FLAG: Fourier-LAGuerre transform

DESCRIPTION

The FLAG code provides functionality to perform fast and exact Fourier-Laguerre and Fourier-Bessel transforms on the ball.

C INSTALLATION

The primary C version of this code can be installed from source by running

git clone [email protected]:astro-informatics/src_flag.git
cd src_flag
mkdir build && cd build
cmake .. && make

Following which one can check the installation by running

ctest

within the build directory.

PYTHON INSTALLATION

FLAG can easily be installed from PyPi by running

pip install pyflag
pip list

or alternatively from source by first compiling the C code and running

pip install .

from the root directory, following which the package may be tested by running

pytest

within the root directory.

MATLAB INSTALLATION

Mex wrappers are available, however they are currently being sunsetted, so installing previously tagged versions is advised.

BASIC USAGE (PYTHON)

First install FLAG for python, then you can call it from any python script 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)

AUTHORS

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

REFERENCES

@article{price:2021:bayesian,
    author  = {Matthew~A.~Price and Jason~D.~McEwen},
    title   = {Bayesian variational regularization on the ball},
    journal = {ArXiv},
    eprint  = {arXiv:2105.05518},
    year    = 2021
}

@article{leistedt:2012:exact,
    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},
}

@article{McEwen:2011:novel,
    author  = {Jason~D.~McEwen and Yves~Wiaux},
    title   = {A novel sampling theorem on the sphere},
    journal = {IEEE Trans. Sig. Proc.},
    year    = 2011,
    volume  = {59},
    number  = {12},
    pages   = {5876-5887},
    doi     = {10.1109/TSP.2011.2166394},
}

LICENSE

FLAG package to perform fast wavelet transform on the sphere<br>
Copyright (C) 2021 Boris Leistedt & Jason McEwen & Matthew Price

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.