Source code for mars.tensor.fft.irfftn

#!/usr/bin/env python
# -*- coding: utf-8 -*-
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# Licensed under the Apache License, Version 2.0 (the "License");
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#      http://www.apache.org/licenses/LICENSE-2.0
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import numpy as np

from ... import opcodes as OperandDef
from ..datasource import tensor as astensor
from .core import TensorRealIFFTNMixin, validate_fftn, TensorRealFFTN


class TensorIRFFTN(TensorRealFFTN, TensorRealIFFTNMixin):
    _op_type_ = OperandDef.IRFFTN

    def __init__(self, shape=None, axes=None, norm=None, **kw):
        super().__init__(_shape=shape, _axes=axes, _norm=norm, **kw)


[docs]def irfftn(a, s=None, axes=None, norm=None): """ Compute the inverse of the N-dimensional FFT of real input. This function computes the inverse of the N-dimensional discrete Fourier Transform for real input over any number of axes in an M-dimensional tensor by means of the Fast Fourier Transform (FFT). In other words, ``irfftn(rfftn(a), a.shape) == a`` to within numerical accuracy. (The ``a.shape`` is necessary like ``len(a)`` is for `irfft`, and for the same reason.) The input should be ordered in the same way as is returned by `rfftn`, i.e. as for `irfft` for the final transformation axis, and as for `ifftn` along all the other axes. Parameters ---------- a : array_like Input tensor. s : sequence of ints, optional Shape (length of each transformed axis) of the output (``s[0]`` refers to axis 0, ``s[1]`` to axis 1, etc.). `s` is also the number of input points used along this axis, except for the last axis, where ``s[-1]//2+1`` points of the input are used. Along any axis, if the shape indicated by `s` is smaller than that of the input, the input is cropped. If it is larger, the input is padded with zeros. If `s` is not given, the shape of the input along the axes specified by `axes` is used. axes : sequence of ints, optional Axes over which to compute the inverse FFT. If not given, the last `len(s)` axes are used, or all axes if `s` is also not specified. Repeated indices in `axes` means that the inverse transform over that axis is performed multiple times. norm : {None, "ortho"}, optional Normalization mode (see `mt.fft`). Default is None. Returns ------- out : Tensor The truncated or zero-padded input, transformed along the axes indicated by `axes`, or by a combination of `s` or `a`, as explained in the parameters section above. The length of each transformed axis is as given by the corresponding element of `s`, or the length of the input in every axis except for the last one if `s` is not given. In the final transformed axis the length of the output when `s` is not given is ``2*(m-1)`` where ``m`` is the length of the final transformed axis of the input. To get an odd number of output points in the final axis, `s` must be specified. Raises ------ ValueError If `s` and `axes` have different length. IndexError If an element of `axes` is larger than than the number of axes of `a`. See Also -------- rfftn : The forward n-dimensional FFT of real input, of which `ifftn` is the inverse. fft : The one-dimensional FFT, with definitions and conventions used. irfft : The inverse of the one-dimensional FFT of real input. irfft2 : The inverse of the two-dimensional FFT of real input. Notes ----- See `fft` for definitions and conventions used. See `rfft` for definitions and conventions used for real input. Examples -------- >>> import mars.tensor as mt >>> a = mt.zeros((3, 2, 2)) >>> a[0, 0, 0] = 3 * 2 * 2 >>> mt.fft.irfftn(a).execute() array([[[ 1., 1.], [ 1., 1.]], [[ 1., 1.], [ 1., 1.]], [[ 1., 1.], [ 1., 1.]]]) """ a = astensor(a) axes = validate_fftn(a, s=s, axes=axes, norm=norm) op = TensorIRFFTN(shape=s, axes=axes, norm=norm, dtype=np.dtype(np.float_)) return op(a)