# Source code for mars.tensor.fft.ifft

```#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Copyright 1999-2021 Alibaba Group Holding Ltd.
#
# 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
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and

import numpy as np

from ... import opcodes as OperandDef
from ..datasource import tensor as astensor
from .core import TensorComplexFFTMixin, validate_fft, TensorStandardFFT

class TensorIFFT(TensorStandardFFT, TensorComplexFFTMixin):
_op_type_ = OperandDef.IFFT

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

[docs]def ifft(a, n=None, axis=-1, norm=None):
"""
Compute the one-dimensional inverse discrete Fourier Transform.

This function computes the inverse of the one-dimensional *n*-point
discrete Fourier transform computed by `fft`.  In other words,
``ifft(fft(a)) == a`` to within numerical accuracy.
For a general description of the algorithm and definitions,
see `mt.fft`.

The input should be ordered in the same way as is returned by `fft`,
i.e.,

* ``a[0]`` should contain the zero frequency term,
* ``a[1:n//2]`` should contain the positive-frequency terms,
* ``a[n//2 + 1:]`` should contain the negative-frequency terms, in
increasing order starting from the most negative frequency.

For an even number of input points, ``A[n//2]`` represents the sum of
the values at the positive and negative Nyquist frequencies, as the two
are aliased together. See `numpy.fft` for details.

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 inverse DFT.  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.

Raises
------
IndexError
If `axes` is larger than the last axis of `a`.

--------
mt.fft : An introduction, with definitions and general explanations.
fft : The one-dimensional (forward) FFT, of which `ifft` is the inverse
ifft2 : The two-dimensional inverse FFT.
ifftn : The n-dimensional inverse FFT.

Notes
-----
If the input parameter `n` is larger than the size of the input, the input
is padded by appending zeros at the end.  Even though this is the common
approach, it might lead to surprising results.  If a different padding is
desired, it must be performed before calling `ifft`.

Examples
--------
>>> import mars.tensor as mt

>>> mt.fft.ifft([0, 4, 0, 0]).execute()
array([ 1.+0.j,  0.+1.j, -1.+0.j,  0.-1.j])

Create and plot a band-limited signal with random phases:

>>> import matplotlib.pyplot as plt
>>> t = mt.arange(400)
>>> n = mt.zeros((400,), dtype=complex)
>>> n[40:60] = mt.exp(1j*mt.random.uniform(0, 2*mt.pi, (20,)))
>>> s = mt.fft.ifft(n)
>>> plt.plot(t.execute(), s.real.execute(), 'b-', t.execute(), s.imag.execute(), 'r--')
...
>>> plt.legend(('real', 'imaginary'))
...
>>> plt.show()

"""
a = astensor(a)
validate_fft(a, axis, norm)
op = TensorIFFT(n=n, axis=axis, norm=norm, dtype=np.dtype(np.complex_))
return op(a)
```