rfftn

rfftn(x: array, /, *, s: Sequence[int] | None = None, axes: Sequence[int] | None = None, norm: Literal['backward', 'ortho', 'forward'] = 'backward') → array

Computes the n-dimensional discrete Fourier transform for real-valued input.

Note

Applying the n-dimensional inverse discrete Fourier transform for real-valued input to the output of this function must return the original (i.e., non-transformed) input array within numerical accuracy (i.e., irfftn(rfftn(x)) == x), provided that the transform and inverse transform are performed with the same arguments (axes and normalization mode) and consistent sizes.

Parameters:

  • x (array) – input array. Must have a real-valued floating-point data type.

  • s (Optional[Sequence[int]]) –

    number of elements over which to compute the transform along axes (dimensions) specified by axes. Let i be the index of the n-th axis specified by axes (i.e., i = axes[n]) and M[i] be the size of the input array along axis i. When s is None, the function must set s equal to a sequence of integers such that s[i] equals M[i] for all i.

    • If s[i] is greater than M[i], axis i must be zero-padded to size s[i].

    • If s[i] is less than M[i], axis i must be trimmed to size s[i].

    • If s[i] equals M[i] or -1, all elements along axis i must be used when computing the transform.

    If s is not None, axes must not be None. Default: None.

  • axes (Optional[Sequence[int]]) –

    axes (dimensions) over which to compute the transform. A valid axis in axes must be an integer on the interval [-N, N), where N is the rank (number of dimensions) of x. If an axis is specified as a negative integer, the function must determine the axis along which to compute the transform by counting backward from the last dimension (where -1 refers to the last dimension).

    If s is provided, the corresponding axes to be transformed must also be provided. If axes is None, the function must compute the transform over all axes. Default: None.

    If axes contains two or more entries which resolve to the same axis (i.e., resolved axes are not unique), the behavior is unspecified and thus implementation-defined.

  • norm (Literal['backward', 'ortho', 'forward']) –

    normalization mode. Should be one of the following modes:

    • 'backward': no normalization.

    • 'ortho': normalize by 1/sqrt(n) (i.e., make the FFT orthonormal).

    • 'forward': normalize by 1/n.

    where n = prod(s), the logical FFT size.

    Default: 'backward'.

Returns:

out (array) – an array transformed along the axes (dimension) specified by axes. The returned array must have a complex floating-point data type whose precision matches the precision of x (e.g., if x is float64, then the returned array must have a complex128 data type). The returned array must have the same shape as x, except for the last transformed axis which must have size s[-1]//2 + 1 and the remaining transformed axes which must have size s[i].

Notes

New in version 2022.12.