# Source code for matplotlib.mlab

"""

Numerical python functions written for compatibility with MATLAB
commands with the same names.

MATLAB compatible functions
---------------------------

:func:cohere
Coherence (normalized cross spectral density)

:func:csd
Cross spectral density using Welch's average periodogram

:func:detrend
Remove the mean or best fit line from an array

:func:find
Return the indices where some condition is true;
numpy.nonzero is similar but more general.

:func:griddata
Interpolate irregularly distributed data to a
regular grid.

:func:prctile
Find the percentiles of a sequence

:func:prepca
Principal Component Analysis

:func:psd
Power spectral density using Welch's average periodogram

:func:rk4
A 4th order runge kutta integrator for 1D or ND systems

:func:specgram
Spectrogram (spectrum over segments of time)

Miscellaneous functions
-----------------------

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

:func:cohere_pairs
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.

:func:rk4
A 4th order Runge-Kutta ODE integrator in case you ever find
yourself stranded without scipy (and the far superior
scipy.integrate tools)

:func:contiguous_regions
Return the indices of the regions spanned by some logical mask

:func:cross_from_below
Return the indices where a 1D array crosses a threshold from below

:func:cross_from_above
Return the indices where a 1D array crosses a threshold from above

:func:complex_spectrum
Return the complex-valued frequency spectrum of a signal

:func:magnitude_spectrum
Return the magnitude of the frequency spectrum of a signal

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

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

:func:detrend_mean
Remove the mean from a line.

:func:demean
Remove the mean from a line. This function is the same as
:func:detrend_mean except for the default *axis*.

:func:detrend_linear
Remove the best fit line from a line.

:func:detrend_none
Return the original line.

:func:stride_windows
Get all windows in an array in a memory-efficient manner

:func:stride_repeat
Repeat an array in a memory-efficient manner

:func:apply_window
Apply a window along a given axis

record array helper functions
-----------------------------

A collection of helper methods for numpyrecord arrays

.. _htmlonly:

See :ref:misc-examples-index

:func:rec2txt
Pretty print a record array

:func:rec2csv
Store record array in CSV file

:func:csv2rec
Import record array from CSV file with type inspection

:func:rec_append_fields

:func:rec_drop_fields
Drop fields from record array

:func:rec_join
Join two record arrays on sequence of fields

:func:recs_join
A simple join of multiple recarrays using a single column as a key

:func:rec_groupby
Summarize data by groups (similar to SQL GROUP BY)

:func:rec_summarize
Helper code to filter rec array fields into new fields

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::

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)

"""

import copy
import csv
import operator
import os
import warnings

import numpy as np

import matplotlib.cbook as cbook
from matplotlib import docstring
from matplotlib.path import Path
import math

[docs]@cbook.deprecated("2.2", alternative='numpy.logspace or numpy.geomspace')
def logspace(xmin, xmax, N):
'''
Return N values logarithmically spaced between xmin and xmax.

'''
return np.exp(np.linspace(np.log(xmin), np.log(xmax), N))

[docs]def window_hanning(x):
'''
Return x times the hanning window of len(x).

--------
:func:window_none
:func:window_none is another window algorithm.
'''
return np.hanning(len(x))*x

[docs]def window_none(x):
'''
No window function; simply return x.

--------
:func:window_hanning
:func:window_hanning is another window algorithm.
'''
return x

[docs]def apply_window(x, window, axis=0, return_window=None):
'''
Apply the given window to the given 1D or 2D array along the given axis.

Parameters
----------
x : 1D or 2D array or sequence
Array or sequence containing the data.

window : function or array.
Either a function to generate a window or an array with length
*x*.shape[*axis*]

axis : integer
The axis over which to do the repetition.
Must be 0 or 1.  The default is 0

return_window : bool
If true, also return the 1D values of the window that was applied
'''
x = np.asarray(x)

if x.ndim < 1 or x.ndim > 2:
raise ValueError('only 1D or 2D arrays can be used')
if axis+1 > x.ndim:
raise ValueError('axis(=%s) out of bounds' % axis)

xshape = list(x.shape)
xshapetarg = xshape.pop(axis)

if cbook.iterable(window):
if len(window) != xshapetarg:
raise ValueError('The len(window) must be the same as the shape '
'of x for the chosen axis')
windowVals = window
else:
windowVals = window(np.ones(xshapetarg, dtype=x.dtype))

if x.ndim == 1:
if return_window:
return windowVals * x, windowVals
else:
return windowVals * x

xshapeother = xshape.pop()

otheraxis = (axis+1) % 2

windowValsRep = stride_repeat(windowVals, xshapeother, axis=otheraxis)

if return_window:
return windowValsRep * x, windowVals
else:
return windowValsRep * x

[docs]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
Specifies the detrend algorithm to use. 'default' is 'mean', which is
the same as :func:detrend_mean. 'constant' is the same. 'linear' is
the same as :func:detrend_linear. 'none' is the same as
:func: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 : integer
The axis along which to do the detrending.

--------
:func:detrend_mean
:func:detrend_mean implements the 'mean' algorithm.

:func:detrend_linear
:func:detrend_linear implements the 'linear' algorithm.

:func:detrend_none
:func:detrend_none implements 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 isinstance(key, str):
raise ValueError("Unknown value for key %s, must be one of: "
"'default', 'constant', 'mean', "
"'linear', or a function" % key)

if not callable(key):
raise ValueError("Unknown value for key %s, must be one of: "
"'default', 'constant', 'mean', "
"'linear', or a function" % key)

x = np.asarray(x)

if axis is not None and axis+1 > x.ndim:
raise ValueError('axis(=%s) out of bounds' % axis)

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)

[docs]def demean(x, axis=0):
'''
Return x minus its mean along the specified axis.

Parameters
----------
x : array or sequence
Array or sequence containing the data
Can have any dimensionality

axis : integer
The axis along which to take the mean.  See numpy.mean for a
description of this argument.

--------
:func:delinear

:func:denone
:func:delinear and :func:denone are other detrend algorithms.

:func:detrend_mean
This function is the same as :func:detrend_mean except for the
default *axis*.
'''
return detrend_mean(x, axis=axis)

[docs]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 : integer
The axis along which to take the mean.  See numpy.mean for a
description of this argument.

--------
:func:demean
This function is the same as :func:demean except for the default
*axis*.

:func:detrend_linear

:func:detrend_none
:func:detrend_linear and :func:detrend_none are other detrend
algorithms.

:func:detrend
:func:detrend is a wrapper around all the detrend algorithms.
'''
x = np.asarray(x)

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)

[docs]def detrend_none(x, axis=None):
'''
Return x: no detrending.

Parameters
----------
x : any object
An object containing the data

axis : integer
This parameter is ignored.
It is included for compatibility with detrend_mean

--------
:func:denone
This function is the same as :func:denone except for the default
*axis*, which has no effect.

:func:detrend_mean

:func:detrend_linear
:func:detrend_mean and :func:detrend_linear are other detrend
algorithms.

:func:detrend
:func:detrend is a wrapper around all the detrend algorithms.
'''
return x

[docs]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 : integer
The axis along which to take the mean.  See numpy.mean for a
description of this argument.

--------
:func:delinear
This function is the same as :func:delinear except for the default
*axis*.

:func:detrend_mean

:func:detrend_none
:func:detrend_mean and :func:detrend_none are other detrend
algorithms.

:func:detrend
:func:detrend is 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)

[docs]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 : integer
The number of data points in each window.

noverlap : integer
Default is 0 (no overlap)

axis : integer
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')

x = np.asarray(x)

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)

[docs]def stride_repeat(x, n, axis=0):
'''
Repeat the values in an array in a memory-efficient manner.  Array x is
stacked vertically n times.

.. 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 : integer
The number of time to repeat the array.

axis : integer
The axis along which the data will run.

References
----------
stackoverflow: Repeat NumPy array without replicating data?
<http://stackoverflow.com/a/5568169>_
'''
if axis not in [0, 1]:
raise ValueError('axis must be 0 or 1')
x = np.asarray(x)
if x.ndim != 1:
raise ValueError('only 1-dimensional arrays can be used')

if n == 1:
if axis == 0:
return np.atleast_2d(x)
else:
return np.atleast_2d(x).T
if n < 1:
raise ValueError('n cannot be less than 1')

# np.lib.stride_tricks.as_strided easily leads to memory corruption for
# non integer shape and strides, i.e. n. See #3845.
n = int(n)

if axis == 0:
shape = (n, x.size)
strides = (0, x.strides[0])
else:
shape = (x.size, n)
strides = (x.strides[0], 0)

return np.lib.stride_tricks.as_strided(x, shape=shape, strides=strides)

def _spectral_helper(x, y=None, NFFT=None, Fs=None, detrend_func=None,
sides=None, scale_by_freq=None, mode=None):
'''
This is a helper function that implements the commonality between the
psd, csd, spectrogram and complex, magnitude, angle, and phase spectrums.
It is *NOT* meant to be used outside of mlab and may change at any time.
'''
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'
elif mode not in ['psd', 'complex', 'magnitude', 'angle', 'phase']:
raise ValueError("Unknown value for mode %s, must be one of: "
"'default', 'psd', 'complex', "
"'magnitude', 'angle', 'phase'" % 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
x = np.asarray(x)
if not same_data:
y = np.asarray(y)

if sides is None or sides == 'default':
if np.iscomplexobj(x):
sides = 'twosided'
else:
sides = 'onesided'
elif sides not in ['onesided', 'twosided']:
raise ValueError("Unknown value for sides %s, must be one of: "
"'default', 'onesided', or 'twosided'" % 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 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':
freqcenter = (pad_to - 1)//2 + 1
else:
scaling_factor = 1.
elif sides == 'onesided':
else:
scaling_factor = 2.

result = stride_windows(x, NFFT, noverlap, axis=0)
result = detrend(result, detrend_func, axis=0)
result, windowVals = apply_window(result, window, axis=0,
return_window=True)
result = np.fft.fft(result, n=pad_to, axis=0)[: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 = apply_window(resultY, window, axis=0)
resultY = np.fft.fft(resultY, n=pad_to, axis=0)[:numFreqs, :]
result = np.conj(result) * resultY
elif mode == 'psd':
result = np.conj(result) * result
elif mode == 'magnitude':
result = np.abs(result) / np.abs(windowVals).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(windowVals).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(windowVals)**2).sum()
else:
# In this case, preserve power in the segment, not amplitude
result /= np.abs(windowVals).sum()**2

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

if sides == 'twosided':
# center the frequency range at zero
freqs = np.concatenate((freqs[freqcenter:], freqs[:freqcenter]))
result = np.concatenate((result[freqcenter:, :],
result[:freqcenter, :]), 0)
# 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(x, mode, Fs=None, window=None, pad_to=None,
sides=None):
'''
This is a helper function that implements the commonality between the
complex, magnitude, angle, and phase spectrums.
It is *NOT* meant to be used outside of mlab and may change at any time.
'''
if mode is None or mode == 'psd' or mode == 'default':
raise ValueError('_single_spectrum_helper does not work with %s mode'
% mode)

