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11 Examples
3
View Complete Implementation : test_utils.py
Copyright Apache License 2.0
Author : awslabs
Copyright Apache License 2.0
Author : awslabs
def test_strided(self):
a = arange(12)
b = a[::2]
low, high = utils.byte_bounds(b)
# the largest pointer address is lost (even numbers only in the
# stride), and compensate addresses for striding by 2
astert_equal(high - low, b.size * 2 * b.itemsize - b.itemsize)
0
View Complete Implementation : helper.py
Copyright MIT License
Author : abhisuri97
Copyright MIT License
Author : abhisuri97
def fftshift(x, axes=None):
"""
Shift the zero-frequency component to the center of the spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to shift. Default is None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
ifftshift : The inverse of `fftshift`.
Examples
--------
>>> freqs = np.fft.fftfreq(10, 0.1)
>>> freqs
array([ 0., 1., 2., 3., 4., -5., -4., -3., -2., -1.])
>>> np.fft.fftshift(freqs)
array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.])
Shift the zero-frequency component only along the second axis:
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.fftshift(freqs, axes=(1,))
array([[ 2., 0., 1.],
[-4., 3., 4.],
[-1., -3., -2.]])
"""
tmp = asarray(x)
ndim = len(tmp.shape)
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = (n+1)//2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
0
View Complete Implementation : helper.py
Copyright MIT License
Author : abhisuri97
Copyright MIT License
Author : abhisuri97
def ifftshift(x, axes=None):
"""
The inverse of `fftshift`. Although identical for even-length `x`, the
functions differ by one sample for odd-length `x`.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to calculate. Defaults to None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
fftshift : Shift zero-frequency component to the center of the spectrum.
Examples
--------
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.ifftshift(np.fft.fftshift(freqs))
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
"""
tmp = asarray(x)
ndim = len(tmp.shape)
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = n-(n+1)//2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
0
View Complete Implementation : helper.py
Copyright MIT License
Author : abhisuri97
Copyright MIT License
Author : abhisuri97
def fftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length `n` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> fourier = np.fft.fft(signal)
>>> n = signal.size
>>> timestep = 0.1
>>> freq = np.fft.fftfreq(n, d=timestep)
>>> freq
array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0 / (n * d)
results = empty(n, int)
N = (n-1)//2 + 1
p1 = arange(0, N, dtype=int)
results[:N] = p1
p2 = arange(-(n//2), 0, dtype=int)
results[N:] = p2
return results * val
0
View Complete Implementation : helper.py
Copyright MIT License
Author : abhisuri97
Copyright MIT License
Author : abhisuri97
def rfftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies
(for usage with rfft, irfft).
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
the Nyquist frequency component is considered to be positive.
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length ``n//2 + 1`` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
>>> fourier = np.fft.rfft(signal)
>>> n = signal.size
>>> sample_rate = 100
>>> freq = np.fft.fftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., -50., -40., -30., -20., -10.])
>>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., 50.])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0/(n*d)
N = n//2 + 1
results = arange(0, N, dtype=int)
return results * val
0
View Complete Implementation : test_helper.py
Copyright MIT License
Author : alvarob96
Copyright MIT License
Author : alvarob96
def test_equal_to_original(self):
""" Test that the new (>=v1.15) implementation (see #10073) is equal to the original (<=v1.14) """
from numpy.compat import integer_types
from numpy.core import asarray, concatenate, arange, take
def original_fftshift(x, axes=None):
""" How fftshift was implemented in v1.14"""
tmp = asarray(x)
ndim = tmp.ndim
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = (n + 1) // 2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
def original_ifftshift(x, axes=None):
""" How ifftshift was implemented in v1.14 """
tmp = asarray(x)
ndim = tmp.ndim
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = n - (n + 1) // 2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
# create possible 2d array combinations and try all possible keywords
# compare output to original functions
for i in range(16):
for j in range(16):
for axes_keyword in [0, 1, None, (0,), (0, 1)]:
inp = np.random.rand(i, j)
astert_array_almost_equal(fft.fftshift(inp, axes_keyword),
original_fftshift(inp, axes_keyword))
astert_array_almost_equal(fft.ifftshift(inp, axes_keyword),
original_ifftshift(inp, axes_keyword))
0
View Complete Implementation : helper.py
Copyright GNU Lesser General Public License v3.0
Author : awrns
Copyright GNU Lesser General Public License v3.0
Author : awrns
def fftshift(x, axes=None):
"""
Shift the zero-frequency component to the center of the spectrum.
