Vehicle-cpp/hkpc/software/scipy/ndimage/_fourier.py

# Copyright (C) 2003-2005 Peter J. Verveer
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import numpy
from numpy.core.multiarray import normalize_axis_index
from . import _ni_support
from . import _nd_image

__all__ = ['fourier_gaussian', 'fourier_uniform', 'fourier_ellipsoid',
           'fourier_shift']


def _get_output_fourier(output, input):
    if output is None:
        if input.dtype.type in [numpy.complex64, numpy.complex128,
                                numpy.float32]:
            output = numpy.zeros(input.shape, dtype=input.dtype)
        else:
            output = numpy.zeros(input.shape, dtype=numpy.float64)
    elif type(output) is type:
        if output not in [numpy.complex64, numpy.complex128,
                          numpy.float32, numpy.float64]:
            raise RuntimeError("output type not supported")
        output = numpy.zeros(input.shape, dtype=output)
    elif output.shape != input.shape:
        raise RuntimeError("output shape not correct")
    return output


def _get_output_fourier_complex(output, input):
    if output is None:
        if input.dtype.type in [numpy.complex64, numpy.complex128]:
            output = numpy.zeros(input.shape, dtype=input.dtype)
        else:
            output = numpy.zeros(input.shape, dtype=numpy.complex128)
    elif type(output) is type:
        if output not in [numpy.complex64, numpy.complex128]:
            raise RuntimeError("output type not supported")
        output = numpy.zeros(input.shape, dtype=output)
    elif output.shape != input.shape:
        raise RuntimeError("output shape not correct")
    return output


def fourier_gaussian(input, sigma, n=-1, axis=-1, output=None):
    """
    Multidimensional Gaussian fourier filter.

    The array is multiplied with the fourier transform of a Gaussian
    kernel.

    Parameters
    ----------
    input : array_like
        The input array.
    sigma : float or sequence
        The sigma of the Gaussian kernel. If a float, `sigma` is the same for
        all axes. If a sequence, `sigma` has to contain one value for each
        axis.
    n : int, optional
        If `n` is negative (default), then the input is assumed to be the
        result of a complex fft.
        If `n` is larger than or equal to zero, the input is assumed to be the
        result of a real fft, and `n` gives the length of the array before
        transformation along the real transform direction.
    axis : int, optional
        The axis of the real transform.
    output : ndarray, optional
        If given, the result of filtering the input is placed in this array.

    Returns
    -------
    fourier_gaussian : ndarray
        The filtered input.

    Examples
    --------
    >>> from scipy import ndimage, datasets
    >>> import numpy.fft
    >>> import matplotlib.pyplot as plt
    >>> fig, (ax1, ax2) = plt.subplots(1, 2)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> ascent = datasets.ascent()
    >>> input_ = numpy.fft.fft2(ascent)
    >>> result = ndimage.fourier_gaussian(input_, sigma=4)
    >>> result = numpy.fft.ifft2(result)
    >>> ax1.imshow(ascent)
    >>> ax2.imshow(result.real)  # the imaginary part is an artifact
    >>> plt.show()
    """
    input = numpy.asarray(input)
    output = _get_output_fourier(output, input)
    axis = normalize_axis_index(axis, input.ndim)
    sigmas = _ni_support._normalize_sequence(sigma, input.ndim)
    sigmas = numpy.asarray(sigmas, dtype=numpy.float64)
    if not sigmas.flags.contiguous:
        sigmas = sigmas.copy()

    _nd_image.fourier_filter(input, sigmas, n, axis, output, 0)
    return output


def fourier_uniform(input, size, n=-1, axis=-1, output=None):
    """
    Multidimensional uniform fourier filter.

    The array is multiplied with the Fourier transform of a box of given
    size.

    Parameters
    ----------
    input : array_like
        The input array.
    size : float or sequence
        The size of the box used for filtering.
        If a float, `size` is the same for all axes. If a sequence, `size` has
        to contain one value for each axis.
    n : int, optional
        If `n` is negative (default), then the input is assumed to be the
        result of a complex fft.
        If `n` is larger than or equal to zero, the input is assumed to be the
        result of a real fft, and `n` gives the length of the array before
        transformation along the real transform direction.
    axis : int, optional
        The axis of the real transform.
    output : ndarray, optional
        If given, the result of filtering the input is placed in this array.

    Returns
    -------
    fourier_uniform : ndarray
        The filtered input.

