# Copyright 2022-2023 XProbe Inc.
# derived from copyright 1999-2021 Alibaba Group Holding Ltd.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
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import numpy as np
from ... import opcodes as OperandDef
from ..datasource import tensor as astensor
from .core import TensorFFTMixin, TensorHermitianFFT, validate_fft
class TensorIHFFT(TensorHermitianFFT, TensorFFTMixin):
_op_type_ = OperandDef.IHFFT
def __init__(self, n=None, axis=-1, norm=None, **kw):
super().__init__(_n=n, _axis=axis, _norm=norm, **kw)
@classmethod
def _get_shape(cls, op, shape):
new_shape = list(shape)
shape = op.n if op.n is not None else shape[op.axis]
if shape % 2 == 0:
shape = (shape // 2) + 1
else:
shape = (shape + 1) // 2
new_shape[op.axis] = shape
return tuple(new_shape)
[docs]def ihfft(a, n=None, axis=-1, norm=None):
"""
Compute the inverse FFT of a signal that has Hermitian symmetry.
Parameters
----------
a : array_like
Input tensor.
n : int, optional
Length of the inverse FFT, the number of points along
transformation axis in the input to use. If `n` is smaller than
the length of the input, the input is cropped. If it is larger,
the input is padded with zeros. If `n` is not given, the length of
the input along the axis specified by `axis` is used.
axis : int, optional
Axis over which to compute the inverse FFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
Normalization mode (see `numpy.fft`). Default is None.
Returns
-------
out : complex Tensor
The truncated or zero-padded input, transformed along the axis
indicated by `axis`, or the last one if `axis` is not specified.
The length of the transformed axis is ``n//2 + 1``.
See also
--------
hfft, irfft
Notes
-----
`hfft`/`ihfft` are a pair analogous to `rfft`/`irfft`, but for the
opposite case: here the signal has Hermitian symmetry in the time
domain and is real in the frequency domain. So here it's `hfft` for
which you must supply the length of the result if it is to be odd:
* even: ``ihfft(hfft(a, 2*len(a) - 2) == a``, within roundoff error,
* odd: ``ihfft(hfft(a, 2*len(a) - 1) == a``, within roundoff error.
Examples
--------
>>> import mars.tensor as mt
>>> spectrum = mt.array([ 15, -4, 0, -1, 0, -4])
>>> mt.fft.ifft(spectrum).execute()
array([ 1.+0.j, 2.-0.j, 3.+0.j, 4.+0.j, 3.+0.j, 2.-0.j])
>>> mt.fft.ihfft(spectrum).execute()
array([ 1.-0.j, 2.-0.j, 3.-0.j, 4.-0.j])
"""
a = astensor(a)
validate_fft(a, axis=axis, norm=norm)
op = TensorIHFFT(n=n, axis=axis, norm=norm, dtype=np.dtype(np.complex_))
return op(a)