'magnitude'.

angle_spectrum : similar to single segment when mode is 'angle'.

phase_spectrum : similar to single segment when mode is 'phase'.

Notes

-----

detrend and scale_by_freq only apply when *mode* is set to 'psd'.

"""

if noverlap is None:

noverlap = 128 # default in _spectral_helper() is noverlap = 0

if NFFT is None:

NFFT = 256 # same default as in _spectral_helper()

if len(x) <= NFFT:

_api.warn_external("Only one segment is calculated since parameter "

f"NFFT (={NFFT}) >= signal length (={len(x)}).")

spec, freqs, t = _spectral_helper(x=x, y=None, NFFT=NFFT, Fs=Fs,

sides=sides,

scale_by_freq=scale_by_freq,

mode=mode)

if mode != 'complex':

spec = spec.real # Needed since helper implements generically

return spec, freqs, t</div>

<div class="viewcode-block" id="cohere"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.cohere">[docs]</a>@docstring.dedent_interpd

def cohere(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,

noverlap=0, pad_to=None, sides='default', scale_by_freq=None):

r"""

The coherence between *x* and *y*. Coherence is the normalized

cross spectral density:

.. math::

C_{xy} = \frac{|P_{xy}|^2}{P_{xx}P_{yy}}

Parameters

----------

x, y

Array or sequence containing the data

%(Spectral)s

%(PSD)s

noverlap : int, default: 0 (no overlap)

The number of points of overlap between segments.

Returns

-------

Cxy : 1-D array

The coherence vector.

freqs : 1-D array

The frequencies for the elements in *Cxy*.

See Also

--------

:func:`psd`, :func:`csd` :

For information about the methods used to compute :math:`P_{xy}`,

:math:`P_{xx}` and :math:`P_{yy}`.

"""

raise ValueError(

"Coherence is calculated by averaging over *NFFT* length "

"segments. Your signal is too short for your choice of *NFFT*.")

Pxx, f = psd(x, NFFT, Fs, detrend, window, noverlap, pad_to, sides,

scale_by_freq)

Pyy, f = psd(y, NFFT, Fs, detrend, window, noverlap, pad_to, sides,

scale_by_freq)

Pxy, f = csd(x, y, NFFT, Fs, detrend, window, noverlap, pad_to, sides,

scale_by_freq)

Cxy = np.abs(Pxy) ** 2 / (Pxx * Pyy)

return Cxy, f</div>

<div class="viewcode-block" id="GaussianKDE"><a class="viewcode-back" href="../../api/mlab_api.html#matplotlib.mlab.GaussianKDE">[docs]</a>class GaussianKDE:

"""

Representation of a kernel-density estimate using Gaussian kernels.

Parameters

----------

dataset : array-like

Datapoints to estimate from. In case of univariate data this is a 1-D

array, otherwise a 2D array with shape (# of dims, # of data).

bw_method : str, scalar or callable, optional

The method used to calculate the estimator bandwidth. This can be

'scott', 'silverman', a scalar constant or a callable. If a

scalar, this will be used directly as `kde.factor`. If a

callable, it should take a `GaussianKDE` instance as only

parameter and return a scalar. If None (default), 'scott' is used.

Attributes

----------

dataset : ndarray

The dataset with which `gaussian_kde` was initialized.

dim : int

Number of dimensions.

num_dp : int

Number of datapoints.

factor : float

The bandwidth factor, obtained from `kde.covariance_factor`, with which

the covariance matrix is multiplied.

covariance : ndarray

The covariance matrix of *dataset*, scaled by the calculated bandwidth

(`kde.factor`).

inv_cov : ndarray

The inverse of *covariance*.

Methods

-------

kde.evaluate(points) : ndarray

Evaluate the estimated pdf on a provided set of points.

kde(points) : ndarray

Same as kde.evaluate(points)

"""

# This implementation with minor modification was too good to pass up.

# from scipy: https://github.com/scipy/scipy/blob/master/scipy/stats/kde.py

def __init__(self, dataset, bw_method=None):

self.dataset = np.atleast_2d(dataset)

if not np.array(self.dataset).size > 1:

raise ValueError("`dataset` input should have multiple elements.")

self.dim, self.num_dp = np.array(self.dataset).shape

if bw_method is None:

pass

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