rfftn_op

→TensorImplPtr

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

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Python wrappers

pylucid.fft.rfftnfunction

N-dimensional real-to-complex DFT.

Computes the DFT of a real signal and stores only the non-redundant half along the last transformed axis (the Hermitian half). The remaining frequencies can be reconstructed by complex conjugation; this storage convention matches numpy.fft.rfftn.

Math

For real input $x$ ,

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

stored over $k_d \in \{0, 1, \dots, N_d/2\}$ only (the last axis is trimmed by Hermitian symmetry; all other axes are stored in full).

Shape

Let L = axes.back(). Then out.shape[L] == n.back() / 2 + 1 when n is supplied, else a.shape[L] / 2 + 1. All other transformed axes follow n (or the input shape).

See Also

irfftn_op : Inverse real DFT. fftn_op : Full complex-to-complex DFT.

Parameters

aTensorImplPtr

Real input tensor (F16/F32).

nvector<int64_t>

Per-axis transform length. Empty means "use input sizes". When supplied, len(n) == len(axes) is required, and the last transformed axis is stored at n.back() / 2 + 1.

axesvector<int>

Axes to transform. Must be non-empty (rfftn requires at least one axis). Negative axes are normalised against the input rank.

Returns

TensorImplPtr

C64 tensor. Shape matches the input except for the last entry of axes, which becomes (n_last) / 2 + 1 where n_last is n.back() (or a.shape[axes.back()] when n is empty).

Raises

LucidError

If a is null, has a non-real dtype, 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). The Python wrapper must remember the original last axis size to disambiguate the inverse.