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fourier_shiftc � � | �v|j j t j t j t j fv r!t j |j |j �� � } n�t j |j t j �� � } n�t | � � t u r[| t j t j t j t j fvrt d� � �t j |j | �� � } n | j |j k rt d� � �| S �N��dtypezoutput type not supportedzoutput shape not correct)
r �type�numpy� complex64�
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�f� � �� � � �%�/�5�+;�<� <� <� � :�;�;� ;���U�[��7�7�7��� � ��� $� $��5�6�6�6� �Mr ���c �^ � t j | � � } t || � � }t || j � � }t j || j � � }t j |t j �� � }|j j s|�
� � }t j | ||||d� � |S )a
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()
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� �U�F�A�t�V�Q�?�?�?� �Mr c �^ � t j | � � } t || � � }t || j � � }t j || j � � }t j |t j �� � }|j j s|�
� � }t j | ||||d� � |S )a
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()
r
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|| j � � }t j || j � � }t j |t j �� � }|j
j s|� � � }t j | ||||d� � |S )ah
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()
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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()
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