.\" Automatically generated by Pod::Man 4.14 (Pod::Simple 3.40) .\" .\" Standard preamble: .\" ======================================================================== .de Sp \" Vertical space (when we can't use .PP) .if t .sp .5v .if n .sp .. .de Vb \" Begin verbatim text .ft CW .nf .ne \\$1 .. .de Ve \" End verbatim text .ft R .fi .. .\" Set up some character translations and predefined strings. \*(-- will .\" give an unbreakable dash, \*(PI will give pi, \*(L" will give a left .\" double quote, and \*(R" will give a right double quote. \*(C+ will .\" give a nicer C++. Capital omega is used to do unbreakable dashes and .\" therefore won't be available. \*(C` and \*(C' expand to `' in nroff, .\" nothing in troff, for use with C<>. .tr \(*W- .ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p' .ie n \{\ . ds -- \(*W- . ds PI pi . if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch . if (\n(.H=4u)&(1m=20u) .ds -- \(*W\h'-12u'\(*W\h'-8u'-\" diablo 12 pitch . ds L" "" . ds R" "" . ds C` "" . ds C' "" 'br\} .el\{\ . ds -- \|\(em\| . ds PI \(*p . ds L" `` . ds R" '' . ds C` . ds C' 'br\} .\" .\" Escape single quotes in literal strings from groff's Unicode transform. .ie \n(.g .ds Aq \(aq .el .ds Aq ' .\" .\" If the F register is >0, we'll generate index entries on stderr for .\" titles (.TH), headers (.SH), subsections (.SS), items (.Ip), and index .\" entries marked with X<> in POD. Of course, you'll have to process the .\" output yourself in some meaningful fashion. .\" .\" Avoid warning from groff about undefined register 'F'. .de IX .. .nr rF 0 .if \n(.g .if rF .nr rF 1 .if (\n(rF:(\n(.g==0)) \{\ . if \nF \{\ . de IX . tm Index:\\$1\t\\n%\t"\\$2" .. . if !\nF==2 \{\ . nr % 0 . nr F 2 . \} . \} .\} .rr rF .\" .\" Accent mark definitions (@(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2). .\" Fear. Run. Save yourself. No user-serviceable parts. . \" fudge factors for nroff and troff .if n \{\ . ds #H 0 . ds #V .8m . ds #F .3m . ds #[ \f1 . ds #] \fP .\} .if t \{\ . ds #H ((1u-(\\\\n(.fu%2u))*.13m) . ds #V .6m . ds #F 0 . ds #[ \& . ds #] \& .\} . \" simple accents for nroff and troff .if n \{\ . ds ' \& . ds ` \& . ds ^ \& . ds , \& . ds ~ ~ . ds / .\} .if t \{\ . ds ' \\k:\h'-(\\n(.wu*8/10-\*(#H)'\'\h"|\\n:u" . ds ` \\k:\h'-(\\n(.wu*8/10-\*(#H)'\`\h'|\\n:u' . ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'^\h'|\\n:u' . ds , \\k:\h'-(\\n(.wu*8/10)',\h'|\\n:u' . ds ~ \\k:\h'-(\\n(.wu-\*(#H-.1m)'~\h'|\\n:u' . ds / \\k:\h'-(\\n(.wu*8/10-\*(#H)'\z\(sl\h'|\\n:u' .\} . \" troff and (daisy-wheel) nroff accents .ds : \\k:\h'-(\\n(.wu*8/10-\*(#H+.1m+\*(#F)'\v'-\*(#V'\z.\h'.2m+\*(#F'.\h'|\\n:u'\v'\*(#V' .ds 8 \h'\*(#H'\(*b\h'-\*(#H' .ds o \\k:\h'-(\\n(.wu+\w'\(de'u-\*(#H)/2u'\v'-.3n'\*(#[\z\(de\v'.3n'\h'|\\n:u'\*(#] .ds d- \h'\*(#H'\(pd\h'-\w'~'u'\v'-.25m'\f2\(hy\fP\v'.25m'\h'-\*(#H' .ds D- D\\k:\h'-\w'D'u'\v'-.11m'\z\(hy\v'.11m'\h'|\\n:u' .ds th \*(#[\v'.3m'\s+1I\s-1\v'-.3m'\h'-(\w'I'u*2/3)'\s-1o\s+1\*(#] .ds Th \*(#[\s+2I\s-2\h'-\w'I'u*3/5'\v'-.3m'o\v'.3m'\*(#] .ds ae a\h'-(\w'a'u*4/10)'e .ds Ae A\h'-(\w'A'u*4/10)'E . \" corrections for vroff .if v .ds ~ \\k:\h'-(\\n(.wu*9/10-\*(#H)'\s-2\u~\d\s+2\h'|\\n:u' .if v .ds ^ \\k:\h'-(\\n(.wu*10/11-\*(#H)'\v'-.4m'^\v'.4m'\h'|\\n:u' . \" for low resolution devices (crt and lpr) .if \n(.H>23 .if \n(.V>19 \ \{\ . ds : e . ds 8 ss . ds o a . ds d- d\h'-1'\(ga . ds D- D\h'-1'\(hy . ds th \o'bp' . ds Th \o'LP' . ds ae ae . ds Ae AE .\} .rm #[ #] #H #V #F C .\" ======================================================================== .\" .IX Title "Math::GSL::Wavelet 3pm" .TH Math::GSL::Wavelet 3pm "2020-11-09" "perl v5.32.0" "User Contributed Perl Documentation" .\" For nroff, turn off justification. Always turn off hyphenation; it makes .