343 lines
11 KiB
Python
343 lines
11 KiB
Python
"""
|
|
Functions which are common and require SciPy Base and Level 1 SciPy
|
|
(special, linalg)
|
|
"""
|
|
|
|
from scipy._lib.deprecation import _deprecated
|
|
from scipy._lib._finite_differences import _central_diff_weights, _derivative
|
|
from numpy import array, frombuffer, load
|
|
|
|
|
|
__all__ = ['central_diff_weights', 'derivative', 'ascent', 'face',
|
|
'electrocardiogram']
|
|
|
|
|
|
@_deprecated(msg="scipy.misc.central_diff_weights is deprecated in "
|
|
"SciPy v1.10.0; and will be completely removed in "
|
|
"SciPy v1.12.0. You may consider using "
|
|
"findiff: https://github.com/maroba/findiff or "
|
|
"numdifftools: https://github.com/pbrod/numdifftools")
|
|
def central_diff_weights(Np, ndiv=1):
|
|
"""
|
|
Return weights for an Np-point central derivative.
|
|
|
|
Assumes equally-spaced function points.
|
|
|
|
If weights are in the vector w, then
|
|
derivative is w[0] * f(x-ho*dx) + ... + w[-1] * f(x+h0*dx)
|
|
|
|
.. deprecated:: 1.10.0
|
|
`central_diff_weights` has been deprecated from
|
|
`scipy.misc.central_diff_weights` in SciPy 1.10.0 and
|
|
it will be completely removed in SciPy 1.12.0.
|
|
You may consider using
|
|
findiff: https://github.com/maroba/findiff or
|
|
numdifftools: https://github.com/pbrod/numdifftools
|
|
|
|
Parameters
|
|
----------
|
|
Np : int
|
|
Number of points for the central derivative.
|
|
ndiv : int, optional
|
|
Number of divisions. Default is 1.
|
|
|
|
Returns
|
|
-------
|
|
w : ndarray
|
|
Weights for an Np-point central derivative. Its size is `Np`.
|
|
|
|
Notes
|
|
-----
|
|
Can be inaccurate for a large number of points.
|
|
|
|
Examples
|
|
--------
|
|
We can calculate a derivative value of a function.
|
|
|
|
>>> from scipy.misc import central_diff_weights
|
|
>>> def f(x):
|
|
... return 2 * x**2 + 3
|
|
>>> x = 3.0 # derivative point
|
|
>>> h = 0.1 # differential step
|
|
>>> Np = 3 # point number for central derivative
|
|
>>> weights = central_diff_weights(Np) # weights for first derivative
|
|
>>> vals = [f(x + (i - Np/2) * h) for i in range(Np)]
|
|
>>> sum(w * v for (w, v) in zip(weights, vals))/h
|
|
11.79999999999998
|
|
|
|
This value is close to the analytical solution:
|
|
f'(x) = 4x, so f'(3) = 12
|
|
|
|
References
|
|
----------
|
|
.. [1] https://en.wikipedia.org/wiki/Finite_difference
|
|
|
|
"""
|
|
return _central_diff_weights(Np, ndiv)
|
|
|
|
|
|
@_deprecated(msg="scipy.misc.derivative is deprecated in "
|
|
"SciPy v1.10.0; and will be completely removed in "
|
|
"SciPy v1.12.0. You may consider using "
|
|
"findiff: https://github.com/maroba/findiff or "
|
|
"numdifftools: https://github.com/pbrod/numdifftools")
|
|
def derivative(func, x0, dx=1.0, n=1, args=(), order=3):
|
|
"""
|
|
Find the nth derivative of a function at a point.
|
|
|
|
Given a function, use a central difference formula with spacing `dx` to
|
|
compute the nth derivative at `x0`.
|
|
|
|
.. deprecated:: 1.10.0
|
|
`derivative` has been deprecated from `scipy.misc.derivative`
|
|
in SciPy 1.10.0 and it will be completely removed in SciPy 1.12.0.
|
|
You may consider using
|
|
findiff: https://github.com/maroba/findiff or
|
|
numdifftools: https://github.com/pbrod/numdifftools
|
|
|
|
Parameters
|
|
----------
|
|
func : function
|
|
Input function.
|
|
x0 : float
|
|
The point at which the nth derivative is found.
|
|
dx : float, optional
|
|
Spacing.
|
|
n : int, optional
|
|
Order of the derivative. Default is 1.
|
|
args : tuple, optional
|
|
Arguments
|
|
order : int, optional
|
|
Number of points to use, must be odd.
|
|
|
|
Notes
|
|
-----
|
|
Decreasing the step size too small can result in round-off error.