This function swaps half-spaces for all axes listed (defaults to all).
Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to shift. Default is None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
ifftshift : The inverse of `fftshift`.
Examples
--------
>>> freqs = np.fft.fftfreq(10, 0.1)
>>> freqs
array([ 0., 1., 2., 3., 4., -5., -4., -3., -2., -1.])
>>> np.fft.fftshift(freqs)
array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.])
Shift the zero-frequency component only along the second axis:
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.fftshift(freqs, axes=(1,))
array([[ 2., 0., 1.],
[-4., 3., 4.],
[-1., -3., -2.]])
"""
tmp = asarray(x)
ndim = tmp.ndim
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = (n+1)//2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
0
View Complete Implementation : helper.py
Copyright GNU Lesser General Public License v3.0
Author : awrns
Copyright GNU Lesser General Public License v3.0
Author : awrns
def ifftshift(x, axes=None):
"""
The inverse of `fftshift`. Although identical for even-length `x`, the
functions differ by one sample for odd-length `x`.
Parameters
----------
x : array_like
Input array.
axes : int or shape tuple, optional
Axes over which to calculate. Defaults to None, which shifts all axes.
Returns
-------
y : ndarray
The shifted array.
See Also
--------
fftshift : Shift zero-frequency component to the center of the spectrum.
Examples
--------
>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
>>> freqs
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
>>> np.fft.ifftshift(np.fft.fftshift(freqs))
array([[ 0., 1., 2.],
[ 3., 4., -4.],
[-3., -2., -1.]])
"""
tmp = asarray(x)
ndim = tmp.ndim
if axes is None:
axes = list(range(ndim))
elif isinstance(axes, integer_types):
axes = (axes,)
y = tmp
for k in axes:
n = tmp.shape[k]
p2 = n-(n+1)//2
mylist = concatenate((arange(p2, n), arange(p2)))
y = take(y, mylist, k)
return y
0
View Complete Implementation : helper.py
Copyright Apache License 2.0
Author : awslabs
Copyright Apache License 2.0
Author : awslabs
@set_module('numpy.fft')
def fftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies.
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length `n` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
>>> fourier = np.fft.fft(signal)
>>> n = signal.size
>>> timestep = 0.1
>>> freq = np.fft.fftfreq(n, d=timestep)
>>> freq
array([ 0. , 1.25, 2.5 , 3.75, -5. , -3.75, -2.5 , -1.25])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0 / (n * d)
results = empty(n, int)
N = (n-1)//2 + 1
p1 = arange(0, N, dtype=int)
results[:N] = p1
p2 = arange(-(n//2), 0, dtype=int)
results[N:] = p2
return results * val
0
View Complete Implementation : helper.py
Copyright Apache License 2.0
Author : awslabs
Copyright Apache License 2.0
Author : awslabs
@set_module('numpy.fft')
def rfftfreq(n, d=1.0):
"""
Return the Discrete Fourier Transform sample frequencies
(for usage with rfft, irfft).
The returned float array `f` contains the frequency bin centers in cycles
per unit of the sample spacing (with zero at the start). For instance, if
the sample spacing is in seconds, then the frequency unit is cycles/second.
Given a window length `n` and a sample spacing `d`::
f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
the Nyquist frequency component is considered to be positive.
Parameters
----------
n : int
Window length.
d : scalar, optional
Sample spacing (inverse of the sampling rate). Defaults to 1.
Returns
-------
f : ndarray
Array of length ``n//2 + 1`` containing the sample frequencies.
Examples
--------
>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
>>> fourier = np.fft.rfft(signal)
>>> n = signal.size
>>> sample_rate = 100
>>> freq = np.fft.fftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., -50., -40., -30., -20., -10.])
>>> freq = np.fft.rfftfreq(n, d=1./sample_rate)
>>> freq
array([ 0., 10., 20., 30., 40., 50.])
"""
if not isinstance(n, integer_types):
raise ValueError("n should be an integer")
val = 1.0/(n*d)
N = n//2 + 1
results = arange(0, N, dtype=int)
return results * val