venv/lib/python3.10/site-packages/scipy/fft/_helper.py

from functools import update_wrapper, lru_cache
import inspect

from ._pocketfft import helper as _helper

import numpy as np
from scipy._lib._array_api import array_namespace


def next_fast_len(target, real=False):
    """Find the next fast size of input data to ``fft``, for zero-padding, etc.

    SciPy's FFT algorithms gain their speed by a recursive divide and conquer
    strategy. This relies on efficient functions for small prime factors of the
    input length. Thus, the transforms are fastest when using composites of the
    prime factors handled by the fft implementation. If there are efficient
    functions for all radices <= `n`, then the result will be a number `x`
    >= ``target`` with only prime factors < `n`. (Also known as `n`-smooth
    numbers)

    Parameters
    ----------
    target : int
        Length to start searching from. Must be a positive integer.
    real : bool, optional
        True if the FFT involves real input or output (e.g., `rfft` or `hfft`
        but not `fft`). Defaults to False.

    Returns
    -------
    out : int
        The smallest fast length greater than or equal to ``target``.

    Notes
    -----
    The result of this function may change in future as performance
    considerations change, for example, if new prime factors are added.

    Calling `fft` or `ifft` with real input data performs an ``'R2C'``
    transform internally.

    Examples
    --------
    On a particular machine, an FFT of prime length takes 11.4 ms:

    >>> from scipy import fft
    >>> import numpy as np
    >>> rng = np.random.default_rng()
    >>> min_len = 93059  # prime length is worst case for speed
    >>> a = rng.standard_normal(min_len)
    >>> b = fft.fft(a)

    Zero-padding to the next regular length reduces computation time to
    1.6 ms, a speedup of 7.3 times:

    >>> fft.next_fast_len(min_len, real=True)
    93312
    >>> b = fft.fft(a, 93312)

    Rounding up to the next power of 2 is not optimal, taking 3.0 ms to
    compute; 1.9 times longer than the size given by ``next_fast_len``:

    >>> b = fft.fft(a, 131072)

    """
    pass


# Directly wrap the c-function good_size but take the docstring etc., from the
# next_fast_len function above
_sig = inspect.signature(next_fast_len)
next_fast_len = update_wrapper(lru_cache(_helper.good_size), next_fast_len)
next_fast_len.__wrapped__ = _helper.good_size
next_fast_len.__signature__ = _sig


def _init_nd_shape_and_axes(x, shape, axes):
    """Handle shape and axes arguments for N-D transforms.

    Returns the shape and axes in a standard form, taking into account negative
    values and checking for various potential errors.

    Parameters
    ----------
    x : array_like
        The input array.
    shape : int or array_like of ints or None
        The shape of the result. If both `shape` and `axes` (see below) are
        None, `shape` is ``x.shape``; if `shape` is None but `axes` is
        not None, then `shape` is ``numpy.take(x.shape, axes, axis=0)``.
        If `shape` is -1, the size of the corresponding dimension of `x` is
        used.
    axes : int or array_like of ints or None
        Axes along which the calculation is computed.
        The default is over all axes.
        Negative indices are automatically converted to their positive
        counterparts.

    Returns
    -------
    shape : tuple
        The shape of the result as a tuple of integers.
    axes : list
        Axes along which the calculation is computed, as a list of integers.

    """
    x = np.asarray(x)
    return _helper._init_nd_shape_and_axes(x, shape, axes)


def fftfreq(n, d=1.0, *, xp=None, device=None):
    """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.
    xp : array_namespace, optional
        The namespace for the return array. Default is None, where NumPy is used.
    device : device, optional
        The device for the return array.
        Only valid when `xp.fft.fftfreq` implements the device parameter.
     
    Returns
    -------
    f : ndarray
        Array of length `n` containing the sample frequencies.

    Examples
    --------
    >>> import numpy as np
    >>> import scipy.fft
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5], dtype=float)
    >>> fourier = scipy.fft.fft(signal)
    >>> n = signal.size
    >>> timestep = 0.1
    >>> freq = scipy.fft.fftfreq(n, d=timestep)
    >>> freq
    array([ 0.  ,  1.25,  2.5 , ..., -3.75, -2.5 , -1.25])

    """
    xp = np if xp is None else xp
    # numpy does not yet support the `device` keyword
    # `xp.__name__ != 'numpy'` should be removed when numpy is compatible
    if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
        return xp.fft.fftfreq(n, d=d, device=device)
    if device is not None:
        raise ValueError('device parameter is not supported for input array type')
    return np.fft.fftfreq(n, d=d)


def rfftfreq(n, d=1.0, *, xp=None, device=None):
    """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.
    xp : array_namespace, optional
        The namespace for the return array. Default is None, where NumPy is used.
    device : device, optional
        The device for the return array.
        Only valid when `xp.fft.rfftfreq` implements the device parameter.

    Returns
    -------
    f : ndarray
        Array of length ``n//2 + 1`` containing the sample frequencies.

    Examples
    --------
    >>> import numpy as np
    >>> import scipy.fft
    >>> signal = np.array([-2, 8, 6, 4, 1, 0, 3, 5, -3, 4], dtype=float)
    >>> fourier = scipy.fft.rfft(signal)
    >>> n = signal.size
    >>> sample_rate = 100
    >>> freq = scipy.fft.fftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20., ..., -30., -20., -10.])
    >>> freq = scipy.fft.rfftfreq(n, d=1./sample_rate)
    >>> freq
    array([  0.,  10.,  20.,  30.,  40.,  50.])

    """
    xp = np if xp is None else xp
    # numpy does not yet support the `device` keyword
    # `xp.__name__ != 'numpy'` should be removed when numpy is compatible
    if hasattr(xp, 'fft') and xp.__name__ != 'numpy':
        return xp.fft.rfftfreq(n, d=d, device=device)
    if device is not None:
        raise ValueError('device parameter is not supported for input array type')
    return np.fft.rfftfreq(n, d=d)


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
    --------
    >>> import numpy as np
    >>> freqs = np.fft.fftfreq(10, 0.1)
    >>> freqs
    array([ 0.,  1.,  2., ..., -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.]])

    """
    xp = array_namespace(x)
    if hasattr(xp, 'fft'):
        return xp.fft.fftshift(x, axes=axes)
    x = np.asarray(x)
    y = np.fft.fftshift(x, axes=axes)
    return xp.asarray(y)


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
    --------
    >>> import numpy as np
    >>> 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.]])

    """
    xp = array_namespace(x)
    if hasattr(xp, 'fft'):
        return xp.fft.ifftshift(x, axes=axes)
    x = np.asarray(x)
    y = np.fft.ifftshift(x, axes=axes)
    return xp.asarray(y)