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy.misc import derivative
|
|
>>> def f(x):
|
|
... return x**3 + x**2
|
|
>>> derivative(f, 1.0, dx=1e-6)
|
|
4.9999999999217337
|
|
|
|
"""
|
|
return _derivative(func, x0, dx, n, args, order)
|
|
|
|
|
|
@_deprecated(msg="scipy.misc.ascent has been deprecated in SciPy v1.10.0;"
|
|
" and will be completely removed in SciPy v1.12.0. "
|
|
"Dataset methods have moved into the scipy.datasets "
|
|
"module. Use scipy.datasets.ascent instead.")
|
|
def ascent():
|
|
"""
|
|
Get an 8-bit grayscale bit-depth, 512 x 512 derived image for easy use in demos
|
|
|
|
The image is derived from accent-to-the-top.jpg at
|
|
http://www.public-domain-image.com/people-public-domain-images-pictures/
|
|
|
|
.. deprecated:: 1.10.0
|
|
`ascent` has been deprecated from `scipy.misc.ascent`
|
|
in SciPy 1.10.0 and it will be completely removed in SciPy 1.12.0.
|
|
Dataset methods have moved into the `scipy.datasets` module.
|
|
Use `scipy.datasets.ascent` instead.
|
|
|
|
Parameters
|
|
----------
|
|
None
|
|
|
|
Returns
|
|
-------
|
|
ascent : ndarray
|
|
convenient image to use for testing and demonstration
|
|
|
|
Examples
|
|
--------
|
|
>>> import scipy.misc
|
|
>>> ascent = scipy.misc.ascent()
|
|
>>> ascent.shape
|
|
(512, 512)
|
|
>>> ascent.max()
|
|
255
|
|
|
|
>>> import matplotlib.pyplot as plt
|
|
>>> plt.gray()
|
|
>>> plt.imshow(ascent)
|
|
>>> plt.show()
|
|
|
|
"""
|
|
import pickle
|
|
import os
|
|
fname = os.path.join(os.path.dirname(__file__),'ascent.dat')
|
|
with open(fname, 'rb') as f:
|
|
ascent = array(pickle.load(f))
|
|
return ascent
|
|
|
|
|
|
@_deprecated(msg="scipy.misc.face has been deprecated in SciPy v1.10.0; "
|
|
"and will be completely removed in SciPy v1.12.0. "
|
|
"Dataset methods have moved into the scipy.datasets "
|
|
"module. Use scipy.datasets.face instead.")
|
|
def face(gray=False):
|
|
"""
|
|
Get a 1024 x 768, color image of a raccoon face.
|
|
|
|
raccoon-procyon-lotor.jpg at http://www.public-domain-image.com
|
|
|
|
.. deprecated:: 1.10.0
|
|
`face` has been deprecated from `scipy.misc.face`
|
|
in SciPy 1.10.0 and it will be completely removed in SciPy 1.12.0.
|
|
Dataset methods have moved into the `scipy.datasets` module.
|
|
Use `scipy.datasets.face` instead.
|
|
|
|
Parameters
|
|
----------
|
|
gray : bool, optional
|
|
If True return 8-bit grey-scale image, otherwise return a color image
|
|
|
|
Returns
|
|
-------
|
|
face : ndarray
|
|
image of a racoon face
|
|
|
|
Examples
|
|
--------
|
|
>>> import scipy.misc
|
|
>>> face = scipy.misc.face()
|
|
>>> face.shape
|
|
(768, 1024, 3)
|
|
>>> face.max()
|
|
255
|
|
>>> face.dtype
|
|
dtype('uint8')
|
|
|
|
>>> import matplotlib.pyplot as plt
|
|
>>> plt.gray()
|
|
>>> plt.imshow(face)
|
|
>>> plt.show()
|
|
|
|
"""
|
|
import bz2
|
|
import os
|
|
with open(os.path.join(os.path.dirname(__file__), 'face.dat'), 'rb') as f:
|
|
rawdata = f.read()
|
|
data = bz2.decompress(rawdata)
|
|
face = frombuffer(data, dtype='uint8')
|
|
face.shape = (768, 1024, 3)
|
|
if gray is True:
|
|
face = (0.21 * face[:,:,0] + 0.71 * face[:,:,1] + 0.07 * face[:,:,2]).astype('uint8')
|
|
return face
|
|
|
|
|
|
@_deprecated(msg="scipy.misc.electrocardiogram has been "
|
|
"deprecated in SciPy v1.10.0; and will "
|
|
"be completely removed in SciPy v1.12.0. "
|
|
"Dataset methods have moved into the scipy.datasets "
|
|
"module. Use scipy.datasets.electrocardiogram instead.")
|
|
def electrocardiogram():
|
|
"""
|
|
Load an electrocardiogram as an example for a 1-D signal.
|
|
|
|
The returned signal is a 5 minute long electrocardiogram (ECG), a medical
|
|
recording of the heart's electrical activity, sampled at 360 Hz.
