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Module « numpy.fft »

Fonction irfftn - module numpy.fft

Signature de la fonction irfftn

def irfftn(a, s=None, axes=None, norm=None, out=None) 

Description

help(numpy.fft.irfftn)

Computes the inverse of `rfftn`.

This function computes the inverse of the N-dimensional discrete
Fourier Transform for real input over any number of axes in an
M-dimensional array 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 array.
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.

    .. versionchanged:: 2.0

        If it is ``-1``, the whole input is used (no padding/trimming).

    If `s` is not given, the shape of the input along the axes
    specified by axes is used. Except for the last axis which is taken to
    be ``2*(m-1)`` where ``m`` is the length of the input along that axis.

    .. deprecated:: 2.0

        If `s` is not ``None``, `axes` must not be ``None`` either.

    .. deprecated:: 2.0

        `s` must contain only ``int`` s, not ``None`` values. ``None``
        values currently mean that the default value for ``n`` is used
        in the corresponding 1-D transform, but this behaviour is
        deprecated.

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.

    .. deprecated:: 2.0

        If `s` is specified, the corresponding `axes` to be transformed
        must be explicitly specified too.

norm : {"backward", "ortho", "forward"}, optional
    Normalization mode (see `numpy.fft`). Default is "backward".
    Indicates which direction of the forward/backward pair of transforms
    is scaled and with what normalization factor.

    .. versionadded:: 1.20.0

        The "backward", "forward" values were added.

out : ndarray, optional
    If provided, the result will be placed in this array. It should be
    of the appropriate shape and dtype for the last transformation.

    .. versionadded:: 2.0.0

Returns
-------
out : ndarray
    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.

The correct interpretation of the hermitian input depends on the shape of
the original data, as given by `s`. This is because each input shape could
correspond to either an odd or even length signal. By default, `irfftn`
assumes an even output length which puts the last entry at the Nyquist
frequency; aliasing with its symmetric counterpart. When performing the
final complex to real transform, the last value is thus treated as purely
real. To avoid losing information, the correct shape of the real input
**must** be given.

Examples
--------
>>> import numpy as np
>>> a = np.zeros((3, 2, 2))
>>> a[0, 0, 0] = 3 * 2 * 2
>>> np.fft.irfftn(a)
array([[[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]],
       [[1.,  1.],
        [1.,  1.]]])

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