NAME

       Math::GSL::Wavelet - 1-D (Real) Wavelets

SYNOPSIS

           use Math::GSL::Wavelet qw/:all/;

DESCRIPTION

       "gsl_wavelet_alloc($T, $k)"
        This function allocates and initializes a wavelet object of type $T, where $T must be one
        of the constants below. The parameter $k selects the specific member of the wavelet
        family.

       "gsl_wavelet_free($w)"
        This function frees the wavelet object $w.

       "gsl_wavelet_name"
       "gsl_wavelet_workspace_alloc($n)"
        This function allocates a workspace for the discrete wavelet transform. To perform a one-
        dimensional transform on $n elements, a workspace of size $n must be provided. For two-
        dimensional transforms of $n-by-$n matrices it is sufficient to allocate a workspace of
        size $n, since the transform operates on individual rows and columns.

       "gsl_wavelet_workspace_free($work)"
        This function frees the allocated workspace work.

       "gsl_wavelet_transform"
       "gsl_wavelet_transform_forward($w, $data, $stride, $n, $work)"
        This functions compute in-place forward discrete wavelet transforms of length $n with
        stride $stride on the array $data. The length of the transform $n is restricted to powers
        of two. For the forward transform, the elements of the original array are replaced by the
        discrete wavelet transform f_i -> w_{j,k} in a packed triangular storage layout, where j
        is the index of the level j = 0 ...  J-1 and k is the index of the coefficient within
        each level, k = 0 ... (2^j)-1.  The total number of levels is J = \log_2(n). The output
        data has the following form,

            (s_{-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ..., d_{j,k}, ..., d_{J-1,2^{J-1}-1})

        where the first element is the smoothing coefficient s_{-1,0}, followed by the detail
        coefficients d_{j,k} for each level j. The backward transform inverts these coefficients
        to obtain the original data. These functions return a status of $GSL_SUCCESS upon
        successful completion. $GSL_EINVAL is returned if $n is not an integer power of 2 or if
        insufficient workspace is provided.

       "gsl_wavelet_transform_inverse"

       This module also contains the following constants with their valid k value for the
       gsl_wavelet_alloc function :

       $gsl_wavelet_daubechies
       $gsl_wavelet_daubechies_centered

       This is the Daubechies wavelet family of maximum phase with k/2 vanishing moments. The
       implemented wavelets are k=4, 6, ..., 20, with k even.

       $gsl_wavelet_haar
       $gsl_wavelet_haar_centered

       This is the Haar wavelet. The only valid choice of k for the Haar wavelet is k=2.

       $gsl_wavelet_bspline
       $gsl_wavelet_bspline_centered

       This is the biorthogonal B-spline wavelet family of order (i,j). The implemented values of
       k = 100*i + j are 103, 105, 202, 204, 206, 208, 301, 303, 305 307, 309.

AUTHORS

       Jonathan "Duke" Leto <jonathan@leto.net> and Thierry Moisan <thierry.moisan@gmail.com>

COPYRIGHT AND LICENSE

       Copyright (C) 2008-2021 Jonathan "Duke" Leto and Thierry Moisan

       This program is free software; you can redistribute it and/or modify it under the same
       terms as Perl itself.