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"""
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 raccoon 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