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=cbook.dedent("""
Fs : scalar
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.

window : callable or ndarray
A function or a vector of length *NFFT*. To create window
vectors see :func:window_hanning, :func:window_none,
:func:numpy.blackman, :func:numpy.hamming,
:func:numpy.bartlett, :func:scipy.signal,
:func:scipy.signal.get_window, etc. The default is
:func:window_hanning.  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'}
Specifies which sides of the spectrum to return.  Default gives the
default behavior, which returns one-sided for real data and both
for complex data.  'onesided' forces the return of a one-sided
spectrum, while 'twosided' forces two-sided.
"""))

docstring.interpd.update(Single_Spectrum=cbook.dedent("""
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
"""))

docstring.interpd.update(PSD=cbook.dedent("""
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
The number of data points used in each block for the FFT.
A power 2 is most efficient.  The default value is 256.
This should *NOT* be used to get zero padding, or the scaling of the

detrend : {'default', 'constant', 'mean', 'linear', 'none'} or callable
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 :func:~matplotlib.mlab.detrend_none,
:func:~matplotlib.mlab.detrend_mean, and
:func:~matplotlib.mlab.detrend_linear, but you can use
a custom function as well.  You can also use a string to choose
one of the functions.  'default', 'constant', and 'mean' call
:func:~matplotlib.mlab.detrend_mean.  'linear' calls
:func:~matplotlib.mlab.detrend_linear.  'none' calls
:func:~matplotlib.mlab.detrend_none.

scale_by_freq : bool, optional
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.
"""))

[docs]@docstring.dedent_interpd
def psd(x, NFFT=None, Fs=None, detrend=None, window=None,
r"""
Compute the power spectral density.

Call signature::

psd(x, NFFT=256, Fs=2, detrend=mlab.detrend_none,
sides='default', scale_by_freq=None)

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 : integer
The number of points of overlap between segments.
The default value is 0 (no overlap).

Returns
-------
Pxx : 1-D array
The values for the power spectrum 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)

--------
:func:specgram
:func:specgram differs in the default overlap; in not returning the
mean of the segment periodograms; and in returning the times of the
segments.

:func:magnitude_spectrum
:func:magnitude_spectrum returns the magnitude spectrum.

:func:csd
:func:csd returns the spectral density between two signals.
"""
Pxx, freqs = csd(x=x, y=None, NFFT=NFFT, Fs=Fs, detrend=detrend,
sides=sides, scale_by_freq=scale_by_freq)
return Pxx.real, freqs

[docs]@docstring.dedent_interpd
def csd(x, y, NFFT=None, Fs=None, detrend=None, window=None,
"""
Compute the cross-spectral density.

Call signature::

csd(x, y, NFFT=256, Fs=2, detrend=mlab.detrend_none,
sides='default', scale_by_freq=None)

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

Parameters
----------
x, y : 1-D arrays or sequences
Arrays or sequences containing the data

%(Spectral)s

%(PSD)s

noverlap : integer
The number of points of overlap between segments.
The default value is 0 (no overlap).

Returns
-------
Pxy : 1-D array
The values for the cross spectrum 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)

--------
:func:psd
:func:psd is the 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,
sides=sides, scale_by_freq=scale_by_freq,
mode='psd')

if Pxy.ndim == 2:
if Pxy.shape[1] > 1:
Pxy = Pxy.mean(axis=1)
else:
Pxy = Pxy[:, 0]
return Pxy, freqs

[docs]@docstring.dedent_interpd
sides=None):
"""
Compute the complex-valued frequency spectrum 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)s

%(Single_Spectrum)s

Returns
-------
spectrum : 1-D array
The values for the complex spectrum (complex valued)

freqs : 1-D array
The frequencies corresponding to the elements in *spectrum*

--------
:func:magnitude_spectrum
:func:magnitude_spectrum returns the absolute value of this function.

:func:angle_spectrum
:func:angle_spectrum returns the angle of this function.

:func:phase_spectrum
:func:phase_spectrum returns the phase (unwrapped angle) of this
function.

:func:specgram
:func:specgram can return the complex spectrum of segments within the
signal.
"""
sides=sides, mode='complex')

[docs]@docstring.dedent_interpd
sides=None):
"""
Compute the magnitude (absolute value) of the frequency spectrum 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)s

%(Single_Spectrum)s

Returns
-------
spectrum : 1-D array
The values for the magnitude spectrum (real valued)

freqs : 1-D array
The frequencies corresponding to the elements in *spectrum*

--------
:func:psd
:func:psd returns the power spectral density.

:func:complex_spectrum
This function returns the absolute value of :func:complex_spectrum.

:func:angle_spectrum
:func:angle_spectrum returns the angles of the corresponding
frequencies.

:func:phase_spectrum
:func:phase_spectrum returns the phase (unwrapped angle) of the
corresponding frequencies.

:func:specgram
:func:specgram can return the magnitude spectrum of segments within
the signal.
"""
sides=sides, mode='magnitude')

[docs]@docstring.dedent_interpd
sides=None):
"""
Compute the angle of the frequency spectrum (wrapped phase spectrum) 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)s

%(Single_Spectrum)s

Returns
-------
spectrum : 1-D array
The values for the angle spectrum in radians (real valued)

freqs : 1-D array
The frequencies corresponding to the elements in *spectrum*

--------
:func:complex_spectrum
This function returns the angle value of :func:complex_spectrum.

:func:magnitude_spectrum
:func:angle_spectrum returns the magnitudes of the corresponding
frequencies.

:func:phase_spectrum
:func:phase_spectrum returns the unwrapped version of this function.

:func:specgram
:func:specgram can return the angle spectrum of segments within the
signal.
"""
sides=sides, mode='angle')

[docs]@docstring.dedent_interpd
sides=None):
"""
Compute the phase of the frequency spectrum (unwrapped angle spectrum) 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)s

%(Single_Spectrum)s

Returns
-------
spectrum : 1-D array
The values for the phase spectrum in radians (real valued)

freqs : 1-D array
The frequencies corresponding to the elements in *spectrum*

--------
:func:complex_spectrum
This function returns the angle value of :func:complex_spectrum.

:func:magnitude_spectrum
:func:magnitude_spectrum returns the magnitudes of the corresponding
frequencies.

:func:angle_spectrum
:func:angle_spectrum returns the wrapped version of this function.

:func:specgram
:func:specgram can return the phase spectrum of segments within the
signal.
"""
sides=sides, mode='phase')

[docs]@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, optional
The number of points of overlap between blocks.  The default
value is 128.
mode : str, optional
What sort of spectrum to use, default is 'psd'.
'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
2-D 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*).

--------
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:
warnings.warn("Only one segment is calculated since parameter NFFT " +
"(=%d) >= signal length (=%d)." % (NFFT, len(x)))

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

_coh_error = """Coherence is calculated by averaging over *NFFT*
length segments.  Your signal is too short for your choice of *NFFT*.
"""

[docs]@docstring.dedent_interpd
def cohere(x, y, NFFT=256, Fs=2, detrend=detrend_none, window=window_hanning,
"""
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 : integer
The number of points of overlap between blocks.  The default value
is 0 (no overlap).

Returns
-------
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.

--------
:func:psd, :func:csd :
For information about the methods used to compute :math:P_{xy},
:math:P_{xx} and :math:P_{yy}.
"""

if len(x) < 2 * NFFT:
raise ValueError(_coh_error)
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

[docs]@cbook.deprecated('2.2')
def donothing_callback(*args):
pass

[docs]@cbook.deprecated('2.2', 'scipy.signal.coherence')
def cohere_pairs(X, ij, NFFT=256, Fs=2, detrend=detrend_none,
window=window_hanning, noverlap=0,
preferSpeedOverMemory=True,
progressCallback=donothing_callback,
returnPxx=False):

"""
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::

ij = []
for i in range(64):
for j in range(i+1,64):
ij.append( (i,j) )

*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, :func:cohere_pairs
will still give significant performance gains over calling
:func:cohere 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
:func:cohere.

Returns
-------
Cxy : dictionary of (*i*, *j*) tuples -> coherence vector for
that pair.  i.e., Cxy[(i,j) = cohere(X[:,i], X[:,j]).
Number of dictionary keys is len(ij).

Phase : dictionary of phases of the cross spectral density at
each frequency for each pair.  Keys are (*i*, *j*).

freqs : vector of frequencies, equal in length to either the
coherence or phase vectors for any (*i*, *j*) key.

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

subplot(211)
plot( freqs, Cxy[(12,19)])
subplot(212)
plot( freqs, Phase[(12,19)])

For a large number of pairs, :func:cohere_pairs can be much more
efficient than just calling :func:cohere for each pair, because
it caches most of the intensive computations.  If :math:N is the
number of pairs, this function is :math:O(N) for most of the
heavy lifting, whereas calling cohere for each pair is
:math:O(N^2).  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 :file:test/cohere_pairs_test.py in the src tree for an
example script that shows that this :func:cohere_pairs and
:func:cohere give the same results for a given pair.

--------
:func:psd
For information about the methods used to compute :math:P_{xy},
:math:P_{xx} and :math:P_{yy}.
"""
numRows, numCols = X.shape

# zero pad if X is too short
if numRows < NFFT:
tmp = X
X = np.zeros((NFFT, numCols), X.dtype)
X[:numRows, :] = tmp
del tmp

numRows, numCols = X.shape
# get all the columns of X that we are interested in by checking
# the ij tuples
allColumns = set()
for i, j in ij:
Ncols = len(allColumns)

# for real X, ignore the negative frequencies
if np.iscomplexobj(X):
numFreqs = NFFT
else:
numFreqs = NFFT//2+1

# cache the FFT of every windowed, detrended NFFT length segment
# of every channel.  If preferSpeedOverMemory, cache the conjugate
# as well
if cbook.iterable(window):
if len(window) != NFFT:
raise ValueError("The length of the window must be equal to NFFT")
windowVals = window
else:
windowVals = window(np.ones(NFFT, X.dtype))
ind = list(range(0, numRows-NFFT+1, NFFT-noverlap))
numSlices = len(ind)
FFTSlices = {}
FFTConjSlices = {}
Pxx = {}
slices = range(numSlices)
normVal = np.linalg.norm(windowVals)**2
for iCol in allColumns:
progressCallback(i/Ncols, 'Cacheing FFTs')
Slices = np.zeros((numSlices, numFreqs), dtype=np.complex_)
for iSlice in slices:
thisSlice = X[ind[iSlice]:ind[iSlice]+NFFT, iCol]
thisSlice = windowVals*detrend(thisSlice)
Slices[iSlice, :] = np.fft.fft(thisSlice)[:numFreqs]

FFTSlices[iCol] = Slices
if preferSpeedOverMemory:
FFTConjSlices[iCol] = np.conj(Slices)
Pxx[iCol] = np.divide(np.mean(abs(Slices)**2, axis=0), normVal)
del Slices, ind, windowVals

# compute the coherences and phases for all pairs using the
# cached FFTs
Cxy = {}
Phase = {}
count = 0
N = len(ij)
for i, j in ij:
count += 1
if count % 10 == 0:
progressCallback(count/N, 'Computing coherences')

if preferSpeedOverMemory:
Pxy = FFTSlices[i] * FFTConjSlices[j]
else:
Pxy = FFTSlices[i] * np.conj(FFTSlices[j])
if numSlices > 1:
Pxy = np.mean(Pxy, axis=0)
#       Pxy = np.divide(Pxy, normVal)
Pxy /= normVal
#       Cxy[(i,j)] = np.divide(np.absolute(Pxy)**2, Pxx[i]*Pxx[j])
Cxy[i, j] = abs(Pxy)**2 / (Pxx[i]*Pxx[j])
Phase[i, j] = np.arctan2(Pxy.imag, Pxy.real)

freqs = Fs/NFFT*np.arange(numFreqs)
if returnPxx:
return Cxy, Phase, freqs, Pxx
else:
return Cxy, Phase, freqs

[docs]@cbook.deprecated('2.2', 'scipy.stats.entropy')
def entropy(y, bins):
r"""
Return the entropy of the data in *y* in units of nat.