    Examples
    --------
    >>> from scipy import ndimage, datasets
    >>> import numpy.fft
    >>> import matplotlib.pyplot as plt
    >>> fig, (ax1, ax2) = plt.subplots(1, 2)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> ascent = datasets.ascent()
    >>> input_ = numpy.fft.fft2(ascent)
    >>> result = ndimage.fourier_uniform(input_, size=20)
    >>> result = numpy.fft.ifft2(result)
    >>> ax1.imshow(ascent)
    >>> ax2.imshow(result.real)  # the imaginary part is an artifact
    >>> plt.show()
    """
    input = numpy.asarray(input)
    output = _get_output_fourier(output, input)
    axis = normalize_axis_index(axis, input.ndim)
    sizes = _ni_support._normalize_sequence(size, input.ndim)
    sizes = numpy.asarray(sizes, dtype=numpy.float64)
    if not sizes.flags.contiguous:
        sizes = sizes.copy()
    _nd_image.fourier_filter(input, sizes, n, axis, output, 1)
    return output


def fourier_ellipsoid(input, size, n=-1, axis=-1, output=None):
    """
    Multidimensional ellipsoid Fourier filter.

    The array is multiplied with the fourier transform of an ellipsoid of
    given sizes.

    Parameters
    ----------
    input : array_like
        The input array.
    size : float or sequence
        The size of the box used for filtering.
        If a float, `size` is the same for all axes. If a sequence, `size` has
        to contain one value for each axis.
    n : int, optional
        If `n` is negative (default), then the input is assumed to be the
        result of a complex fft.
        If `n` is larger than or equal to zero, the input is assumed to be the
        result of a real fft, and `n` gives the length of the array before
        transformation along the real transform direction.
    axis : int, optional
        The axis of the real transform.
    output : ndarray, optional
        If given, the result of filtering the input is placed in this array.

    Returns
    -------
    fourier_ellipsoid : ndarray
        The filtered input.

    Notes
    -----
    This function is implemented for arrays of rank 1, 2, or 3.

    Examples
    --------
    >>> from scipy import ndimage, datasets
    >>> import numpy.fft
    >>> import matplotlib.pyplot as plt
    >>> fig, (ax1, ax2) = plt.subplots(1, 2)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> ascent = datasets.ascent()
    >>> input_ = numpy.fft.fft2(ascent)
    >>> result = ndimage.fourier_ellipsoid(input_, size=20)
    >>> result = numpy.fft.ifft2(result)
    >>> ax1.imshow(ascent)
    >>> ax2.imshow(result.real)  # the imaginary part is an artifact
    >>> plt.show()
    """
    input = numpy.asarray(input)
    if input.ndim > 3:
        raise NotImplementedError("Only 1d, 2d and 3d inputs are supported")
    output = _get_output_fourier(output, input)
    if output.size == 0:
        # The C code has a bug that can result in a segfault with arrays
        # that have size 0 (gh-17270), so check here.
        return output
    axis = normalize_axis_index(axis, input.ndim)
    sizes = _ni_support._normalize_sequence(size, input.ndim)
    sizes = numpy.asarray(sizes, dtype=numpy.float64)
    if not sizes.flags.contiguous:
        sizes = sizes.copy()
    _nd_image.fourier_filter(input, sizes, n, axis, output, 2)
    return output


def fourier_shift(input, shift, n=-1, axis=-1, output=None):
    """
    Multidimensional Fourier shift filter.

    The array is multiplied with the Fourier transform of a shift operation.

    Parameters
    ----------
    input : array_like
        The input array.
    shift : float or sequence
        The size of the box used for filtering.
        If a float, `shift` is the same for all axes. If a sequence, `shift`
        has to contain one value for each axis.
    n : int, optional
        If `n` is negative (default), then the input is assumed to be the
        result of a complex fft.
        If `n` is larger than or equal to zero, the input is assumed to be the
        result of a real fft, and `n` gives the length of the array before
        transformation along the real transform direction.
    axis : int, optional
        The axis of the real transform.
    output : ndarray, optional
        If given, the result of shifting the input is placed in this array.

    Returns
    -------
    fourier_shift : ndarray
        The shifted input.

    Examples
    --------
    >>> from scipy import ndimage, datasets
    >>> import matplotlib.pyplot as plt
    >>> import numpy.fft
    >>> fig, (ax1, ax2) = plt.subplots(1, 2)
    >>> plt.gray()  # show the filtered result in grayscale
    >>> ascent = datasets.ascent()
    >>> input_ = numpy.fft.fft2(ascent)
    >>> result = ndimage.fourier_shift(input_, shift=200)
    >>> result = numpy.fft.ifft2(result)
    >>> ax1.imshow(ascent)
    >>> ax2.imshow(result.real)  # the imaginary part is an artifact
    >>> plt.show()
    """
    input = numpy.asarray(input)
    output = _get_output_fourier_complex(output, input)
    axis = normalize_axis_index(axis, input.ndim)
    shifts = _ni_support._normalize_sequence(shift, input.ndim)
    shifts = numpy.asarray(shifts, dtype=numpy.float64)
    if not shifts.flags.contiguous:
        shifts = shifts.copy()
    _nd_image.fourier_shift(input, shifts, n, axis, output)
    return output