package scipy

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Multidimensional ellipsoid Fourier filter.

The array is multiplied with the fourier transform of a 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. None is returned in this case.

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, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.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()

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. None is returned in this case.

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

Examples -------- >>> from scipy import ndimage, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.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()

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. None is returned in this case.

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

Examples -------- >>> from scipy import ndimage, misc >>> import matplotlib.pyplot as plt >>> import numpy.fft >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.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()

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. None is returned in this case.

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

Examples -------- >>> from scipy import ndimage, misc >>> import numpy.fft >>> import matplotlib.pyplot as plt >>> fig, (ax1, ax2) = plt.subplots(1, 2) >>> plt.gray() # show the filtered result in grayscale >>> ascent = misc.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()

normalize_axis_index(axis, ndim, msg_prefix=None)

Normalizes an axis index, `axis`, such that is a valid positive index into the shape of array with `ndim` dimensions. Raises an AxisError with an appropriate message if this is not possible.

Used internally by all axis-checking logic.

.. versionadded:: 1.13.0

Parameters ---------- axis : int The un-normalized index of the axis. Can be negative ndim : int The number of dimensions of the array that `axis` should be normalized against msg_prefix : str A prefix to put before the message, typically the name of the argument

Returns ------- normalized_axis : int The normalized axis index, such that `0 <= normalized_axis < ndim`

Raises ------ AxisError If the axis index is invalid, when `-ndim <= axis < ndim` is false.

Examples -------- >>> normalize_axis_index(0, ndim=3) 0 >>> normalize_axis_index(1, ndim=3) 1 >>> normalize_axis_index(-1, ndim=3) 2

>>> normalize_axis_index(3, ndim=3) Traceback (most recent call last): ... AxisError: axis 3 is out of bounds for array of dimension 3 >>> normalize_axis_index(-4, ndim=3, msg_prefix='axes_arg') Traceback (most recent call last): ... AxisError: axes_arg: axis -4 is out of bounds for array of dimension 3