.. math::

-\sum p_i \ln(p_i)

where :math:p_i is the probability of observing *y* in the
:math:i^{th} bin of *bins*.  *bins* can be a number of bins or a
range of bins; see :func:numpy.histogram.

Compare *S* with analytic calculation for a Gaussian::

x = mu + sigma * randn(200000)
Sanalytic = 0.5 * ( 1.0 + log(2*pi*sigma**2.0) )
"""
n, bins = np.histogram(y, bins)
n = n.astype(float)

n = np.take(n, np.nonzero(n)[0])         # get the positive

p = np.divide(n, len(y))

delta = bins[1] - bins[0]
S = -1.0 * np.sum(p * np.log(p)) + np.log(delta)
return S

[docs]@cbook.deprecated('2.2', 'scipy.stats.norm.pdf')
def normpdf(x, *args):
"Return the normal pdf evaluated at *x*; args provides *mu*, *sigma*"
mu, sigma = args
return 1./(np.sqrt(2*np.pi)*sigma)*np.exp(-0.5 * (1./sigma*(x - mu))**2)

[docs]@cbook.deprecated('2.2')
def find(condition):
"Return the indices where ravel(condition) is true"
res, = np.nonzero(np.ravel(condition))
return res

[docs]@cbook.deprecated('2.2')
def longest_contiguous_ones(x):
"""
Return the indices of the longest stretch of contiguous ones in *x*,
assuming *x* is a vector of zeros and ones.  If there are two
equally long stretches, pick the first.
"""
x = np.ravel(x)
if len(x) == 0:
return np.array([])

ind = (x == 0).nonzero()[0]
if len(ind) == 0:
return np.arange(len(x))
if len(ind) == len(x):
return np.array([])

y = np.zeros((len(x)+2,), x.dtype)
y[1:-1] = x
dif = np.diff(y)
up = (dif == 1).nonzero()[0]
dn = (dif == -1).nonzero()[0]
i = (dn-up == max(dn - up)).nonzero()[0][0]
ind = np.arange(up[i], dn[i])

return ind

[docs]@cbook.deprecated('2.2')
def longest_ones(x):
'''alias for longest_contiguous_ones'''
return longest_contiguous_ones(x)

[docs]@cbook.deprecated('2.2')
class PCA(object):
def __init__(self, a, standardize=True):
"""
compute the SVD of a and store data for PCA.  Use project to
project the data onto a reduced set of dimensions

Parameters
----------
a : np.ndarray
A numobservations x numdims array
standardize : bool
True if input data are to be standardized. If False, only centering
will be carried out.

Attributes
----------
a
A centered unit sigma version of input a.

numrows, numcols
The dimensions of a.

mu
A numdims array of means of a. This is the vector that points
to the origin of PCA space.

sigma
A numdims array of standard deviation of a.

fracs
The proportion of variance of each of the principal components.

s
The actual eigenvalues of the decomposition.

Wt
The weight vector for projecting a numdims point or array into
PCA space.

Y
A projected into PCA space.

Notes
-----
The factor loadings are in the Wt factor, i.e., the factor loadings
for the first principal component are given by Wt[0]. This row is
also the first eigenvector.

"""
n, m = a.shape
if n < m:
raise RuntimeError('we assume data in a is organized with '
'numrows>numcols')

self.numrows, self.numcols = n, m
self.mu = a.mean(axis=0)
self.sigma = a.std(axis=0)
self.standardize = standardize

a = self.center(a)

self.a = a

U, s, Vh = np.linalg.svd(a, full_matrices=False)

# Note: .H indicates the conjugate transposed / Hermitian.

# The SVD is commonly written as a = U s V.H.
# If U is a unitary matrix, it means that it satisfies U.H = inv(U).

# The rows of Vh are the eigenvectors of a.H a.
# The columns of U are the eigenvectors of a a.H.
# For row i in Vh and column i in U, the corresponding eigenvalue is
# s[i]**2.

self.Wt = Vh

# save the transposed coordinates
Y = np.dot(Vh, a.T).T
self.Y = Y

# save the eigenvalues
self.s = s**2

# and now the contribution of the individual components
vars = self.s / len(s)
self.fracs = vars/vars.sum()

[docs]    def project(self, x, minfrac=0.):
'''
project x onto the principle axes, dropping any axes where fraction
of variance<minfrac
'''
x = np.asarray(x)
if x.shape[-1] != self.numcols:
raise ValueError('Expected an array with dims[-1]==%d' %
self.numcols)
Y = np.dot(self.Wt, self.center(x).T).T
if x.ndim == 2:
else:
return Yreduced

[docs]    def center(self, x):
'''
center and optionally standardize the data using the mean and sigma
from training set a
'''
if self.standardize:
return (x - self.mu)/self.sigma
else:
return (x - self.mu)

@staticmethod
def _get_colinear():
c0 = np.array([
0.19294738,  0.6202667,   0.45962655,  0.07608613,  0.135818,
0.83580842,  0.07218851,  0.48318321,  0.84472463,  0.18348462,
0.81585306,  0.96923926,  0.12835919,  0.35075355,  0.15807861,
0.837437,    0.10824303,  0.1723387,   0.43926494,  0.83705486])

c1 = np.array([
-1.17705601, -0.513883,   -0.26614584,  0.88067144,  1.00474954,
-1.1616545,   0.0266109,   0.38227157,  1.80489433,  0.21472396,
-1.41920399, -2.08158544, -0.10559009,  1.68999268,  0.34847107,
-0.4685737,   1.23980423, -0.14638744, -0.35907697,  0.22442616])

c2 = c0 + 2*c1
c3 = -3*c0 + 4*c1
a = np.array([c3, c0, c1, c2]).T
return a

[docs]@cbook.deprecated('2.2', 'numpy.percentile')
def prctile(x, p=(0.0, 25.0, 50.0, 75.0, 100.0)):
"""
Return the percentiles of *x*.  *p* can either be a sequence of
percentile values or a scalar.  If *p* is a sequence, the ith
element of the return sequence is the *p*(i)-th percentile of *x*.
If *p* is a scalar, the largest value of *x* less than or equal to
the *p* percentage point in the sequence is returned.
"""

# This implementation derived from scipy.stats.scoreatpercentile
def _interpolate(a, b, fraction):
"""Returns the point at the given fraction between a and b, where
'fraction' must be between 0 and 1.
"""
return a + (b - a) * fraction

per = np.array(p)
values = np.sort(x, axis=None)

idxs = per / 100 * (values.shape[0] - 1)
ai = idxs.astype(int)
bi = ai + 1
frac = idxs % 1

# handle cases where attempting to interpolate past last index
cond = bi >= len(values)
if per.ndim:
ai[cond] -= 1
bi[cond] -= 1
frac[cond] += 1
else:
if cond:
ai -= 1
bi -= 1
frac += 1

return _interpolate(values[ai], values[bi], frac)

[docs]@cbook.deprecated('2.2')
def prctile_rank(x, p):
"""
Return the rank for each element in *x*, return the rank
0..len(*p*).  e.g., if *p* = (25, 50, 75), the return value will be a
len(*x*) array with values in [0,1,2,3] where 0 indicates the
value is less than the 25th percentile, 1 indicates the value is
>= the 25th and < 50th percentile, ... and 3 indicates the value
is above the 75th percentile cutoff.

*p* is either an array of percentiles in [0..100] or a scalar which
indicates how many quantiles of data you want ranked.
"""

if not cbook.iterable(p):
p = np.arange(100.0/p, 100.0, 100.0/p)
else:
p = np.asarray(p)

if p.max() <= 1 or p.min() < 0 or p.max() > 100:
raise ValueError('percentiles should be in range 0..100, not 0..1')

ptiles = prctile(x, p)
return np.searchsorted(ptiles, x)

[docs]@cbook.deprecated('2.2')
def center_matrix(M, dim=0):
"""
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.)
"""
M = np.asarray(M, float)
if dim:
M = (M - M.mean(axis=0)) / M.std(axis=0)
else:
M = (M - M.mean(axis=1)[:, np.newaxis])
M = M / M.std(axis=1)[:, np.newaxis]
return M

[docs]@cbook.deprecated('2.2', 'scipy.integrate.ode')
def rk4(derivs, y0, t):
"""
Integrate 1D or ND system of ODEs using 4-th order Runge-Kutta.
This is a toy implementation which may be useful if you find
yourself stranded on a system w/o scipy.  Otherwise use
:func:scipy.integrate.

Parameters
----------
y0
initial state vector

t
sample times

derivs
returns the derivative of the system and has the
signature dy = derivs(yi, ti)

Examples
--------

A 2D system::

def derivs6(x,t):
d1 =  x[0] + 2*x[1]
d2 =  -3*x[0] + 4*x[1]
return (d1, d2)
dt = 0.0005
t = arange(0.0, 2.0, dt)
y0 = (1,2)
yout = rk4(derivs6, y0, t)

A 1D system::

alpha = 2
def derivs(x,t):
return -alpha*x + exp(-t)

y0 = 1
yout = rk4(derivs, y0, t)

If you have access to scipy, you should probably be using the
scipy.integrate tools rather than this function.
"""

try:
Ny = len(y0)
except TypeError:
yout = np.zeros((len(t),), float)
else:
yout = np.zeros((len(t), Ny), float)

yout[0] = y0
i = 0

for i in np.arange(len(t)-1):

thist = t[i]
dt = t[i+1] - thist
dt2 = dt/2.0
y0 = yout[i]

k1 = np.asarray(derivs(y0, thist))
k2 = np.asarray(derivs(y0 + dt2*k1, thist+dt2))
k3 = np.asarray(derivs(y0 + dt2*k2, thist+dt2))
k4 = np.asarray(derivs(y0 + dt*k3, thist+dt))
yout[i+1] = y0 + dt/6.0*(k1 + 2*k2 + 2*k3 + k4)
return yout

[docs]@cbook.deprecated('2.2')
def bivariate_normal(X, Y, sigmax=1.0, sigmay=1.0,
mux=0.0, muy=0.0, sigmaxy=0.0):
"""
Bivariate Gaussian distribution for equal shape *X*, *Y*.

