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298 lines
9.6 KiB
Python
298 lines
9.6 KiB
Python
"""
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Discrete Fourier Transforms - basic.py
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"""
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import numpy as np
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import functools
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from . import pypocketfft as pfft
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from .helper import (_asfarray, _init_nd_shape_and_axes, _datacopied,
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_fix_shape, _fix_shape_1d, _normalization,
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_workers)
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def c2c(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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""" Return discrete Fourier transform of real or complex sequence. """
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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overwrite_x = overwrite_x or _datacopied(tmp, x)
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norm = _normalization(norm, forward)
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workers = _workers(workers)
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if n is not None:
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tmp, copied = _fix_shape_1d(tmp, n, axis)
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overwrite_x = overwrite_x or copied
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elif tmp.shape[axis] < 1:
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raise ValueError("invalid number of data points ({0}) specified"
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.format(tmp.shape[axis]))
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out = (tmp if overwrite_x and tmp.dtype.kind == 'c' else None)
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return pfft.c2c(tmp, (axis,), forward, norm, out, workers)
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fft = functools.partial(c2c, True)
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fft.__name__ = 'fft'
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ifft = functools.partial(c2c, False)
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ifft.__name__ = 'ifft'
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def r2c(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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"""
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Discrete Fourier transform of a real sequence.
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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norm = _normalization(norm, forward)
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workers = _workers(workers)
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if not np.isrealobj(tmp):
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raise TypeError("x must be a real sequence")
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if n is not None:
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tmp, _ = _fix_shape_1d(tmp, n, axis)
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elif tmp.shape[axis] < 1:
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raise ValueError("invalid number of data points ({0}) specified"
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.format(tmp.shape[axis]))
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# Note: overwrite_x is not utilised
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return pfft.r2c(tmp, (axis,), forward, norm, None, workers)
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rfft = functools.partial(r2c, True)
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rfft.__name__ = 'rfft'
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ihfft = functools.partial(r2c, False)
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ihfft.__name__ = 'ihfft'
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def c2r(forward, x, n=None, axis=-1, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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"""
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Return inverse discrete Fourier transform of real sequence x.
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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norm = _normalization(norm, forward)
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workers = _workers(workers)
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# TODO: Optimize for hermitian and real?
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if np.isrealobj(tmp):
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tmp = tmp + 0.j
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# Last axis utilizes hermitian symmetry
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if n is None:
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n = (tmp.shape[axis] - 1) * 2
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if n < 1:
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raise ValueError("Invalid number of data points ({0}) specified"
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.format(n))
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else:
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tmp, _ = _fix_shape_1d(tmp, (n//2) + 1, axis)
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# Note: overwrite_x is not utilized
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return pfft.c2r(tmp, (axis,), n, forward, norm, None, workers)
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hfft = functools.partial(c2r, True)
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hfft.__name__ = 'hfft'
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irfft = functools.partial(c2r, False)
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irfft.__name__ = 'irfft'
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def fft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete Fourier transform.
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return fftn(x, s, axes, norm, overwrite_x, workers)
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def ifft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete inverse Fourier transform of real or complex sequence.
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return ifftn(x, s, axes, norm, overwrite_x, workers)
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def rfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete Fourier transform of a real sequence
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return rfftn(x, s, axes, norm, overwrite_x, workers)
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def irfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete inverse Fourier transform of a real sequence
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return irfftn(x, s, axes, norm, overwrite_x, workers)
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def hfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete Fourier transform of a Hermitian sequence
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return hfftn(x, s, axes, norm, overwrite_x, workers)
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def ihfft2(x, s=None, axes=(-2,-1), norm=None, overwrite_x=False, workers=None,
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*, plan=None):
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"""
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2-D discrete inverse Fourier transform of a Hermitian sequence
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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return ihfftn(x, s, axes, norm, overwrite_x, workers)
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def c2cn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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"""
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Return multidimensional discrete Fourier transform.
