

 
Manual Reference Pages  MATH::GSL::WAVELET (3)
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NAME
Math::GSL::Wavelet  1D (Real) Wavelets
CONTENTS
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 onedimensional transform on $n elements, a workspace of size $n must
be provided. For twodimensional transforms of $nby$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 inplace 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 ...
J1 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_{J1,2^{J1}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 Bspline 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) 20082011 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.
perl v5.20.3  MATH::GSL::WAVELET (3)  20160403 
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