See bivariate normal
<http://mathworld.wolfram.com/BivariateNormalDistribution.html>_
at mathworld.
"""
Xmu = X-mux
Ymu = Y-muy

rho = sigmaxy/(sigmax*sigmay)
z = Xmu**2/sigmax**2 + Ymu**2/sigmay**2 - 2*rho*Xmu*Ymu/(sigmax*sigmay)
denom = 2*np.pi*sigmax*sigmay*np.sqrt(1-rho**2)
return np.exp(-z/(2*(1-rho**2))) / denom

[docs]@cbook.deprecated('2.2')
def get_xyz_where(Z, Cond):
"""
*Z* and *Cond* are *M* x *N* matrices.  *Z* are data and *Cond* is
a boolean matrix where some condition is satisfied.  Return value
is (*x*, *y*, *z*) where *x* and *y* are the indices into *Z* and
*z* are the values of *Z* at those indices.  *x*, *y*, and *z* are
1D arrays.
"""
X, Y = np.indices(Z.shape)
return X[Cond], Y[Cond], Z[Cond]

[docs]@cbook.deprecated('2.2')
def get_sparse_matrix(M, N, frac=0.1):
"""
Return a *M* x *N* sparse matrix with *frac* elements randomly
filled.
"""
data = np.zeros((M, N))*0.
for i in range(int(M*N*frac)):
x = np.random.randint(0, M-1)
y = np.random.randint(0, N-1)
data[x, y] = np.random.rand()
return data

[docs]@cbook.deprecated('2.2', 'numpy.hypot')
def dist(x, y):
"""
Return the distance between two points.
"""
d = x-y
return np.sqrt(np.dot(d, d))

[docs]@cbook.deprecated('2.2')
def dist_point_to_segment(p, s0, s1):
"""
Get the distance of a point to a segment.

*p*, *s0*, *s1* are *xy* sequences

This algorithm from
http://geomalgorithms.com/a02-_lines.html
"""
p = np.asarray(p, float)
s0 = np.asarray(s0, float)
s1 = np.asarray(s1, float)
v = s1 - s0
w = p - s0

c1 = np.dot(w, v)
if c1 <= 0:
return dist(p, s0)

c2 = np.dot(v, v)
if c2 <= c1:
return dist(p, s1)

b = c1 / c2
pb = s0 + b * v
return dist(p, pb)

[docs]@cbook.deprecated('2.2')
def segments_intersect(s1, s2):
"""
Return *True* if *s1* and *s2* intersect.
*s1* and *s2* are defined as::

s1: (x1, y1), (x2, y2)
s2: (x3, y3), (x4, y4)
"""
(x1, y1), (x2, y2) = s1
(x3, y3), (x4, y4) = s2

den = ((y4-y3) * (x2-x1)) - ((x4-x3)*(y2-y1))

n1 = ((x4-x3) * (y1-y3)) - ((y4-y3)*(x1-x3))
n2 = ((x2-x1) * (y1-y3)) - ((y2-y1)*(x1-x3))

if den == 0:
# lines parallel
return False

u1 = n1/den
u2 = n2/den

return 0.0 <= u1 <= 1.0 and 0.0 <= u2 <= 1.0

[docs]@cbook.deprecated('2.2')
def fftsurr(x, detrend=detrend_none, window=window_none):
"""
Compute an FFT phase randomized surrogate of *x*.
"""
if cbook.iterable(window):
x = window*detrend(x)
else:
x = window(detrend(x))
z = np.fft.fft(x)
a = 2.*np.pi*1j
phase = a * np.random.rand(len(x))
z = z*np.exp(phase)
return np.fft.ifft(z).real

[docs]@cbook.deprecated('2.2')
def movavg(x, n):
"""
Compute the len(*n*) moving average of *x*.
"""
w = np.empty((n,), dtype=float)
w[:] = 1.0/n
return np.convolve(x, w, mode='valid')

# the following code was written and submitted by Fernando Perez
# from the ipython numutils package under a BSD license
# begin fperez functions

"""
A set of convenient utilities for numerical work.

Most of this module requires numpy or is meant to be used with it.

Copyright (c) 2001-2004, Fernando Perez. <[email protected]>

This license was generated from the BSD license template as found in:

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

* Redistributions of source code must retain the above copyright notice,
this list of conditions and the following disclaimer.

* Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.

* Neither the name of the IPython project nor the names of its
contributors may be used to endorse or promote products derived from
this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE
FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

"""

# *****************************************************************************
# Globals
# ****************************************************************************
# function definitions
exp_safe_MIN = math.log(2.2250738585072014e-308)
exp_safe_MAX = 1.7976931348623157e+308

[docs]@cbook.deprecated("2.2", 'numpy.exp')
def exp_safe(x):
"""
Compute exponentials which safely underflow to zero.

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

if type(x) is np.ndarray:
return np.exp(np.clip(x, exp_safe_MIN, exp_safe_MAX))
else:
return math.exp(x)

[docs]@cbook.deprecated("2.2", alternative='numpy.array(list(map(...)))')
def amap(fn, *args):
"""
amap(function, sequence[, sequence, ...]) -> array.

Works like :func:map, but it returns an array.  This is just a
convenient shorthand for numpy.array(map(...)).
"""
return np.array(list(map(fn, *args)))

[docs]@cbook.deprecated("2.2")
def rms_flat(a):
"""
Return the root mean square of all the elements of *a*, flattened out.
"""
return np.sqrt(np.mean(np.abs(a) ** 2))

[docs]@cbook.deprecated("2.2", alternative='numpy.linalg.norm(a, ord=1)')
def l1norm(a):
"""
Return the *l1* norm of *a*, flattened out.

Implemented as a separate function (not a call to :func:norm for speed).
"""
return np.sum(np.abs(a))

[docs]@cbook.deprecated("2.2", alternative='numpy.linalg.norm(a, ord=2)')
def l2norm(a):
"""
Return the *l2* norm of *a*, flattened out.

Implemented as a separate function (not a call to :func:norm for speed).
"""
return np.sqrt(np.sum(np.abs(a) ** 2))

[docs]@cbook.deprecated("2.2", alternative='numpy.linalg.norm(a.flat, ord=p)')
def norm_flat(a, p=2):
"""
norm(a,p=2) -> l-p norm of a.flat

Return the l-p norm of *a*, considered as a flat array.  This is NOT a true
matrix norm, since arrays of arbitrary rank are always flattened.

*p* can be a number or the string 'Infinity' to get the L-infinity norm.
"""
# This function was being masked by a more general norm later in
# the file.  We may want to simply delete it.
if p == 'Infinity':
return np.max(np.abs(a))
else:
return np.sum(np.abs(a) ** p) ** (1 / p)

[docs]@cbook.deprecated("2.2", 'numpy.arange')
def frange(xini, xfin=None, delta=None, **kw):
"""
frange([start,] stop[, step, keywords]) -> array of floats

Return a numpy ndarray containing a progression of floats. Similar to
:func:numpy.arange, but defaults to a closed interval.

frange(x0, x1) returns [x0, x0+1, x0+2, ..., x1]; *start*
defaults to 0, and the endpoint *is included*. This behavior is
different from that of :func:range and
:func:numpy.arange. This is deliberate, since :func:frange
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 :func:range can be obtained by
setting the keyword *closed* = 0, in this case, :func:frange
basically becomes :func:numpy.arange.

When *step* is given, it specifies the increment (or
decrement). All arguments can be floating point numbers.

frange(x0,x1,d) returns [x0,x0+d,x0+2d,...,xfin] where
*xfin* <= *x1*.

:func:frange 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). :func:numpy.arange
doesn't offer this option.

Examples::

>>> frange(3)
array([ 0.,  1.,  2.,  3.])
>>> frange(3,closed=0)
array([ 0.,  1.,  2.])
>>> frange(1,6,2)
array([1, 3, 5])   or 1,3,5,7, depending on floating point vagueries
>>> frange(1,6.5,npts=5)
array([ 1.   ,  2.375,  3.75 ,  5.125,  6.5  ])
"""

# defaults
kw.setdefault('closed', 1)
endpoint = kw['closed'] != 0

# funny logic to allow the *first* argument to be optional (like range())
# This was modified with a simpler version from a similar frange() found
# at http://aspn.activestate.com/ASPN/Cookbook/Python/Recipe/66472
if xfin is None:
xfin = xini + 0.0
xini = 0.0

if delta is None:
delta = 1.0

# compute # of points, spacing and return final list
try:
npts = kw['npts']
delta = (xfin-xini) / (npts-endpoint)
except KeyError:
npts = int(np.round((xfin-xini)/delta)) + endpoint
# round finds the nearest, so the endpoint can be up to
# delta/2 larger than xfin.

return np.arange(npts)*delta+xini
# end frange()

[docs]@cbook.deprecated("2.2", 'numpy.identity')
def identity(n, rank=2, dtype='l', typecode=None):
"""
Returns the identity matrix of shape (*n*, *n*, ..., *n*) (rank *r*).

For ranks higher than 2, this object is simply a multi-index Kronecker
delta::

/  1  if i0=i1=...=iR,
id[i0,i1,...,iR] = -|
\\  0  otherwise.

Optionally a *dtype* (or typecode) may be given (it defaults to 'l').

Since rank defaults to 2, this function behaves in the default case (when
only *n* is given) like numpy.identity(n) -- but surprisingly, it is
much faster.
"""
if typecode is not None:
dtype = typecode
iden = np.zeros((n,)*rank, dtype)
for i in range(n):
idx = (i,)*rank
iden[idx] = 1
return iden

[docs]@cbook.deprecated("2.2")
"""
Return the representation of a *number* in any given *base*.
"""
chars = '0123456789ABCDEFGHIJKLMNOPQRSTUVWXYZ'
if number < base:
return (padding - 1) * chars[0] + chars[int(number)]
max_exponent = int(math.log(number)/math.log(base))
max_power = int(base) ** max_exponent
base_repr(number - max_power * lead_digit, base,

[docs]@cbook.deprecated("2.2")
def binary_repr(number, max_length=1025):
"""
Return the binary representation of the input *number* as a
string.

This is more efficient than using :func:base_repr 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.
"""

#   assert number < 2L << max_length
shifts = map(operator.rshift, max_length * [number],
range(max_length - 1, -1, -1))
digits = list(map(operator.mod, shifts, max_length * [2]))
if not digits.count(1):
return 0
digits = digits[digits.index(1):]
return ''.join(map(repr, digits)).replace('L', '')

[docs]@cbook.deprecated("2.2", 'numpy.log2')
def log2(x, ln2=math.log(2.0)):
"""
Return the log(*x*) in base 2.

