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