/
fourier.py
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/
fourier.py
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# Copyright (C) 2003-2005 Peter J. Verveer
#
# Redistribution and use in source and binary forms, with or without
# modification, are permitted provided that the following conditions
# are met:
#
# 1. Redistributions of source code must retain the above copyright
# notice, this list of conditions and the following disclaimer.
#
# 2. Redistributions in binary form must reproduce the above
# copyright notice, this list of conditions and the following
# disclaimer in the documentation and/or other materials provided
# with the distribution.
#
# 3. The name of the author may not be used to endorse or promote
# products derived from this software without specific prior
# written permission.
#
# THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
# OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
# WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
# DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE
# GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY,
# WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
# NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
# SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
from __future__ import division, print_function, absolute_import
import numpy
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)
return_value = output
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)
return_value = output
else:
if output.shape != input.shape:
raise RuntimeError("output shape not correct")
return_value = None
return output, return_value
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)
return_value = output
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)
return_value = output
else:
if output.shape != input.shape:
raise RuntimeError("output shape not correct")
return_value = None
return output, return_value
def fourier_gaussian(input, sigma, n=-1, axis=-1, output=None):
"""
Multi-dimensional 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 or None
The filtered input. If `output` is given as a parameter, None is
returned.
"""
input = numpy.asarray(input)
output, return_value = _get_output_fourier(output, input)
axis = _ni_support._check_axis(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 return_value
def fourier_uniform(input, size, n=-1, axis=-1, output=None):
"""
Multi-dimensional 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 or None
The filtered input. If `output` is given as a parameter, None is
returned.
"""
input = numpy.asarray(input)
output, return_value = _get_output_fourier(output, input)
axis = _ni_support._check_axis(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 return_value
def fourier_ellipsoid(input, size, n=-1, axis=-1, output=None):
"""
Multi-dimensional 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 or None
The filtered input. If `output` is given as a parameter, None is
returned.
Notes
-----
This function is implemented for arrays of rank 1, 2, or 3.
"""
input = numpy.asarray(input)
output, return_value = _get_output_fourier(output, input)
axis = _ni_support._check_axis(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 return_value
def fourier_shift(input, shift, n=-1, axis=-1, output=None):
"""
Multi-dimensional 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 or None
The shifted input. If `output` is given as a parameter, None is
returned.
"""
input = numpy.asarray(input)
output, return_value = _get_output_fourier_complex(output, input)
axis = _ni_support._check_axis(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 return_value