This is a _slow_ function but which is guaranteed to return the correct
integer value if the input is an integer exact power of 2.
"""
try:
bin_n = binary_repr(x)[1:]
except (AssertionError, TypeError):
return math.log(x)/ln2
else:
if '1' in bin_n:
return math.log(x)/ln2
else:
return len(bin_n)

[docs]@cbook.deprecated("2.2")
def ispower2(n):
"""
Returns the log base 2 of *n* if *n* is a power of 2, zero otherwise.

Note the potential ambiguity if *n* == 1: 2**0 == 1, interpret accordingly.
"""

bin_n = binary_repr(n)[1:]
if '1' in bin_n:
return 0
else:
return len(bin_n)

[docs]@cbook.deprecated("2.2")
def isvector(X):
"""
Like the MATLAB function with the same name, returns *True*
if the supplied numpy array or matrix *X* looks like a vector,
meaning it has a one non-singleton axis (i.e., it can have
multiple axes, but all must have length 1, except for one of
them).

If you just want to see if the array has 1 axis, use X.ndim == 1.
"""
return np.prod(X.shape) == np.max(X.shape)

# end fperez numutils code

[docs]@cbook.deprecated("2.2", 'numpy.isnan')
def safe_isnan(x):
':func:numpy.isnan for arbitrary types'
if isinstance(x, str):
return False
try:
b = np.isnan(x)
except NotImplementedError:
return False
except TypeError:
return False
else:
return b

[docs]@cbook.deprecated("2.2", 'numpy.isinf')
def safe_isinf(x):
':func:numpy.isinf for arbitrary types'
if isinstance(x, str):
return False
try:
b = np.isinf(x)
except NotImplementedError:
return False
except TypeError:
return False
else:
return b

[docs]@cbook.deprecated("2.2")
def rec_append_fields(rec, names, arrs, dtypes=None):
"""
Return a new record array with field names populated with data
from arrays in *arrs*.  If appending a single field, then *names*,
*arrs* and *dtypes* do not have to be lists. They can just be the
values themselves.
"""
if (not isinstance(names, str) and cbook.iterable(names)
and len(names) and isinstance(names[0], str)):
if len(names) != len(arrs):
raise ValueError("number of arrays do not match number of names")
else:  # we have only 1 name and 1 array
names = [names]
arrs = [arrs]
arrs = list(map(np.asarray, arrs))
if dtypes is None:
dtypes = [a.dtype for a in arrs]
elif not cbook.iterable(dtypes):
dtypes = [dtypes]
if len(arrs) != len(dtypes):
if len(dtypes) == 1:
dtypes = dtypes * len(arrs)
else:
raise ValueError("dtypes must be None, a single dtype or a list")
old_dtypes = rec.dtype.descr
newdtype = np.dtype(old_dtypes + list(zip(names, dtypes)))
newrec = np.recarray(rec.shape, dtype=newdtype)
for field in rec.dtype.fields:
newrec[field] = rec[field]
for name, arr in zip(names, arrs):
newrec[name] = arr
return newrec

[docs]@cbook.deprecated("2.2")
def rec_drop_fields(rec, names):
"""
Return a new numpy record array with fields in *names* dropped.
"""

names = set(names)

newdtype = np.dtype([(name, rec.dtype[name]) for name in rec.dtype.names
if name not in names])

newrec = np.recarray(rec.shape, dtype=newdtype)
for field in newdtype.names:
newrec[field] = rec[field]

return newrec

[docs]@cbook.deprecated("2.2")
def rec_keep_fields(rec, names):
"""
Return a new numpy record array with only fields listed in names
"""

if isinstance(names, str):
names = names.split(',')

arrays = []
for name in names:
arrays.append(rec[name])

return np.rec.fromarrays(arrays, names=names)

[docs]@cbook.deprecated("2.2")
def rec_groupby(r, groupby, stats):
"""
*r* is a numpy record array

*groupby* is a sequence of record array attribute names that
together form the grouping key.  e.g., ('date', 'productcode')

*stats* is a sequence of (*attr*, *func*, *outname*) tuples which
will call x = func(attr) and assign *x* to the record array
output with attribute *outname*.  For example::

stats = ( ('sales', len, 'numsales'), ('sales', np.mean, 'avgsale') )

Return record array has *dtype* names for each attribute name in
the *groupby* argument, with the associated group values, and
for each outname name in the *stats* argument, with the associated
stat summary output.
"""
# build a dictionary from groupby keys-> list of indices into r with
# those keys
rowd = {}
for i, row in enumerate(r):
key = tuple([row[attr] for attr in groupby])
rowd.setdefault(key, []).append(i)

rows = []
# sort the output by groupby keys
for key in sorted(rowd):
row = list(key)
# get the indices for this groupby key
ind = rowd[key]
thisr = r[ind]
# call each stat function for this groupby slice
row.extend([func(thisr[attr]) for attr, func, outname in stats])
rows.append(row)

# build the output record array with groupby and outname attributes
attrs, funcs, outnames = list(zip(*stats))
names = list(groupby)
names.extend(outnames)
return np.rec.fromrecords(rows, names=names)

[docs]@cbook.deprecated("2.2")
def rec_summarize(r, summaryfuncs):
"""
*r* is a numpy record array

*summaryfuncs* is a list of (*attr*, *func*, *outname*) tuples
which will apply *func* to the array *r*[attr] and assign the
output to a new attribute name *outname*.  The returned record
array is identical to *r*, with extra arrays for each element in
*summaryfuncs*.

"""

names = list(r.dtype.names)
arrays = [r[name] for name in names]

for attr, func, outname in summaryfuncs:
names.append(outname)
arrays.append(np.asarray(func(r[attr])))

return np.rec.fromarrays(arrays, names=names)

[docs]@cbook.deprecated("2.2")
def rec_join(key, r1, r2, jointype='inner', defaults=None, r1postfix='1',
r2postfix='2'):
"""
Join record arrays *r1* and *r2* on *key*; *key* is a tuple of
field names -- if *key* is a string it is assumed to be a single
attribute name. If *r1* and *r2* have equal values on all the keys
in the *key* tuple, then their fields will be merged into a new
record array containing the intersection of the fields of *r1* and
*r2*.

*r1* (also *r2*) must not have any duplicate keys.

The *jointype* keyword can be 'inner', 'outer', 'leftouter'.  To
do a rightouter join just reverse *r1* and *r2*.

The *defaults* keyword is a dictionary filled with
{column_name:default_value} pairs.

The keywords *r1postfix* and *r2postfix* are postfixed to column names
(other than keys) that are both in *r1* and *r2*.
"""

if isinstance(key, str):
key = (key, )

for name in key:
if name not in r1.dtype.names:
raise ValueError('r1 does not have key field %s' % name)
if name not in r2.dtype.names:
raise ValueError('r2 does not have key field %s' % name)

def makekey(row):
return tuple([row[name] for name in key])

r1d = {makekey(row): i for i, row in enumerate(r1)}
r2d = {makekey(row): i for i, row in enumerate(r2)}

r1keys = set(r1d)
r2keys = set(r2d)

common_keys = r1keys & r2keys

r1ind = np.array([r1d[k] for k in common_keys])
r2ind = np.array([r2d[k] for k in common_keys])

common_len = len(common_keys)
left_len = right_len = 0
if jointype == "outer" or jointype == "leftouter":
left_keys = r1keys.difference(r2keys)
left_ind = np.array([r1d[k] for k in left_keys])
left_len = len(left_ind)
if jointype == "outer":
right_keys = r2keys.difference(r1keys)
right_ind = np.array([r2d[k] for k in right_keys])
right_len = len(right_ind)

def key_desc(name):
'''
if name is a string key, use the larger size of r1 or r2 before
merging
'''
dt1 = r1.dtype[name]
if dt1.type != np.string_:
return (name, dt1.descr[0][1])

dt2 = r2.dtype[name]
if dt1 != dt2:
raise ValueError("The '{}' fields in arrays 'r1' and 'r2' must "
"have the same dtype".format(name))
if dt1.num > dt2.num:
return (name, dt1.descr[0][1])
else:
return (name, dt2.descr[0][1])

keydesc = [key_desc(name) for name in key]

def mapped_r1field(name):
"""
The column name in *newrec* that corresponds to the column in *r1*.
"""
if name in key or name not in r2.dtype.names:
return name
else:
return name + r1postfix

def mapped_r2field(name):
"""
The column name in *newrec* that corresponds to the column in *r2*.
"""
if name in key or name not in r1.dtype.names:
return name
else:
return name + r2postfix

r1desc = [(mapped_r1field(desc[0]), desc[1]) for desc in r1.dtype.descr
if desc[0] not in key]
r2desc = [(mapped_r2field(desc[0]), desc[1]) for desc in r2.dtype.descr
if desc[0] not in key]
all_dtypes = keydesc + r1desc + r2desc
newdtype = np.dtype(all_dtypes)
newrec = np.recarray((common_len + left_len + right_len,), dtype=newdtype)

if defaults is not None:
for thiskey in defaults:
if thiskey not in newdtype.names:
warnings.warn('rec_join defaults key="%s" not in new dtype '
'names "%s"' % (thiskey, newdtype.names))

for name in newdtype.names:
dt = newdtype[name]
if dt.kind in ('f', 'i'):
newrec[name] = 0

if jointype != 'inner' and defaults is not None:
# fill in the defaults enmasse
newrec_fields = list(newrec.dtype.fields)
for k, v in defaults.items():
if k in newrec_fields:
newrec[k] = v

for field in r1.dtype.names:
newfield = mapped_r1field(field)
if common_len:
newrec[newfield][:common_len] = r1[field][r1ind]
if (jointype == "outer" or jointype == "leftouter") and left_len:
newrec[newfield][common_len:(common_len+left_len)] = (
r1[field][left_ind]
)

for field in r2.dtype.names:
newfield = mapped_r2field(field)
if field not in key and common_len:
newrec[newfield][:common_len] = r2[field][r2ind]
if jointype == "outer" and right_len:
newrec[newfield][-right_len:] = r2[field][right_ind]

newrec.sort(order=key)

return newrec

[docs]@cbook.deprecated("2.2")
def recs_join(key, name, recs, jointype='outer', missing=0., postfixes=None):
"""
Join a sequence of record arrays on single column key.

This function only joins a single column of the multiple record arrays

*key*
is the column name that acts as a key

*name*
is the name of the column that we want to join

*recs*
is a list of record arrays to join

*jointype*
is a string 'inner' or 'outer'

*missing*
is what any missing field is replaced by

*postfixes*
if not None, a len recs sequence of postfixes

returns a record array with columns [rowkey, name0, name1, ... namen-1].
or if postfixes [PF0, PF1, ..., PFN-1] are supplied,
[rowkey, namePF0, namePF1, ... namePFN-1].

Example::

r = recs_join("date", "close", recs=[r0, r1], missing=0.)

