# maxframe.tensor.fft.irfftn

### maxframe.tensor.fft.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** – 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.
* **Return type:**
  Tensor
* **Raises:**
  * [**ValueError**](https://docs.python.org/3/library/exceptions.html#ValueError) – If s and axes have different length.
  * [**IndexError**](https://docs.python.org/3/library/exceptions.html#IndexError) – If an element of axes is larger than than the number of axes of a.

#### SEE ALSO
[`rfftn`](maxframe.tensor.fft.rfftn.md#maxframe.tensor.fft.rfftn)
: The forward n-dimensional FFT of real input, of which ifftn is the inverse.

[`fft`](maxframe.tensor.fft.fft.md#maxframe.tensor.fft.fft)
: The one-dimensional FFT, with definitions and conventions used.

[`irfft`](maxframe.tensor.fft.irfft.md#maxframe.tensor.fft.irfft)
: The inverse of the one-dimensional FFT of real input.

[`irfft2`](maxframe.tensor.fft.irfft2.md#maxframe.tensor.fft.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

```pycon
>>> import maxframe.tensor as mt
```

```pycon
>>> 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.]]])
```
