Math::Libgsl::Wavelet

An interface to libgsl, the Gnu Scientific Library - Wavelet Transform

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NAME

Math::Libgsl::Wavelet - An interface to libgsl, the Gnu Scientific Library - Wavelet Transform

SYNOPSIS

use Math::Libgsl::Wavelet;
use Math::Libgsl::Constants;

constant \N    = 256;
constant \kind =   4;

my @data;
for ^N X ^N -> ($i, $j) {
  @data[$i * N + $j] = ($i * N + $j).Num / (N * N);
}

my Math::Libgsl::Wavelet $w .= new: DAUBECHIES, kind;
my @fdata = $w.forward2d(@data);

DESCRIPTION

Math::Libgsl::Wavelet is an interface to the Wavelet Transform functions of libgsl, the Gnu Scientific Library.

new(UInt:D variant!)

new(UInt:D :variant!)

The constructor accepts two simple or named arguments: the type of wavelet function and the specific member of the wavelet family.

The available wavelet functions are:

DAUBECHIES
DAUBECHIES_CENTERED
HAAR
HAAR_CENTERED
BSPLINE
BSPLINE_CENTERED

There are two methods for dealing with 1D transforms (direct and inverse):

forward1d(@data, UInt:D _ < @data.elems / 2 } = 1, UInt:D _) } = @data.elems --> List)

Forward 1D transform.

The @data array is the only mandatory argument. The array may be larger than the set of values that one wants to transform; in that case the size arguments define the set of values that will be transformed.

inverse1d(@data, UInt:D _ < @data.elems / 2 } = 1, UInt:D _) } = @data.elems --> List)

Inverse 1D transform.

forward2d(@data!, UInt:D dim) } = sqrt(@data.elems).UInt, UInt:D _ ≥ dim, :$nonstandard --> List)

forward2d(Math::Libgsl::Matrix data.matrix.size1 == data.matrix.size1) }, :$nonstandard --> Math::Libgsl::Matrix)

Forward 2D transform.

There are two forms of this method: one accepts an array as its first argument, the other works on a Math::Libgsl::Matrix object.

The first form takes an array @data which represents a square matrix that must have a number of elements which is a power of 2. The @data array may contain more values than those one wants to transform; in this case the tda is the physical row length.

The second form accepts a square Math::Libgsl::Matrix object whose sizes are powers of 2.

Both forms allow for a named argument :$nonstandard, which selects the non-standard form of the computation as detailed in the C library documentation.

inverse2d(@data!, UInt:D dim) } = sqrt(@data.elems).UInt, UInt:D _ ≥ dim, :$nonstandard --> List)

inverse2d(Math::Libgsl::Matrix data.matrix.size1 == data.matrix.size1) }, :$nonstandard --> Math::Libgsl::Matrix)

Inverse 2D transform.

There are two forms of this method: one accepts an array as its first argument, the other works on a Math::Libgsl::Matrix object.

The second form accepts a square Math::Libgsl::Matrix object whose sizes are powers of 2.

Both forms allow for a named argument :$nonstandard, which selects the non-standard form of the computation as detailed in the C library documentation.

C Library Documentation

For more details on libgsl see https://www.gnu.org/software/gsl/. The excellent C Library manual is available here https://www.gnu.org/software/gsl/doc/html/index.html, or here https://www.gnu.org/software/gsl/doc/latex/gsl-ref.pdf in PDF format.

Prerequisites

This module requires the libgsl library to be installed. Please follow the instructions below based on your platform:

Debian Linux and Ubuntu 20.04+

sudo apt install libgsl23 libgsl-dev libgslcblas0

That command will install libgslcblas0 as well, since it's used by the GSL.

Ubuntu 18.04

libgsl23 and libgslcblas0 have a missing symbol on Ubuntu 18.04. I solved the issue installing the Debian Buster version of those three libraries:

Installation

To install it using zef (a module management tool):

$ zef install Math::Libgsl::Wavelet

AUTHOR

Fernando Santagata [email protected]

COPYRIGHT AND LICENSE

This library is free software; you can redistribute it and/or modify it under the Artistic License 2.0.