"""
results = []
aligned_iters = cbook.align_iterators(operator.attrgetter(key),
*[iter(r) for r in recs])

def extract(r):
if r is None:
return missing
else:
return r[name]

if jointype == "outer":
for rowkey, row in aligned_iters:
results.append([rowkey] + list(map(extract, row)))
elif jointype == "inner":
for rowkey, row in aligned_iters:
if None not in row:  # throw out any Nones
results.append([rowkey] + list(map(extract, row)))

if postfixes is None:
postfixes = ['%d' % i for i in range(len(recs))]
names = ",".join([key] + ["%s%s" % (name, postfix)
for postfix in postfixes])
return np.rec.fromrecords(results, names=names)

[docs]@cbook.deprecated("2.2")
def csv2rec(fname, comments='#', skiprows=0, checkrows=0, delimiter=',',
converterd=None, names=None, missing='', missingd=None,
use_mrecords=False, dayfirst=False, yearfirst=False):
"""
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.

- *fname*: can be a filename or a file handle.  Support for gzipped
files is automatic, if the filename ends in '.gz'

- *comments*: the character used to indicate the start of a comment
in the file, or *None* to switch off the removal of comments

- *skiprows*: is the number of rows from the top to skip

- *checkrows*: is the number of rows to check to validate the column
data type.  When set to zero all rows are validated.

- *converterd*: if not *None*, is a dictionary mapping column number or
munged column name to a converter function.

- *names*: if not None, is a list of header names.  In this case, no

- *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'

- *missing*: a string whose value signals a missing field regardless of
the column it appears in

- *use_mrecords*: if True, return an mrecords.fromrecords record array if
any of the data are missing

- *dayfirst*: default is False so that MM-DD-YY has precedence over
DD-MM-YY.  See
for further information.

- *yearfirst*: default is False so that MM-DD-YY has precedence over
YY-MM-DD. See
for further information.

If no rows are found, *None* is returned
"""

if converterd is None:
converterd = dict()

if missingd is None:
missingd = {}

import dateutil.parser
import datetime

fh = cbook.to_filehandle(fname)

delimiter = str(delimiter)

class FH:
"""
For space-delimited files, we want different behavior than
comma or tab.  Generally, we want multiple spaces to be
treated as a single separator, whereas with comma and tab we
want multiple commas to return multiple (empty) fields.  The
join/strip trick below effects this.
"""
def __init__(self, fh):
self.fh = fh

def close(self):
self.fh.close()

def seek(self, arg):
self.fh.seek(arg)

def fix(self, s):
return ' '.join(s.split())

def __next__(self):
return self.fix(next(self.fh))

def __iter__(self):
for line in self.fh:
yield self.fix(line)

if delimiter == ' ':
fh = FH(fh)

if skiprows:
if i >= (skiprows-1):
break

def ismissing(name, val):
"Should the value val in column name be masked?"
return val == missing or val == missingd.get(name) or val == ''

def with_default_value(func, default):
def newfunc(name, val):
if ismissing(name, val):
return default
else:
return func(val)
return newfunc

def mybool(x):
if x == 'True':
return True
elif x == 'False':
return False
else:
raise ValueError('invalid bool')

dateparser = dateutil.parser.parse

def mydateparser(x):
# try and return a datetime object
d = dateparser(x, dayfirst=dayfirst, yearfirst=yearfirst)
return d

mydateparser = with_default_value(mydateparser, datetime.datetime(1, 1, 1))

myfloat = with_default_value(float, np.nan)
myint = with_default_value(int, -1)
mystr = with_default_value(str, '')
mybool = with_default_value(mybool, None)

def mydate(x):
# try and return a date object
d = dateparser(x, dayfirst=dayfirst, yearfirst=yearfirst)

if d.hour > 0 or d.minute > 0 or d.second > 0:
raise ValueError('not a date')
return d.date()
mydate = with_default_value(mydate, datetime.date(1, 1, 1))

def get_func(name, item, func):
# promote functions in this order
funcs = [mybool, myint, myfloat, mydate, mydateparser, mystr]
for func in funcs[funcs.index(func):]:
try:
func(name, item)
except Exception:
continue
return func
raise ValueError('Could not find a working conversion function')

# map column names that clash with builtins -- TODO - extend this list
itemd = {
'return': 'return_',
'file':   'file_',
'print':  'print_',
}

converters = None
i = 0
if (len(row) and comments is not None and
continue
if i == 0:
converters = [mybool]*len(row)
if checkrows and i > checkrows:
break
i += 1

for j, (name, item) in enumerate(zip(names, row)):
func = converterd.get(j)
if func is None:
func = converterd.get(name)
if func is None:
func = converters[j]
if len(item.strip()):
func = get_func(name, item, func)
else:
# how should we handle custom converters and defaults?
func = with_default_value(func, None)
converters[j] = func
return converters

# Get header and remove invalid characters

if (len(row) and comments is not None and
continue
break

# remove these chars
delete = set(r"""~!@#\$%^&*()-=+~\|}[]{';: /?.>,<""")

names = []
seen = dict()
item = item.strip().lower().replace(' ', '_')
item = ''.join([c for c in item if c not in delete])
if not len(item):
item = 'column%d' % i

item = itemd.get(item, item)
cnt = seen.get(item, 0)
if cnt > 0:
names.append(item + '_%d' % cnt)
else:
names.append(item)
seen[item] = cnt+1

else:
if isinstance(names, str):
names = [n.strip() for n in names.split(',')]

# get the converter functions by inspecting checkrows
if converters is None:
raise ValueError('Could not find any valid data in CSV file')

# reset the reader and start over
fh.seek(0)

while True:
# skip past any comments and consume one line of column header
if (len(row) and comments is not None and
continue
break

# iterate over the remaining rows and convert the data to date
# objects, ints, or floats as appropriate
rows = []
if not len(row):
continue
continue
# Ensure that the row returned always has the same nr of elements
row.extend([''] * (len(converters) - len(row)))
rows.append([func(name, val)
for func, name, val in zip(converters, names, row)])
for name, val in zip(names, row)])
fh.close()

if not len(rows):
return None

else:
r = np.rec.fromrecords(rows, names=names)
return r

# a series of classes for describing the format intentions of various rec views
[docs]@cbook.deprecated("2.2")
class FormatObj(object):
[docs]    def tostr(self, x):
return self.toval(x)

[docs]    def toval(self, x):
return str(x)

[docs]    def fromstr(self, s):
return s

def __hash__(self):
"""
override the hash function of any of the formatters, so that we don't
create duplicate excel format styles
"""
return hash(self.__class__)

[docs]@cbook.deprecated("2.2")
class FormatString(FormatObj):
[docs]    def tostr(self, x):
val = repr(x)
return val[1:-1]

[docs]@cbook.deprecated("2.2")
class FormatFormatStr(FormatObj):
def __init__(self, fmt):
self.fmt = fmt

[docs]    def tostr(self, x):
if x is None:
return 'None'
return self.fmt % self.toval(x)

[docs]@cbook.deprecated("2.2")
class FormatFloat(FormatFormatStr):
def __init__(self, precision=4, scale=1.):
FormatFormatStr.__init__(self, '%%1.%df' % precision)
self.precision = precision
self.scale = scale

def __hash__(self):
return hash((self.__class__, self.precision, self.scale))

[docs]    def toval(self, x):
if x is not None:
x = x * self.scale
return x

[docs]    def fromstr(self, s):
return float(s)/self.scale

[docs]@cbook.deprecated("2.2")
class FormatInt(FormatObj):

[docs]    def tostr(self, x):
return '%d' % int(x)

[docs]    def toval(self, x):
return int(x)

[docs]    def fromstr(self, s):
return int(s)

[docs]@cbook.deprecated("2.2")
class FormatBool(FormatObj):
[docs]    def toval(self, x):
return str(x)

[docs]    def fromstr(self, s):
return bool(s)

[docs]@cbook.deprecated("2.2")
class FormatPercent(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=100.)

[docs]@cbook.deprecated("2.2")
class FormatThousands(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=1e-3)

[docs]@cbook.deprecated("2.2")
class FormatMillions(FormatFloat):
def __init__(self, precision=4):
FormatFloat.__init__(self, precision, scale=1e-6)

[docs]@cbook.deprecated("2.2", alternative='date.strftime')
class FormatDate(FormatObj):
def __init__(self, fmt):
self.fmt = fmt

def __hash__(self):
return hash((self.__class__, self.fmt))

[docs]    def toval(self, x):
if x is None:
return 'None'
return x.strftime(self.fmt)

[docs]    def fromstr(self, x):
import dateutil.parser
return dateutil.parser.parse(x).date()

[docs]@cbook.deprecated("2.2", alternative='datetime.strftime')
class FormatDatetime(FormatDate):
def __init__(self, fmt='%Y-%m-%d %H:%M:%S'):
FormatDate.__init__(self, fmt)

[docs]    def fromstr(self, x):
import dateutil.parser
return dateutil.parser.parse(x)

[docs]@cbook.deprecated("2.2")
def get_formatd(r, formatd=None):
'build a formatd guaranteed to have a key for every dtype name'
defaultformatd = {
np.bool_: FormatBool(),
np.int16: FormatInt(),
np.int32: FormatInt(),
np.int64: FormatInt(),
np.float32: FormatFloat(),
np.float64: FormatFloat(),
np.object_: FormatObj(),
np.string_: FormatString()}

if formatd is None:
formatd = dict()

for i, name in enumerate(r.dtype.names):
dt = r.dtype[name]
format = formatd.get(name)
if format is None:
format = defaultformatd.get(dt.type, FormatObj())
formatd[name] = format
return formatd

[docs]@cbook.deprecated("2.2")
def csvformat_factory(format):
format = copy.deepcopy(format)
if isinstance(format, FormatFloat):
format.scale = 1.  # override scaling for storage
format.fmt = '%r'
return format

[docs]@cbook.deprecated("2.2", alternative='numpy.recarray.tofile')
"""
Returns a textual representation of a record array.

Parameters
----------
r: numpy recarray

space between each column

precision: number of decimal places to use for floats.
Set to an integer to apply to all floats.  Set to a
list of integers to apply precision individually.
Precision for non-floats is simply ignored.

fields : list
If not None, a list of field names to print.  fields
can be a list of strings like ['field1', 'field2'] or a single
comma separated string like 'field1,field2'

Examples
--------

For precision=[0,2,3], the output is ::

ID    Price   Return
ABC   12.54    0.234
XYZ    6.32   -0.076
"""

if fields is not None:
r = rec_keep_fields(r, fields)

if cbook.is_numlike(precision):
precision = [precision]*len(r.dtype)

def get_type(item, atype=int):
tdict = {None: int, int: float, float: str}
try:
atype(str(item))
except:
return get_type(item, tdict[atype])
return atype

def get_justify(colname, column, precision):
ntype = column.dtype

if np.issubdtype(ntype, np.character):
fixed_width = int(ntype.str[2:])
length = max(len(colname), fixed_width)
return 0, length+padding, "%s"  # left justify

if np.issubdtype(ntype, np.integer):
length = max(len(colname),
np.max(list(map(len, list(map(str, column))))))
return 1, length+padding, "%d"  # right justify

if np.issubdtype(ntype, np.floating):
fmt = "%." + str(precision) + "f"
length = max(
len(colname),
np.max(list(map(len, list(map(lambda x: fmt % x, column)))))
)
return 1, length+padding, fmt   # right justify

return (0,
max(len(colname),
"%s")

precision[i])
for i, colname in enumerate(r.dtype.names)]

if i == 0:
else:
if pjust == 0 and just == 1:
elif pjust == 1 and just == 0:
else:

if just == 0:
else:
if get_type(item) == float:
item = (prec % float(item))
elif get_type(item) == int:
item = (prec % int(item))

textl = []
for i, row in enumerate(r):
for j, colitem in enumerate(row)]))
if i == 0:
textl[0] = textl[0].rstrip()

text = os.linesep.join(textl)
return text

[docs]@cbook.deprecated("2.2", alternative='numpy.recarray.tofile')
def rec2csv(r, fname, delimiter=',', formatd=None, missing='',
"""
Save the data from numpy recarray *r* into a
comma-/space-/tab-delimited file.  The record array dtype names
will be used for column headers.

