Source code for mars.tensor.fft.hfft

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# 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
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# 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, validate_fft, TensorHermitianFFT

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)

    def _get_shape(cls, op, shape):
        new_shape = list(shape)
        if op.n is not None:
            new_shape[op.axis] = op.n
            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)