# 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 $type!, UInt:D $variant!)

### new(UInt:D :$type!, UInt:D :$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 $stride where { $_ < @data.elems / 2 } = 1, UInt:D $size where { is-powerof2($_) } = @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 **$stride** and **$size** arguments define the set of values that will be transformed.

### inverse1d(@data, UInt:D $stride where { $_ < @data.elems / 2 } = 1, UInt:D $size where { is-powerof2($_) } = @data.elems --> List)

Inverse 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 **$stride** and **$size** arguments define the set of values that will be transformed.

### forward2d(@data!, UInt:D $dim? where { is-powerof2($dim) } = sqrt(@data.elems).UInt, UInt:D $tda? where { $_ ≥ $dim } = $dim, :$nonstandard --> List)

### forward2d(Math::Libgsl::Matrix $data! where { $data.matrix.size1 == $data.matrix.size2 && is-powerof2($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 **$size** argument is the dimension of the (square) matrix to be processed and **$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 $dim? where { is-powerof2($dim) } = sqrt(@data.elems).UInt, UInt:D $tda? where { $_ ≥ $dim } = $dim, :$nonstandard --> List)

### inverse2d(Math::Libgsl::Matrix $data! where { $data.matrix.size1 == $data.matrix.size2 && is-powerof2($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 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 **$size** argument is the dimension of the (square) matrix to be processed and **$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.

# 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:

http://http.us.debian.org/debian/pool/main/g/gsl/libgslcblas0_2.5+dfsg-6_amd64.deb

http://http.us.debian.org/debian/pool/main/g/gsl/libgsl23_2.5+dfsg-6_amd64.deb

http://http.us.debian.org/debian/pool/main/g/gsl/libgsl-dev_2.5+dfsg-6_amd64.deb

# Installation

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

```
$ zef install Math::Libgsl::Wavelet
```

# AUTHOR

Fernando Santagata nando.santagata@gmail.com

# COPYRIGHT AND LICENSE

Copyright 2022 Fernando Santagata

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