*fname*: can be a filename or a file handle.  Support for gzipped
files is automatic, if the filename ends in '.gz'

names in the first row

for formatd type FormatFloat, we override the precision to store
full precision floats in the CSV file

--------
:func:csv2rec
For information about *missing* and *missingd*, which can be used to
"""

delimiter = str(delimiter)

if missingd is None:
missingd = dict()

return mval
else:
return func(val)
return newfunc

if r.ndim != 1:
raise ValueError('rec2csv only operates on 1 dimensional recarrays')

formatd = get_formatd(r, formatd)
funcs = []
for i, name in enumerate(r.dtype.names):

fh, opened = cbook.to_filehandle(fname, 'wb', return_opened=True)
writer = csv.writer(fh, delimiter=delimiter)

# Our list of specials for missing values
mvals = []
mvals.append(missingd.get(name, missing))

if len(r):
row = r[0]

for row in r:
else:
if opened:
fh.close()

[docs]@cbook.deprecated('2.2', alternative='scipy.interpolate.griddata')
def griddata(x, y, z, xi, yi, interp='nn'):
"""
Interpolates from a nonuniformly spaced grid to some other grid.

Fits a surface of the form z = f(x, y) to the data in the
(usually) nonuniformly spaced vectors (x, y, z), then
interpolates this surface at the points specified by
(xi, yi) to produce zi.

Parameters
----------
x, y, z : 1d array_like
Coordinates of grid points to interpolate from.
xi, yi : 1d or 2d array_like
Coordinates of grid points to interpolate to.
interp : string key from {'nn', 'linear'}
Interpolation algorithm, either 'nn' for natural neighbor, or
'linear' for linear interpolation.

Returns
-------
2d float array
Array of values interpolated at (xi, yi) points.  Array
will be masked is any of (xi, yi) are outside the convex
hull of (x, y).

Notes
-----
If interp is 'nn' (the default), uses natural neighbor
interpolation based on Delaunay triangulation.  This option is
only available if the mpl_toolkits.natgrid module is installed.
The (xi, yi) grid must be regular and monotonically increasing
in this case.

If interp is 'linear', linear interpolation is used via
matplotlib.tri.LinearTriInterpolator.

Instead of using griddata, more flexible functionality and other
interpolation options are available using a
matplotlib.tri.Triangulation and a matplotlib.tri.TriInterpolator.
"""
# Check input arguments.
x = np.asanyarray(x, dtype=np.float64)
y = np.asanyarray(y, dtype=np.float64)
z = np.asanyarray(z, dtype=np.float64)
if x.shape != y.shape or x.shape != z.shape or x.ndim != 1:
raise ValueError("x, y and z must be equal-length 1-D arrays")

xi = np.asanyarray(xi, dtype=np.float64)
yi = np.asanyarray(yi, dtype=np.float64)
if xi.ndim != yi.ndim:
raise ValueError("xi and yi must be arrays with the same number of "
"dimensions (1 or 2)")
if xi.ndim == 2 and xi.shape != yi.shape:
raise ValueError("if xi and yi are 2D arrays, they must have the same "
"shape")
if xi.ndim == 1:
xi, yi = np.meshgrid(xi, yi)

if interp == 'nn':
use_nn_interpolation = True
elif interp == 'linear':
use_nn_interpolation = False
else:
raise ValueError("interp keyword must be one of 'linear' (for linear "
"interpolation) or 'nn' (for natural neighbor "
"interpolation).  Default is 'nn'.")

z = z.compressed()

if use_nn_interpolation:
try:
from mpl_toolkits.natgrid import _natgrid
except ImportError:
raise RuntimeError(
"To use interp='nn' (Natural Neighbor interpolation) in "
"griddata, natgrid must be installed. Either install it "
"from http://github.com/matplotlib/natgrid or use "

if xi.ndim == 2:
# natgrid expects 1D xi and yi arrays.
xi = xi[0, :]
yi = yi[:, 0]

# Override default natgrid internal parameters.
_natgrid.seti(b'ext', 0)
_natgrid.setr(b'nul', np.nan)

if np.min(np.diff(xi)) < 0 or np.min(np.diff(yi)) < 0:
raise ValueError("Output grid defined by xi,yi must be monotone "
"increasing")

# Allocate array for output (buffer will be overwritten by natgridd)
zi = np.empty((yi.shape[0], xi.shape[0]), np.float64)

# Natgrid requires each array to be contiguous rather than e.g. a view
# that is a non-contiguous slice of another array.  Use numpy.require
# to deal with this, which will copy if necessary.
x = np.require(x, requirements=['C'])
y = np.require(y, requirements=['C'])
z = np.require(z, requirements=['C'])
xi = np.require(xi, requirements=['C'])
yi = np.require(yi, requirements=['C'])
_natgrid.natgridd(x, y, z, xi, yi, zi)

# Mask points on grid outside convex hull of input data.
if np.any(np.isnan(zi)):
return zi
else:
# Linear interpolation performed using a matplotlib.tri.Triangulation
# and a matplotlib.tri.LinearTriInterpolator.
from .tri import Triangulation, LinearTriInterpolator
triang = Triangulation(x, y)
interpolator = LinearTriInterpolator(triang, z)
return interpolator(xi, yi)

##################################################
# Linear interpolation algorithms
##################################################
[docs]@cbook.deprecated("2.2", alternative="numpy.interp")
def less_simple_linear_interpolation(x, y, xi, extrap=False):
"""
This function provides simple (but somewhat less so than
:func:cbook.simple_linear_interpolation) linear interpolation.
:func:simple_linear_interpolation will give a list of point
between a start and an end, while this does true linear
interpolation at an arbitrary set of points.

This is very inefficient linear interpolation meant to be used
only for a small number of points in relatively non-intensive use
cases.  For real linear interpolation, use scipy.
"""
x = np.asarray(x)
y = np.asarray(y)
xi = np.atleast_1d(xi)

s = list(y.shape)
s[0] = len(xi)
yi = np.tile(np.nan, s)

for ii, xx in enumerate(xi):
bb = x == xx
if np.any(bb):
jj, = np.nonzero(bb)
yi[ii] = y[jj[0]]
elif xx < x[0]:
if extrap:
yi[ii] = y[0]
elif xx > x[-1]:
if extrap:
yi[ii] = y[-1]
else:
jj, = np.nonzero(x < xx)
jj = max(jj)

yi[ii] = y[jj] + (xx-x[jj])/(x[jj+1]-x[jj]) * (y[jj+1]-y[jj])

return yi

[docs]@cbook.deprecated("2.2")
def slopes(x, y):
"""
:func:slopes calculates the slope *y*'(*x*)

The slope is estimated using the slope obtained from that of a
parabola through any three consecutive points.

This method should be superior to that described in the appendix
of A CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russel
W. Stineman (Creative Computing July 1980) in at least one aspect:

Circles for interpolation demand a known aspect ratio between
*x*- and *y*-values.  For many functions, however, the abscissa
are given in different dimensions, so an aspect ratio is
completely arbitrary.

The parabola method gives very similar results to the circle
method for most regular cases but behaves much better in special
cases.

Norbert Nemec, Institute of Theoretical Physics, University or
Regensburg, April 2006 Norbert.Nemec at physik.uni-regensburg.de

(inspired by a original implementation by Halldor Bjornsson,
Icelandic Meteorological Office, March 2006 halldor at vedur.is)
"""
# Cast key variables as float.
x = np.asarray(x, float)
y = np.asarray(y, float)

yp = np.zeros(y.shape, float)

dx = x[1:] - x[:-1]
dy = y[1:] - y[:-1]
dydx = dy/dx
yp[1:-1] = (dydx[:-1] * dx[1:] + dydx[1:] * dx[:-1])/(dx[1:] + dx[:-1])
yp[0] = 2.0 * dy[0]/dx[0] - yp[1]
yp[-1] = 2.0 * dy[-1]/dx[-1] - yp[-2]
return yp

[docs]@cbook.deprecated("2.2")
def stineman_interp(xi, x, y, yp=None):
"""
Given data vectors *x* and *y*, the slope vector *yp* and a new
abscissa vector *xi*, the function :func:stineman_interp uses
Stineman interpolation to calculate a vector *yi* corresponding to
*xi*.

Here's an example that generates a coarse sine curve, then
interpolates over a finer abscissa::

x = linspace(0,2*pi,20);  y = sin(x); yp = cos(x)
xi = linspace(0,2*pi,40);
yi = stineman_interp(xi,x,y,yp);
plot(x,y,'o',xi,yi)

The interpolation method is described in the article A
CONSISTENTLY WELL BEHAVED METHOD OF INTERPOLATION by Russell
W. Stineman. The article appeared in the July 1980 issue of
Creative Computing with a note from the editor stating that while
they were:

not an academic journal but once in a while something serious
and original comes in adding that this was
"apparently a real solution" to a well known problem.

For *yp* = *None*, the routine automatically determines the slopes
using the :func:slopes routine.

*x* is assumed to be sorted in increasing order.

For values xi[j] < x[0] or xi[j] > x[-1], the routine
tries an extrapolation.  The relevance of the data obtained from
this, of course, is questionable...

