Source code for mars.tensor.fft.ihfft

#!/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 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)

    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
            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)