# 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,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
import numpy as np
from ... import opcodes as OperandDef
from ..datasource import tensor as astensor
from .core import TensorFFTMixin, TensorHermitianFFT, validate_fft
class TensorHFFT(TensorHermitianFFT, TensorFFTMixin):
_op_type_ = OperandDef.HFFT
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)
if op.n is not None:
new_shape[op.axis] = op.n
else:
new_shape[op.axis] = 2 * (shape[op.axis] - 1)
return tuple(new_shape)
[docs]def hfft(a, n=None, axis=-1, norm=None):
"""
Compute the FFT of a signal that has Hermitian symmetry, i.e., a real
spectrum.
Parameters
----------
a : array_like
The input tensor.
n : int, optional
Length of the transformed axis of the output. For `n` output
points, ``n//2 + 1`` input points are necessary. If the input is
longer than this, it is cropped. If it is shorter than this, it is
padded with zeros. If `n` is not given, it is determined from the
length of the input along the axis specified by `axis`.
axis : int, optional
Axis over which to compute the FFT. If not given, the last
axis is used.
norm : {None, "ortho"}, optional
Normalization mode (see `mt.fft`). Default is None.
Returns
-------
out : 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`, or, if `n` is not given,
``2*m - 2`` where ``m`` is the length of the transformed axis of
the input. To get an odd number of output points, `n` must be
specified, for instance as ``2*m - 1`` in the typical case,
Raises
------
IndexError
If `axis` is larger than the last axis of `a`.
See also
--------
rfft : Compute the one-dimensional FFT for real input.
ihfft : The inverse of `hfft`.
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
>>> signal = mt.array([1, 2, 3, 4, 3, 2])
>>> mt.fft.fft(signal).execute()
array([ 15.+0.j, -4.+0.j, 0.+0.j, -1.-0.j, 0.+0.j, -4.+0.j])
>>> mt.fft.hfft(signal[:4]).execute() # Input first half of signal
array([ 15., -4., 0., -1., 0., -4.])
>>> mt.fft.hfft(signal, 6).execute() # Input entire signal and truncate
array([ 15., -4., 0., -1., 0., -4.])
>>> signal = mt.array([[1, 1.j], [-1.j, 2]])
>>> (mt.conj(signal.T) - signal).execute() # check Hermitian symmetry
array([[ 0.-0.j, 0.+0.j],
[ 0.+0.j, 0.-0.j]])
>>> freq_spectrum = mt.fft.hfft(signal)
>>> freq_spectrum.execute()
array([[ 1., 1.],
[ 2., -2.]])
"""
a = astensor(a)
validate_fft(a, axis=axis, norm=norm)
op = TensorHFFT(n=n, axis=axis, norm=norm, dtype=np.dtype(np.float_))
return op(a)