irfftn_op

→TensorImplPtr

int irfftn_op(const int & a, const int & n, const int & axes)

source edit

Python wrappers

pylucid.fft.irfftnfunction

N-dimensional inverse real DFT (complex Hermitian-half to real).

Reconstructs the real signal from a Hermitian-half spectrum produced by rfftn. The last transformed axis is expanded from the stored length $n_{\text{last}}/2 + 1$ back to $n_{\text{last}}$ . Uses the "backward" normalisation convention (divides by $\prod_j N_j$ ).

Math

x[n_1, \dots, n_d] = \frac{1}{\prod_j N_j} \sum_{k_1=0}^{N_1-1} \cdots \sum_{k_d=0}^{N_d-1} X[k_1, \dots, k_d] \, \exp\!\left( +2\pi i \sum_{j=1}^{d} \frac{k_j n_j}{N_j} \right) ,

reconstructed assuming $X$ is Hermitian-symmetric along the last transformed axis ( $X[\dots, N_d - k_d] = \overline{X[\dots, k_d]}$ ).

Shape

out.shape[axes[i]] == n[i] when n is supplied; otherwise out.shape[axes.back()] == 2 * (a.shape[axes.back()] - 1) and other transformed axes are unchanged.

See Also

rfftn_op : Forward real-input DFT. ifftn_op : Inverse of full complex-to-complex DFT.

Parameters

aTensorImplPtr

Complex input (C64), shaped as the output of rfftn.

nvector<int64_t>

Per-axis transform length. The last entry specifies the original real-input length along axes.back(); when n is empty, the default 2 * (a.shape[axes.back()] - 1) is used.

axesvector<int>

Axes to transform. Must be non-empty. Negative values are normalised against the input rank.

Returns

TensorImplPtr

F32 tensor. Shape follows a except that axes[i] is replaced by n[i] (with the default applied to the last axis when n is empty).

Raises

LucidError

If a is null, not C64, axes is empty, or len(n) != len(axes) when n is non-empty.

Notes

FFT bypasses IBackend dispatch and calls MLX directly (see _Detail.h). When the original real length was odd, n.back() must be supplied explicitly — the default formula assumes even length.