314 lines
9.8 KiB
Python
314 lines
9.8 KiB
Python
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from functools import update_wrapper, lru_cache
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import inspect
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from ._pocketfft import helper as _helper
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import numpy as np
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from scipy._lib._array_api import array_namespace
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def next_fast_len(target, real=False):
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"""Find the next fast size of input data to ``fft``, for zero-padding, etc.
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SciPy's FFT algorithms gain their speed by a recursive divide and conquer
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strategy. This relies on efficient functions for small prime factors of the
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input length. Thus, the transforms are fastest when using composites of the
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prime factors handled by the fft implementation. If there are efficient
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functions for all radices <= `n`, then the result will be a number `x`
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>= ``target`` with only prime factors < `n`. (Also known as `n`-smooth
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numbers)
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Parameters
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----------
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target : int
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Length to start searching from. Must be a positive integer.
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real : bool, optional
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True if the FFT involves real input or output (e.g., `rfft` or `hfft`
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but not `fft`). Defaults to False.
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Returns
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-------
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out : int
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The smallest fast length greater than or equal to ``target``.
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Notes
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-----
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The result of this function may change in future as performance
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considerations change, for example, if new prime factors are added.
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Calling `fft` or `ifft` with real input data performs an ``'R2C'``
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transform internally.
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Examples
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--------
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On a particular machine, an FFT of prime length takes 11.4 ms:
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>>> from scipy import fft
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>>> import numpy as np
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>>> rng = np.random.default_rng()
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>>> min_len = 93059 # prime length is worst case for speed
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>>> a = rng.standard_normal(min_len)
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>>> b = fft.fft(a)
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Zero-padding to the next regular length reduces computation time to
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1.6 ms, a speedup of 7.3 times:
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>>> fft.next_fast_len(min_len, real=True)
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93312
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>>> b = fft.fft(a, 93312)
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Rounding up to the next power of 2 is not optimal, taking 3.0 ms to
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compute; 1.9 times longer than the size given by ``next_fast_len``:
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>>> b = fft.fft(a, 131072)
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"""
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pass
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# Directly wrap the c-function good_size but take the docstring etc., from the
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# next_fast_len function above
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_sig = inspect.signature(next_fast_len)
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next_fast_len = update_wrapper(lru_cache(_helper.good_size), next_fast_len)
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next_fast_len.__wrapped__ = _helper.good_size
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next_fast_len.__signature__ = _sig
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def _init_nd_shape_and_axes(x, shape, axes):
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"""Handle shape and axes arguments for N-D transforms.
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Returns the shape and axes in a standard form, taking into account negative
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values and checking for various potential errors.
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Parameters
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----------
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x : array_like
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The input array.
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shape : int or array_like of ints or None
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The shape of the result. If both `shape` and `axes` (see below) are
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None, `shape` is ``x.shape``; if `shape` is None but `axes` is
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not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
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If `shape` is -1, the size of the corresponding dimension of `x` is
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used.
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axes : int or array_like of ints or None
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Axes along which the calculation is computed.
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The default is over all axes.
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Negative indices are automatically converted to their positive
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counterparts.
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Returns
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-------
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shape : tuple
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The shape of the result as a tuple of integers.
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axes : list
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Axes along which the calculation is computed, as a list of integers.
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"""
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x = np.asarray(x)
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return _helper._init_nd_shape_and_axes(x, shape, axes)
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def fftfreq(n, d=1.0, *, xp=None, device=None):
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"""Return the Discrete Fourier Transform sample frequencies.
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The returned float array `f` contains the frequency bin centers in cycles
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per unit of the sample spacing (with zero at the start). For instance, if
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the sample spacing is in seconds, then the frequency unit is cycles/second.
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Given a window length `n` and a sample spacing `d`::
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f = [0, 1, ..., n/2-1, -n/2, ..., -1] / (d*n) if n is even
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f = [0, 1, ..., (n-1)/2, -(n-1)/2, ..., -1] / (d*n) if n is odd
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Parameters
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----------
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n : int
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Window length.
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d : scalar, optional
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Sample spacing (inverse of the sampling rate). Defaults to 1.
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xp : array_namespace, optional
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The namespace for the return array. Default is None, where NumPy is used.
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device : device, optional
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The device for the return array.
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Only valid when `xp.fft.fftfreq` implements the device parameter.
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Returns
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-------
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f : ndarray
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Array of length `n` containing the sample frequencies.
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Examples
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--------
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>>> import numpy as np
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>>> import scipy.fft
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>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
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>>> fourier = scipy.fft.fft(signal)
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>>> n = signal.size
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>>> timestep = 0.1
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>>> freq = scipy.fft.fftfreq(n, d=timestep)
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>>> freq
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array([ 0. , 1.25, 2.5 , ..., -3.75, -2.5 , -1.25])
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"""
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xp = np if xp is None else xp
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# numpy does not yet support the `device` keyword
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# `xp.__name__ != 'numpy'` should be removed when numpy is compatible
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if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
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return xp.fft.fftfreq(n, d=d, device=device)
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if device is not None:
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raise ValueError('device parameter is not supported for input array type')
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return np.fft.fftfreq(n, d=d)
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def rfftfreq(n, d=1.0, *, xp=None, device=None):
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"""Return the Discrete Fourier Transform sample frequencies
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(for usage with rfft, irfft).
