qttools.fft

source package qttools.fft

Functions

• fft_convolve — Computes the convolution of two arrays using FFT over the first axis (energy axis).

• fft_circular_convolve — Computes the circular convolution of two arrays using the FFT.

• fft_convolve_kpoints — Computes the convolution of two arrays using the FFT.

• fft_correlate_kpoints — Computes the correlation of two arrays using FFT.

source fft_convolve(a: NDArray, b: NDArray) → NDArray

Computes the convolution of two arrays using FFT over the first axis (energy axis).

Parameters

• a : NDArray — First array.

• b : NDArray — Second array.

Returns

• NDArray — The convolution of the two arrays.

source fft_circular_convolve(a: NDArray, b: NDArray, axes: tuple[int]) → NDArray

Computes the circular convolution of two arrays using the FFT.

Parameters

• a : NDArray — First array.

• b : NDArray — Second array.

• axes : tuple[int] — The axes over which to perform the convolution.

Returns

• NDArray — The circular convolution of the two arrays.

source fft_convolve_kpoints(a: NDArray, b: NDArray) → NDArray

Computes the convolution of two arrays using the FFT.

The first axis is assumed to be the energy axis, the other axes are k-points and the last axis is the orbital index.

Over the k-point axes, a circular convolution is performed.

Parameters

• a : NDArray — First array.

• b : NDArray — Second array.

• Returns

• -------

• NDArray — The convolution of the two arrays.

source fft_correlate_kpoints(a: NDArray, b: NDArray) → NDArray

Computes the correlation of two arrays using FFT.

The first axis is assumed to be the energy axis, the other axes are k-points and the last axis is the orbital index.

Over the k-point axes, a circular correlation is performed.

Parameters

• a : NDArray — First array.

• b : NDArray — Second array.

Returns

• NDArray — The cross-correlation of the two arrays.