FLAGLET: Fourier-Laguerre Wavelets on the Ball

DESCRIPTION

The FLAGLET code provides functionality to perform fast and exact wavelet transform on the ball. More details may be found in the extensive documentation.

C INSTALLATION

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

git clone git@github.com:astro-informatics/src_flaglet.git
cd src_flaglet
mkdir build && cd build
cmake .. && make

Following which one can check the installation by running

ctest

within the build directory.

PYTHON INSTALLATION

FLAGLET can easily be installed from PyPi by running

pip install pyflaglet
pip list

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

pip install .

from the root directory, following which the installation can be tested by running

pytest

from the root directory.

MATLAB INSTALLATION

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

BASIC USAGE

First install FLAGLET for python, then you can call it from any python script to perform forward and inverse flaglet transforms and their adjoints by

import pyflaglet as flaglet
import numpy as np

parameters = flaglet.flaglet_parameters(<specify parameters>)

# Create a random complex signal (c indexing)
f_size = flaglet.flaglet_f_dim(parameters)
rng = np.random.default_rng()
f = rng.normal(size=(f_size)) + 1j*rng.normal(size=(f_size))

# Compute e.g. the Forward transform
f_wav, f_scal = flaglet.flaglet_forward(f, parameters)

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},
}

@article{Leistedt:2015:3dlensing,
    author  = {Boris~Leistedt and Jason~D.~McEwen and Thomas~D.~Kitching and Hiranya~V.Peiris},
    title   = {3D weak lensing with spin wavelets on the ball},
    journal = {Physical Review D.},
    year    = 2015,
    volume  = {92},
    number  = {12},
    pages   = {123010},
    doi     = {10.1103/PhysRevD.92.123010},
}

@article{McEwen:2015:3dlensing,
    author  = {Jason~D.~McEwen and Martin~Büttner and Boris~Leistedt and Hiranya~V.Peiris and Yves~Wiaux},
    title   = {A Novel Sampling Theorem on the Rotation Group},
    journal = {IEEE Sig. Proc. Letters},
    year    = 2015,
    volume  = {22},
    number  = {12},
    pages   = {2425-2429},
    doi     = {10.1109/LSP.2015.2490676},
}

@article{McEwen:2015:s2spinwavelets,
    author  = {Jason~D.~McEwen and Boris~Leistedt and Martin~Büttner and Hiranya~V.Peiris and Yves~Wiaux },
    title   = {Directional spin wavelets on the sphere},
    journal = {arXiv e-prints},
    eprint  = {1509.06749},
    year    = 2015,
}

@article{leistedt:2013:s2let,
    title   = {S2LET: A code to perform fast wavelet analysis on the sphere},
    author  = {Boris~Leistedt and Jason~D.~McEwen and Pierre~Vandergheynst and Yves~Wiaux},
    journal = {Astronomy & Astrophysics},
    volume  = {558},
    pages   = {A128},
    year    = 2013,
}

LICENSE

FLAGLET is released under the GPL-3 license (see LICENSE.txt).

FLAGLET 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.