|
|
|
|
.. deprecated:: 1.10.0
|
|
`electrocardiogram` has been deprecated from
|
|
`scipy.misc.electrocardiogram` in SciPy 1.10.0 and it will be
|
|
completely removed in SciPy 1.12.0.
|
|
Dataset methods have moved into the `scipy.datasets` module.
|
|
Use `scipy.datasets.electrocardiogram` instead.
|
|
|
|
Returns
|
|
-------
|
|
ecg : ndarray
|
|
The electrocardiogram in millivolt (mV) sampled at 360 Hz.
|
|
|
|
Notes
|
|
-----
|
|
The provided signal is an excerpt (19:35 to 24:35) from the `record 208`_
|
|
(lead MLII) provided by the MIT-BIH Arrhythmia Database [1]_ on
|
|
PhysioNet [2]_. The excerpt includes noise induced artifacts, typical
|
|
heartbeats as well as pathological changes.
|
|
|
|
.. _record 208: https://physionet.org/physiobank/database/html/mitdbdir/records.htm#208
|
|
|
|
.. versionadded:: 1.1.0
|
|
|
|
References
|
|
----------
|
|
.. [1] Moody GB, Mark RG. The impact of the MIT-BIH Arrhythmia Database.
|
|
IEEE Eng in Med and Biol 20(3):45-50 (May-June 2001).
|
|
(PMID: 11446209); :doi:`10.13026/C2F305`
|
|
.. [2] Goldberger AL, Amaral LAN, Glass L, Hausdorff JM, Ivanov PCh,
|
|
Mark RG, Mietus JE, Moody GB, Peng C-K, Stanley HE. PhysioBank,
|
|
PhysioToolkit, and PhysioNet: Components of a New Research Resource
|
|
for Complex Physiologic Signals. Circulation 101(23):e215-e220;
|
|
:doi:`10.1161/01.CIR.101.23.e215`
|
|
|
|
Examples
|
|
--------
|
|
>>> from scipy.misc import electrocardiogram
|
|
>>> ecg = electrocardiogram()
|
|
>>> ecg
|
|
array([-0.245, -0.215, -0.185, ..., -0.405, -0.395, -0.385])
|
|
>>> ecg.shape, ecg.mean(), ecg.std()
|
|
((108000,), -0.16510875, 0.5992473991177294)
|
|
|
|
As stated the signal features several areas with a different morphology.
|
|
E.g., the first few seconds show the electrical activity of a heart in
|
|
normal sinus rhythm as seen below.
|
|
|
|
>>> import numpy as np
|
|
>>> import matplotlib.pyplot as plt
|
|
>>> fs = 360
|
|
>>> time = np.arange(ecg.size) / fs
|
|
>>> plt.plot(time, ecg)
|
|
>>> plt.xlabel("time in s")
|
|
>>> plt.ylabel("ECG in mV")
|
|
>>> plt.xlim(9, 10.2)
|
|
>>> plt.ylim(-1, 1.5)
|
|
>>> plt.show()
|
|
|
|
After second 16, however, the first premature ventricular contractions, also
|
|
called extrasystoles, appear. These have a different morphology compared to
|
|
typical heartbeats. The difference can easily be observed in the following
|
|
plot.
|
|
|
|
>>> plt.plot(time, ecg)
|
|
>>> plt.xlabel("time in s")
|
|
>>> plt.ylabel("ECG in mV")
|
|
>>> plt.xlim(46.5, 50)
|
|
>>> plt.ylim(-2, 1.5)
|
|
>>> plt.show()
|
|
|
|
At several points large artifacts disturb the recording, e.g.:
|
|
|
|
>>> plt.plot(time, ecg)
|
|
>>> plt.xlabel("time in s")
|
|
>>> plt.ylabel("ECG in mV")
|
|
>>> plt.xlim(207, 215)
|
|
>>> plt.ylim(-2, 3.5)
|
|
>>> plt.show()
|
|
|
|
Finally, examining the power spectrum reveals that most of the biosignal is
|
|
made up of lower frequencies. At 60 Hz the noise induced by the mains
|
|
electricity can be clearly observed.
|
|
|
|
>>> from scipy.signal import welch
|
|
>>> f, Pxx = welch(ecg, fs=fs, nperseg=2048, scaling="spectrum")
|
|
>>> plt.semilogy(f, Pxx)
|
|
>>> plt.xlabel("Frequency in Hz")
|
|
>>> plt.ylabel("Power spectrum of the ECG in mV**2")
|
|
>>> plt.xlim(f[[0, -1]])
|
|
>>> plt.show()
|
|
"""
|
|
import os
|
|
file_path = os.path.join(os.path.dirname(__file__), "ecg.dat")
|
|
with load(file_path) as file:
|
|
ecg = file["ecg"].astype(int) # np.uint16 -> int
|
|
# Convert raw output of ADC to mV: (ecg - adc_zero) / adc_gain
|
|
ecg = (ecg - 1024) / 200.0
|
|
return ecg
|