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Fast Fourier-Laguerre transform on the ball

Project description


The FLAG code provides functionality to perform fast and exact Fourier-Laguerre and Fourier-Bessel transforms on the ball. More details may be found in the extensive documentation.


First install flag for python by running

pip install pyflag

Then you can call it from python to perform forward and inverse flag transforms and their adjoints by

import pyflag as flag
import numpy as np

L = 10                          # Angular bandlimit
P = 5                           # Radial bandlimit
tau = 1                         # Laguerre scaling factor
spin = 0                        # Spin of signal
reality = 0                     # Real or complex signals

# Create a random complex signal (c indexing)
f = np.random.rand(P, L, 2*L-1) + 1j*np.random.rand(P, L, 2*L-1)
f = f.flatten('C')

# Compute e.g. the Forward transform
flmp = flag.flag_analysis(f, L, tau, P, spin, reality)


B. Leistedt, J. D. McEwen, and M. A. Price


    author  = {Matthew~A.~Price and Jason~D.~McEwen},
    title   = {Bayesian variational regularization on the ball},
    journal = {ArXiv},
    eprint  = {arXiv:2105.05518},
    year    = 2021
    author  = {Boris~Leistedt and Jason~D.~McEwen},
    title   = {Exact Wavelets on the Ball},
    journal = {IEEE Trans. Sig. Proc.},
    year    = 2012,
    volume  = {60},
    number  = {12},
    pages   = {6257-6269},
    doi     = {10.1109/TSP.2012.2215030},
    author  = {Jason~D.~McEwen and Yves~Wiaux},
    title   = {A novel sampling theorem on the
    journal = {IEEE Trans. Sig. Proc.},
    year    = 2011,
    volume  = {59},
    number  = {12},
    pages   = {5876-5887},
    doi     = {10.1109/TSP.2011.2166394},


FLAG package to perform fast wavelet transform on the sphere<br> Copyright (C) 2012 Boris Leistedt & Jason McEwen

This program is free software; you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation; either version 2 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details (LICENSE.txt).

You should have received a copy of the GNU General Public License along with this program; if not, write to the Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

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