\" way too many mistakes in technical documents. .if n .ad l .nh .SH "NAME" Math::GSL::Wavelet \- 1\-D (Real) Wavelets .SH "SYNOPSIS" .IX Header "SYNOPSIS" .Vb 1 \& use Math::GSL::Wavelet qw/:all/; .Ve .SH "DESCRIPTION" .IX Header "DESCRIPTION" .ie n .IP """gsl_wavelet_alloc($T, $k)""" 1 .el .IP "\f(CWgsl_wavelet_alloc($T, $k)\fR" 1 .IX Item "gsl_wavelet_alloc($T, $k)" This function allocates and initializes a wavelet object of type \f(CW$T\fR, where \f(CW$T\fR must be one of the constants below. The parameter \f(CW$k\fR selects the specific member of the wavelet family. .ie n .IP """gsl_wavelet_free($w)""" 1 .el .IP "\f(CWgsl_wavelet_free($w)\fR" 1 .IX Item "gsl_wavelet_free($w)" This function frees the wavelet object \f(CW$w\fR. .ie n .IP """gsl_wavelet_name""" 1 .el .IP "\f(CWgsl_wavelet_name\fR" 1 .IX Item "gsl_wavelet_name" .PD 0 .ie n .IP """gsl_wavelet_workspace_alloc($n)""" 1 .el .IP "\f(CWgsl_wavelet_workspace_alloc($n)\fR" 1 .IX Item "gsl_wavelet_workspace_alloc($n)" .PD This function allocates a workspace for the discrete wavelet transform. To perform a one-dimensional transform on \f(CW$n\fR elements, a workspace of size \f(CW$n\fR must be provided. For two-dimensional transforms of \f(CW$n\fR\-by\-$n matrices it is sufficient to allocate a workspace of size \f(CW$n\fR, since the transform operates on individual rows and columns. .ie n .IP """gsl_wavelet_workspace_free($work)""" 1 .el .IP "\f(CWgsl_wavelet_workspace_free($work)\fR" 1 .IX Item "gsl_wavelet_workspace_free($work)" This function frees the allocated workspace work. .ie n .IP """gsl_wavelet_transform""" 1 .el .IP "\f(CWgsl_wavelet_transform\fR" 1 .IX Item "gsl_wavelet_transform" .PD 0 .ie n .IP """gsl_wavelet_transform_forward($w, $data, $stride, $n, $work)""" 1 .el .IP "\f(CWgsl_wavelet_transform_forward($w, $data, $stride, $n, $work)\fR" 1 .IX Item "gsl_wavelet_transform_forward($w, $data, $stride, $n, $work)" .PD This functions compute in-place forward discrete wavelet transforms of length \f(CW$n\fR with stride \f(CW$stride\fR on the array \f(CW$data\fR. The length of the transform \f(CW$n\fR is restricted to powers of two. For the forward transform, the elements of the original array are replaced by the discrete wavelet transform f_i \-> w_{j,k} in a packed triangular storage layout, where j is the index of the level j = 0 ... J\-1 and k is the index of the coefficient within each level, k = 0 ... (2^j)\-1. The total number of levels is J = \elog_2(n). The output data has the following form, .RS 1 .Sp .Vb 1 \& (s_{\-1,0}, d_{0,0}, d_{1,0}, d_{1,1}, d_{2,0}, ..., d_{j,k}, ..., d_{J\-1,2^{J\-1}\-1}) .Ve .RE .RS 1 .Sp where the first element is the smoothing coefficient s_{\-1,0}, followed by the detail coefficients d_{j,k} for each level j. The backward transform inverts these coefficients to obtain the original data. These functions return a status of \f(CW$GSL_SUCCESS\fR upon successful completion. \f(CW$GSL_EINVAL\fR is returned if \f(CW$n\fR is not an integer power of 2 or if insufficient workspace is provided. .RE .ie n .IP """gsl_wavelet_transform_inverse""" 1 .el .IP "\f(CWgsl_wavelet_transform_inverse\fR" 1 .IX Item "gsl_wavelet_transform_inverse" .PP This module also contains the following constants with their valid k value for the gsl_wavelet_alloc function : .ie n .IP "$gsl_wavelet_daubechies" 1 .el .IP "\f(CW$gsl_wavelet_daubechies\fR" 1 .IX Item "$gsl_wavelet_daubechies" .PD 0 .ie n .IP "$gsl_wavelet_daubechies_centered" 1 .el .IP "\f(CW$gsl_wavelet_daubechies_centered\fR" 1 .IX Item "$gsl_wavelet_daubechies_centered" .PD .PP 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. .ie n .IP "$gsl_wavelet_haar" 1 .el .IP "\f(CW$gsl_wavelet_haar\fR" 1 .IX Item "$gsl_wavelet_haar" .PD 0 .ie n .IP "$gsl_wavelet_haar_centered" 1 .el .IP "\f(CW$gsl_wavelet_haar_centered\fR" 1 .IX Item "$gsl_wavelet_haar_centered" .PD .PP This is the Haar wavelet. The only valid choice of k for the Haar wavelet is k=2. .ie n .IP "$gsl_wavelet_bspline" 1 .el .IP "\f(CW$gsl_wavelet_bspline\fR" 1 .IX Item "$gsl_wavelet_bspline" .PD 0 .ie n .IP "$gsl_wavelet_bspline_centered" 1 .el .IP "\f(CW$gsl_wavelet_bspline_centered\fR" 1 .IX Item "$gsl_wavelet_bspline_centered" .PD .PP 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. .SH "AUTHORS" .IX Header "AUTHORS" Jonathan \*(L"Duke\*(R" Leto and Thierry Moisan .SH "COPYRIGHT AND LICENSE" .IX Header "COPYRIGHT AND LICENSE" Copyright (C) 2008\-2020 Jonathan \*(L"Duke\*(R" Leto and Thierry Moisan .PP This program is free software; you can redistribute it and/or modify it under the same terms as Perl itself.