FFT Computations

Source Code: FFT

FFT.py
 1# Copyright (C) 2025 Sukanta Basu
 2#
 3# This program is free software: you can redistribute it and/or modify
 4# it under the terms of the GNU General Public License as published by
 5# the Free Software Foundation, either version 3 of the License, or
 6# (at your option) any later version.
 7#
 8# This program is distributed in the hope that it will be useful,
 9# but WITHOUT ANY WARRANTY; without even the implied warranty of
10# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
11# GNU General Public License for more details.
12#
13# You should have received a copy of the GNU General Public License
14# along with this program.  If not, see <https://www.gnu.org/licenses/>.
15
16"""
17File: FFT.py
18==================
19
20:Author: Sukanta Basu
21:AI Assistance: Claude Code (Anthropic) and Codex (OpenAI) are used for documentation,
22                code restructuring, and performance optimization
23:Date: 2025-4-3
24:Description: performs FFT-based operations using JAX
25"""
26
27# ============================================================
28#  Imports
29# ============================================================
30
31import jax
32import jax.numpy as jnp
33
34from ..initialization.Preprocess import Constant
35mx, my, nx_rfft, ny_rfft, mx_rfft, my_rfft = Constant()
36
37
38# ============================================================
39#  Compute real fft of a variable F
40# ============================================================
41
42
43@jax.jit
44def FFT(F):
45    """
46    Parameters:
47    -----------
48    F : ndarray
49        3D input field with shape (nx, ny, nz)
50
51    Returns:
52    --------
53    F_fft : ndarray in Jax format
54        rfft2 of a field
55    """
56
57    F_fft = jnp.fft.rfft2(F, axes=(0, 1))
58
59    return F_fft
60
61
62# ============================================================
63#  Compute real fft of a padded variable F_pad
64# ============================================================
65
66
67@jax.jit
68def FFT_pad(F_pad):
69    """
70    Parameters:
71    -----------
72    F_pad : ndarray with shape (mx=1.5*nx, my=1.5*ny, nz)
73        3D input field
74
75    Returns:
76    --------
77    F_pad_fft : ndarray in Jax format
78        rfft2 of a padded field
79    """
80
81    # Compute 2D real FFT along x and y axes
82    F_pad_fft = jnp.fft.rfft2(F_pad, axes=(0, 1))
83
84    return F_pad_fft