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The returned float array `f` contains the frequency bin centers in cycles
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per unit of the sample spacing (with zero at the start). For instance, if
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the sample spacing is in seconds, then the frequency unit is cycles/second.
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Given a window length `n` and a sample spacing `d`::
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f = [0, 1, ..., n/2-1, n/2] / (d*n) if n is even
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f = [0, 1, ..., (n-1)/2-1, (n-1)/2] / (d*n) if n is odd
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Unlike `fftfreq` (but like `scipy.fftpack.rfftfreq`)
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the Nyquist frequency component is considered to be positive.
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Parameters
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----------
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n : int
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Window length.
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d : scalar, optional
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Sample spacing (inverse of the sampling rate). Defaults to 1.
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xp : array_namespace, optional
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The namespace for the return array. Default is None, where NumPy is used.
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device : device, optional
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The device for the return array.
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Only valid when `xp.fft.rfftfreq` implements the device parameter.
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Returns
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-------
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f : ndarray
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Array of length ``n//2 + 1`` containing the sample frequencies.
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Examples
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--------
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>>> import numpy as np
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>>> import scipy.fft
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>>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
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>>> fourier = scipy.fft.rfft(signal)
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>>> n = signal.size
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>>> sample_rate = 100
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>>> freq = scipy.fft.fftfreq(n, d=1./sample_rate)
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>>> freq
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array([ 0., 10., 20., ..., -30., -20., -10.])
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>>> freq = scipy.fft.rfftfreq(n, d=1./sample_rate)
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>>> freq
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array([ 0., 10., 20., 30., 40., 50.])
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"""
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xp = np if xp is None else xp
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# numpy does not yet support the `device` keyword
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# `xp.__name__ != 'numpy'` should be removed when numpy is compatible
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if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
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return xp.fft.rfftfreq(n, d=d, device=device)
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if device is not None:
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raise ValueError('device parameter is not supported for input array type')
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return np.fft.rfftfreq(n, d=d)
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def fftshift(x, axes=None):
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"""Shift the zero-frequency component to the center of the spectrum.
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This function swaps half-spaces for all axes listed (defaults to all).
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Note that ``y[0]`` is the Nyquist component only if ``len(x)`` is even.
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Parameters
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----------
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x : array_like
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Input array.
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axes : int or shape tuple, optional
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Axes over which to shift. Default is None, which shifts all axes.
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Returns
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-------
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y : ndarray
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The shifted array.
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See Also
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--------
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ifftshift : The inverse of `fftshift`.
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Examples
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--------
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>>> import numpy as np
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>>> freqs = np.fft.fftfreq(10, 0.1)
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>>> freqs
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array([ 0., 1., 2., ..., -3., -2., -1.])
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>>> np.fft.fftshift(freqs)
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array([-5., -4., -3., -2., -1., 0., 1., 2., 3., 4.])
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Shift the zero-frequency component only along the second axis:
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>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
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>>> freqs
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array([[ 0., 1., 2.],
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[ 3., 4., -4.],
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[-3., -2., -1.]])
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>>> np.fft.fftshift(freqs, axes=(1,))
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array([[ 2., 0., 1.],
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[-4., 3., 4.],
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[-1., -3., -2.]])
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"""
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xp = array_namespace(x)
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if hasattr(xp, 'fft'):
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return xp.fft.fftshift(x, axes=axes)
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x = np.asarray(x)
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y = np.fft.fftshift(x, axes=axes)
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return xp.asarray(y)
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def ifftshift(x, axes=None):
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"""The inverse of `fftshift`. Although identical for even-length `x`, the
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functions differ by one sample for odd-length `x`.
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Parameters
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----------
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x : array_like
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Input array.
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axes : int or shape tuple, optional
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Axes over which to calculate. Defaults to None, which shifts all axes.
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Returns
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-------
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y : ndarray
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The shifted array.
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See Also
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--------
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fftshift : Shift zero-frequency component to the center of the spectrum.
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Examples
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--------
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>>> import numpy as np
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>>> freqs = np.fft.fftfreq(9, d=1./9).reshape(3, 3)
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>>> freqs
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array([[ 0., 1., 2.],
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[ 3., 4., -4.],
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[-3., -2., -1.]])
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>>> np.fft.ifftshift(np.fft.fftshift(freqs))
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array([[ 0., 1., 2.],
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[ 3., 4., -4.],
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[-3., -2., -1.]])
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"""
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xp = array_namespace(x)
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if hasattr(xp, 'fft'):
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return xp.fft.ifftshift(x, axes=axes)
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x = np.asarray(x)
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y = np.fft.ifftshift(x, axes=axes)
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return xp.asarray(y)
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