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"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
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overwrite_x = overwrite_x or _datacopied(tmp, x)
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workers = _workers(workers)
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if len(axes) == 0:
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return x
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tmp, copied = _fix_shape(tmp, shape, axes)
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overwrite_x = overwrite_x or copied
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norm = _normalization(norm, forward)
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out = (tmp if overwrite_x and tmp.dtype.kind == 'c' else None)
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return pfft.c2c(tmp, axes, forward, norm, out, workers)
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fftn = functools.partial(c2cn, True)
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fftn.__name__ = 'fftn'
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ifftn = functools.partial(c2cn, False)
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ifftn.__name__ = 'ifftn'
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def r2cn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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"""Return multidimensional discrete Fourier transform of real input"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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if not np.isrealobj(tmp):
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raise TypeError("x must be a real sequence")
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shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
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tmp, _ = _fix_shape(tmp, shape, axes)
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norm = _normalization(norm, forward)
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workers = _workers(workers)
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if len(axes) == 0:
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raise ValueError("at least 1 axis must be transformed")
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# Note: overwrite_x is not utilized
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return pfft.r2c(tmp, axes, forward, norm, None, workers)
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rfftn = functools.partial(r2cn, True)
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rfftn.__name__ = 'rfftn'
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ihfftn = functools.partial(r2cn, False)
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ihfftn.__name__ = 'ihfftn'
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def c2rn(forward, x, s=None, axes=None, norm=None, overwrite_x=False,
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workers=None, *, plan=None):
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"""Multidimensional inverse discrete fourier transform with real output"""
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if plan is not None:
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raise NotImplementedError('Passing a precomputed plan is not yet '
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'supported by scipy.fft functions')
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tmp = _asfarray(x)
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# TODO: Optimize for hermitian and real?
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if np.isrealobj(tmp):
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tmp = tmp + 0.j
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noshape = s is None
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shape, axes = _init_nd_shape_and_axes(tmp, s, axes)
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if len(axes) == 0:
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raise ValueError("at least 1 axis must be transformed")
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if noshape:
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shape[-1] = (x.shape[axes[-1]] - 1) * 2
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norm = _normalization(norm, forward)
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workers = _workers(workers)
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# Last axis utilizes hermitian symmetry
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lastsize = shape[-1]
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shape[-1] = (shape[-1] // 2) + 1
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tmp, _ = _fix_shape(tmp, shape, axes)
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# Note: overwrite_x is not utilized
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return pfft.c2r(tmp, axes, lastsize, forward, norm, None, workers)
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hfftn = functools.partial(c2rn, True)
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hfftn.__name__ = 'hfftn'
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irfftn = functools.partial(c2rn, False)
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irfftn.__name__ = 'irfftn'
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def r2r_fftpack(forward, x, n=None, axis=-1, norm=None, overwrite_x=False):
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"""FFT of a real sequence, returning fftpack half complex format"""
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tmp = _asfarray(x)
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overwrite_x = overwrite_x or _datacopied(tmp, x)
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norm = _normalization(norm, forward)
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workers = _workers(None)
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if tmp.dtype.kind == 'c':
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raise TypeError('x must be a real sequence')
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if n is not None:
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tmp, copied = _fix_shape_1d(tmp, n, axis)
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overwrite_x = overwrite_x or copied
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elif tmp.shape[axis] < 1:
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raise ValueError("invalid number of data points ({0}) specified"
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.format(tmp.shape[axis]))
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out = (tmp if overwrite_x else None)
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return pfft.r2r_fftpack(tmp, (axis,), forward, forward, norm, out, workers)
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rfft_fftpack = functools.partial(r2r_fftpack, True)
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rfft_fftpack.__name__ = 'rfft_fftpack'
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irfft_fftpack = functools.partial(r2r_fftpack, False)
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irfft_fftpack.__name__ = 'irfft_fftpack'
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