Original implementation by Halldor Bjornsson, Icelandic
Meteorolocial Office, March 2006 halldor at vedur.is

Completely reworked and optimized for Python by Norbert Nemec,
Institute of Theoretical Physics, University or Regensburg, April
2006 Norbert.Nemec at physik.uni-regensburg.de
"""

# Cast key variables as float.
x = np.asarray(x, float)
y = np.asarray(y, float)
if x.shape != y.shape:
raise ValueError("'x' and 'y' must be of same shape")

if yp is None:
yp = slopes(x, y)
else:
yp = np.asarray(yp, float)

xi = np.asarray(xi, float)
yi = np.zeros(xi.shape, float)

# calculate linear slopes
dx = x[1:] - x[:-1]
dy = y[1:] - y[:-1]
s = dy/dx  # note length of s is N-1 so last element is #N-2

# find the segment each xi is in
# this line actually is the key to the efficiency of this implementation
idx = np.searchsorted(x[1:-1], xi)

# now we have generally: x[idx[j]] <= xi[j] <= x[idx[j]+1]
# except at the boundaries, where it may be that xi[j] < x[0] or
# xi[j] > x[-1]

# the y-values that would come out from a linear interpolation:
sidx = s.take(idx)
xidx = x.take(idx)
yidx = y.take(idx)
xidxp1 = x.take(idx+1)
yo = yidx + sidx * (xi - xidx)

# the difference that comes when using the slopes given in yp
# using the yp slope of the left point
dy1 = (yp.take(idx) - sidx) * (xi - xidx)
# using the yp slope of the right point
dy2 = (yp.take(idx+1)-sidx) * (xi - xidxp1)

dy1dy2 = dy1*dy2
# The following is optimized for Python. The solution actually
# does more calculations than necessary but exploiting the power
# of numpy, this is far more efficient than coding a loop by hand
# in Python
yi = yo + dy1dy2 * np.choose(np.array(np.sign(dy1dy2), np.int32)+1,
((2*xi-xidx-xidxp1)/((dy1-dy2)*(xidxp1-xidx)),
0.0,
1/(dy1+dy2),))
return yi

[docs]class GaussianKDE(object):
"""
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 2-D 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
isString = isinstance(bw_method, str)

if bw_method is None:
pass
elif (isString and bw_method == 'scott'):
self.covariance_factor = self.scotts_factor
elif (isString and bw_method == 'silverman'):
self.covariance_factor = self.silverman_factor
elif (np.isscalar(bw_method) and not isString):
self._bw_method = 'use constant'
self.covariance_factor = lambda: bw_method
elif callable(bw_method):
self._bw_method = bw_method
self.covariance_factor = lambda: self._bw_method(self)
else:
raise ValueError("bw_method should be 'scott', 'silverman', a "
"scalar or a callable")

# Computes the covariance matrix for each Gaussian kernel using
# covariance_factor().

self.factor = self.covariance_factor()
# Cache covariance and inverse covariance of the data
if not hasattr(self, '_data_inv_cov'):
self.data_covariance = np.atleast_2d(
np.cov(
self.dataset,
rowvar=1,
bias=False))
self.data_inv_cov = np.linalg.inv(self.data_covariance)

self.covariance = self.data_covariance * self.factor ** 2
self.inv_cov = self.data_inv_cov / self.factor ** 2
self.norm_factor = np.sqrt(
np.linalg.det(
2 * np.pi * self.covariance)) * self.num_dp

[docs]    def scotts_factor(self):
return np.power(self.num_dp, -1. / (self.dim + 4))

[docs]    def silverman_factor(self):
return np.power(
self.num_dp * (self.dim + 2.0) / 4.0, -1. / (self.dim + 4))

#  Default method to calculate bandwidth, can be overwritten by subclass
covariance_factor = scotts_factor

[docs]    def evaluate(self, points):
"""Evaluate the estimated pdf on a set of points.

Parameters
----------
points : (# of dimensions, # of points)-array
Alternatively, a (# of dimensions,) vector can be passed in and
treated as a single point.

Returns
-------
values : (# of points,)-array
The values at each point.

Raises
------
ValueError : if the dimensionality of the input points is different
than the dimensionality of the KDE.

"""
points = np.atleast_2d(points)

dim, num_m = np.array(points).shape
if dim != self.dim:
raise ValueError("points have dimension {}, dataset has dimension "
"{}".format(dim, self.dim))

result = np.zeros((num_m,), dtype=float)

if num_m >= self.num_dp:
# there are more points than data, so loop over data
for i in range(self.num_dp):
diff = self.dataset[:, i, np.newaxis] - points
tdiff = np.dot(self.inv_cov, diff)
energy = np.sum(diff * tdiff, axis=0) / 2.0
result = result + np.exp(-energy)
else:
# loop over points
for i in range(num_m):
diff = self.dataset - points[:, i, np.newaxis]
tdiff = np.dot(self.inv_cov, diff)
energy = np.sum(diff * tdiff, axis=0) / 2.0
result[i] = np.sum(np.exp(-energy), axis=0)

result = result / self.norm_factor

return result

__call__ = evaluate

##################################################
# Code related to things in and around polygons
##################################################
[docs]@cbook.deprecated("2.2")
def inside_poly(points, verts):
"""
*points* is a sequence of *x*, *y* points.
*verts* is a sequence of *x*, *y* vertices of a polygon.

Return value is a sequence of indices into points for the points
that are inside the polygon.
"""
# Make a closed polygon path
poly = Path(verts)

# Check to see which points are contained within the Path
return [idx for idx, p in enumerate(points) if poly.contains_point(p)]

[docs]@cbook.deprecated("2.2")
def poly_below(xmin, xs, ys):
"""
Given a sequence of *xs* and *ys*, return the vertices of a
polygon that has a horizontal base at *xmin* and an upper bound at
the *ys*.  *xmin* is a scalar.

Intended for use with :meth:matplotlib.axes.Axes.fill, e.g.,::

xv, yv = poly_below(0, x, y)
ax.fill(xv, yv)
"""
if any(isinstance(var, np.ma.MaskedArray) for var in [xs, ys]):
numpy = np.ma
else:
numpy = np

xs = numpy.asarray(xs)
ys = numpy.asarray(ys)
Nx = len(xs)
Ny = len(ys)
if Nx != Ny:
raise ValueError("'xs' and 'ys' must have the same length")
x = xmin*numpy.ones(2*Nx)
y = numpy.ones(2*Nx)
x[:Nx] = xs
y[:Nx] = ys
y[Nx:] = ys[::-1]
return x, y

[docs]@cbook.deprecated("2.2")
def poly_between(x, ylower, yupper):
"""
Given a sequence of *x*, *ylower* and *yupper*, return the polygon
that fills the regions between them.  *ylower* or *yupper* can be
scalar or iterable.  If they are iterable, they must be equal in
length to *x*.

Return value is *x*, *y* arrays for use with
:meth:matplotlib.axes.Axes.fill.
"""
if any(isinstance(var, np.ma.MaskedArray) for var in [ylower, yupper, x]):
numpy = np.ma
else:
numpy = np

Nx = len(x)
if not cbook.iterable(ylower):
ylower = ylower*numpy.ones(Nx)

if not cbook.iterable(yupper):
yupper = yupper*numpy.ones(Nx)

x = numpy.concatenate((x, x[::-1]))
y = numpy.concatenate((yupper, ylower[::-1]))
return x, y

[docs]@cbook.deprecated('2.2')
def is_closed_polygon(X):
"""
Tests whether first and last object in a sequence are the same.  These are
presumably coordinates on a polygonal curve, in which case this function
tests if that curve is closed.
"""
return np.all(X[0] == X[-1])

[docs]@cbook.deprecated("2.2", message='Moved to matplotlib.cbook')
"""
return a list of (ind0, ind1) such that mask[ind0:ind1].all() is
True and we cover all such regions
"""

[docs]@cbook.deprecated("2.2")
def cross_from_below(x, threshold):
"""
return the indices into *x* where *x* crosses some threshold from
below, e.g., the i's where::

x[i-1]<threshold and x[i]>=threshold

Example code::

import matplotlib.pyplot as plt

t = np.arange(0.0, 2.0, 0.1)
s = np.sin(2*np.pi*t)

fig, ax = plt.subplots()
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)
ax.vlines(t[ind], -1, 1)

plt.show()

--------
:func:cross_from_above and :func:contiguous_regions

"""
x = np.asarray(x)
ind = np.nonzero((x[:-1] < threshold) & (x[1:] >= threshold))[0]
if len(ind):
return ind+1
else:
return ind

[docs]@cbook.deprecated("2.2")
def cross_from_above(x, threshold):
"""
return the indices into *x* where *x* crosses some threshold from
below, e.g., the i's where::

x[i-1]>threshold and x[i]<=threshold

--------
:func:cross_from_below and :func:contiguous_regions

"""
x = np.asarray(x)
ind = np.nonzero((x[:-1] >= threshold) & (x[1:] < threshold))[0]
if len(ind):
return ind+1
else:
return ind

##################################################
# Vector and path length geometry calculations
##################################################
[docs]@cbook.deprecated('2.2')
def vector_lengths(X, P=2., axis=None):
"""
Finds the length of a set of vectors in *n* dimensions.  This is
like the :func:numpy.norm function for vectors, but has the ability to
work over a particular axis of the supplied array or matrix.

Computes (sum((x_i)^P))^(1/P) for each {x_i} being the
elements of *X* along the given axis.  If *axis* is *None*,
compute over all elements of *X*.
"""
X = np.asarray(X)
return (np.sum(X**(P), axis=axis))**(1./P)

[docs]@cbook.deprecated('2.2')
def distances_along_curve(X):
"""
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.
"""
X = np.diff(X, axis=0)
return vector_lengths(X, axis=1)

[docs]@cbook.deprecated('2.2')
def path_length(X):
"""
Computes the distance travelled along a polygonal curve in *N* dimensions.

Where *X* is an *M* x *N* array or matrix.  Returns an array of
length *M* consisting of the distance along the curve at each point
(i.e., the rows of *X*).
"""
X = distances_along_curve(X)
return np.concatenate((np.zeros(1), np.cumsum(X)))

[docs]@cbook.deprecated('2.2')
def quad2cubic(q0x, q0y, q1x, q1y, q2x, q2y):
"""
Converts a quadratic Bezier curve to a cubic approximation.

The inputs are the *x* and *y* coordinates of the three control
points of a quadratic curve, and the output is a tuple of *x* and
*y* coordinates of the four control points of the cubic curve.
"""
# TODO: Candidate for deprecation -- no longer used internally

# c0x, c0y = q0x, q0y
c1x, c1y = q0x + 2./3. * (q1x - q0x), q0y + 2./3. * (q1y - q0y)
c2x, c2y = c1x + 1./3. * (q2x - q0x), c1y + 1./3. * (q2y - q0y)
# c3x, c3y = q2x, q2y
return q0x, q0y, c1x, c1y, c2x, c2y, q2x, q2y

[docs]@cbook.deprecated("2.2")
def offset_line(y, yerr):
"""
Offsets an array *y* by +/- an error and returns a tuple
(y - err, y + err).

The error term can be:

* A scalar. In this case, the returned tuple is obvious.
* A vector of the same length as *y*. The quantities y +/- err are computed
component-wise.
* A tuple of length 2. In this case, yerr[0] is the error below *y* and
yerr[1] is error above *y*. For example::

import numpy as np
import matplotlib.pyplot as plt

x = np.linspace(0, 2*np.pi, num=100, endpoint=True)
y = np.sin(x)
y_minus, y_plus = mlab.offset_line(y, 0.1)
plt.plot(x, y)
plt.fill_between(x, y_minus, y2=y_plus)
plt.show()

"""
if cbook.is_numlike(yerr) or (cbook.iterable(yerr) and
len(yerr) == len(y)):
ymin = y - yerr
ymax = y + yerr
elif len(yerr) == 2:
ymin, ymax = y - yerr[0], y + yerr[1]
else:
raise ValueError("yerr must be scalar, 1xN or 2xN")
return ymin, ymax
`