https://github.com/astro-informatics/src_flaglet

Fast and exact wavelet transform on the 3-dimensional ball

https://github.com/astro-informatics/src_flaglet

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Fast and exact wavelet transform on the 3-dimensional ball

README.rst

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|logo| FLAGLET: Fourier-Laguerre Wavelets on the Ball
=====================================================

.. |logo| raw:: html

   

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

.. code-block:: bash

     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

.. code-block:: bash

     ctest

within the build directory.

PYTHON INSTALLATION
================================
``FLAGLET`` can easily be installed from PyPi by running

.. code-block:: bash

    pip install pyflaglet
    pip list

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

.. code-block:: bash 

    pip install .

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

.. code-block:: bash 

     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 

.. code-block:: python

    import pyflaglet as flaglet
    import numpy as np 

    parameters = flaglet.flaglet_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
================================

.. code-block::

    @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
    }

.. code-block::

    @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},
    }

.. code-block::

    @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},
    }

.. code-block::

    @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},
    }

.. code-block::

    @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},
    }

.. code-block::

    @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,
    }

.. code-block::

    @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 `_).

.. code-block::

     FLAGLET package to perform fast wavelet transform on the sphere

     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.

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