Source code for mars.tensor.fft.fft

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2020 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 TensorComplexFFTMixin, validate_fft, TensorStandardFFT

class TensorFFT(TensorStandardFFT, TensorComplexFFTMixin):
    _op_type_ = OperandDef.FFT

    def __init__(self, n=None, axis=-1, norm=None, **kw):
        super().__init__(_n=n, _axis=axis, _norm=norm, **kw)

[docs]def fft(a, n=None, axis=-1, norm=None): """ Compute the one-dimensional discrete Fourier Transform. This function computes the one-dimensional *n*-point discrete Fourier Transform (DFT) with the efficient Fast Fourier Transform (FFT) algorithm [CT]. Parameters ---------- a : array_like Input tensor, can be complex. n : int, optional Length of the transformed axis of the output. 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 FFT. If not given, the last axis is used. norm : {None, "ortho"}, optional Normalization mode (see `mt.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. Raises ------ IndexError if `axes` is larger than the last axis of `a`. See Also -------- mt.fft : for definition of the DFT and conventions used. ifft : The inverse of `fft`. fft2 : The two-dimensional FFT. fftn : The *n*-dimensional FFT. rfftn : The *n*-dimensional FFT of real input. fftfreq : Frequency bins for given FFT parameters. Notes ----- FFT (Fast Fourier Transform) refers to a way the discrete Fourier Transform (DFT) can be calculated efficiently, by using symmetries in the calculated terms. The symmetry is highest when `n` is a power of 2, and the transform is therefore most efficient for these sizes. The DFT is defined, with the conventions used in this implementation, in the documentation for the `numpy.fft` module. References ---------- .. [CT] Cooley, James W., and John W. Tukey, 1965, "An algorithm for the machine calculation of complex Fourier series," *Math. Comput.* 19: 297-301. Examples -------- >>> import mars.tensor as mt >>> mt.fft.fft(mt.exp(2j * mt.pi * mt.arange(8) / 8)).execute() array([-2.33486982e-16+1.14423775e-17j, 8.00000000e+00-6.89018570e-16j, 2.33486982e-16+2.33486982e-16j, 0.00000000e+00+0.00000000e+00j, -1.14423775e-17+2.33486982e-16j, 0.00000000e+00+1.99159850e-16j, 1.14423775e-17+1.14423775e-17j, 0.00000000e+00+0.00000000e+00j]) In this example, real input has an FFT which is Hermitian, i.e., symmetric in the real part and anti-symmetric in the imaginary part, as described in the `numpy.fft` documentation: >>> import matplotlib.pyplot as plt >>> t = mt.arange(256) >>> sp = mt.fft.fft(mt.sin(t)) >>> freq = mt.fft.fftfreq(t.shape[-1]) >>> plt.plot(freq.execute(), sp.real.execute(), freq.execute(), sp.imag.execute()) [<matplotlib.lines.Line2D object at 0x...>, <matplotlib.lines.Line2D object at 0x...>] >>> """ a = astensor(a) validate_fft(a, axis, norm) op = TensorFFT(n=n, axis=axis, norm=norm, dtype=np.dtype(np.complex_)) return op(a)