/* wavelet/bspline.c
*
* Copyright (C) 2004 Ivo Alxneit
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 3 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Coefficients are from A. Cohen, I. Daubechies, and J.-C. Feauveau;
* "Biorthogonal Bases of Compactly Supported Wavelets", Communications
* on Pure and Applied Mathematics, 45 (1992) 485--560 (table 6.1).
*
* Note the following errors in table 1:
*
* N = 2, N~ = 4, m0~
* the second term in z^-1 (45/64 z^-1) should be left out.
*
* N = 3, N~ = 7, m0~
* the term 336z^-3 should read 363z^-3.
*/
#include <config.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_wavelet.h>
static const double h1_103[6] = { -0.0883883476483184405501055452631,
0.0883883476483184405501055452631,
M_SQRT1_2,
M_SQRT1_2,
0.0883883476483184405501055452631,
-0.0883883476483184405501055452631
};
static const double g2_103[6] = { -0.0883883476483184405501055452631,
-0.0883883476483184405501055452631,
M_SQRT1_2,
-(M_SQRT1_2),
0.0883883476483184405501055452631,
0.0883883476483184405501055452631
};
static const double h1_105[10] = { 0.0165728151840597076031447897368,
-0.0165728151840597076031447897368,
-0.1215339780164378557563951247368,
0.1215339780164378557563951247368,
M_SQRT1_2,
M_SQRT1_2,
0.1215339780164378557563951247368,
-0.1215339780164378557563951247368,
-0.0165728151840597076031447897368,
0.0165728151840597076031447897368
};
static const double g2_105[10] = { 0.0165728151840597076031447897368,
0.0165728151840597076031447897368,
-0.1215339780164378557563951247368,
-0.1215339780164378557563951247368,
M_SQRT1_2,
-(M_SQRT1_2),
0.1215339780164378557563951247368,
0.1215339780164378557563951247368,
-0.0165728151840597076031447897368,
-0.0165728151840597076031447897368
};
static const double g1_1[10] = { 0.0, 0.0, 0.0, 0.0,
M_SQRT1_2,
-(M_SQRT1_2),
0.0, 0.0, 0.0, 0.0
};
static const double h2_1[10] = { 0.0, 0.0, 0.0, 0.0,
M_SQRT1_2,
M_SQRT1_2,
0.0, 0.0, 0.0, 0.0
};
static const double h1_202[6] = { -0.1767766952966368811002110905262,
0.3535533905932737622004221810524,
1.0606601717798212866012665431573,
0.3535533905932737622004221810524,
-0.1767766952966368811002110905262,
0.0
};
static const double g2_202[6] = { 0.0,
-0.1767766952966368811002110905262,
-0.3535533905932737622004221810524,
1.0606601717798212866012665431573,
-0.3535533905932737622004221810524,
-0.1767766952966368811002110905262
};
static const double h1_204[10] = { 0.0331456303681194152062895794737,
-0.0662912607362388304125791589473,
-0.1767766952966368811002110905262,
0.4198446513295125926130013399998,
0.9943689110435824561886873842099,
0.4198446513295125926130013399998,
-0.1767766952966368811002110905262,
-0.0662912607362388304125791589473,
0.0331456303681194152062895794737,
0.0
};
static const double g2_204[10] = { 0.0,
0.0331456303681194152062895794737,
0.0662912607362388304125791589473,
-0.1767766952966368811002110905262,
-0.4198446513295125926130013399998,
0.9943689110435824561886873842099,
-0.4198446513295125926130013399998,
-0.1767766952966368811002110905262,
0.0662912607362388304125791589473,
0.0331456303681194152062895794737
};
static const double h1_206[14] = { -0.0069053396600248781679769957237,
0.0138106793200497563359539914474,
0.0469563096881691715422435709210,
-0.1077232986963880994204411332894,
-0.1698713556366120029322340948025,
0.4474660099696121052849093228945,
0.9667475524034829435167794013152,
0.4474660099696121052849093228945,
-0.1698713556366120029322340948025,
-0.1077232986963880994204411332894,
0.0469563096881691715422435709210,
0.0138106793200497563359539914474,
-0.0069053396600248781679769957237,
0.0
};
static const double g2_206[14] = { 0.0,
-0.0069053396600248781679769957237,
-0.0138106793200497563359539914474,
0.0469563096881691715422435709210,
0.1077232986963880994204411332894,
-0.1698713556366120029322340948025,
-0.4474660099696121052849093228945,
0.9667475524034829435167794013152,
-0.4474660099696121052849093228945,
-0.1698713556366120029322340948025,
0.1077232986963880994204411332894,
0.0469563096881691715422435709210,
-0.0138106793200497563359539914474,
-0.0069053396600248781679769957237,
};
static const double h1_208[18] = { 0.0015105430506304420992449678146,
-0.0030210861012608841984899356291,
-0.0129475118625466465649568669819,
0.0289161098263541773284036695929,
0.0529984818906909399392234421792,
-0.1349130736077360572068505539514,
-0.1638291834340902345352542235443,
0.4625714404759165262773590010400,
0.9516421218971785225243297231697,
0.4625714404759165262773590010400,
-0.1638291834340902345352542235443,
-0.1349130736077360572068505539514,
0.0529984818906909399392234421792,
0.0289161098263541773284036695929,
-0.0129475118625466465649568669819,
-0.0030210861012608841984899356291,
0.0015105430506304420992449678146,
0.0
};
static const double g2_208[18] = { 0.0,
0.0015105430506304420992449678146,
0.0030210861012608841984899356291,
-0.0129475118625466465649568669819,
-0.0289161098263541773284036695929,
0.0529984818906909399392234421792,
0.1349130736077360572068505539514,
-0.1638291834340902345352542235443,
-0.4625714404759165262773590010400,
0.9516421218971785225243297231697,
-0.4625714404759165262773590010400,
-0.1638291834340902345352542235443,
0.1349130736077360572068505539514,
0.0529984818906909399392234421792,
-0.0289161098263541773284036695929,
-0.0129475118625466465649568669819,
0.0030210861012608841984899356291,
0.0015105430506304420992449678146,
};
static const double h2_2[18] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.3535533905932737622004221810524,
0.7071067811865475244008443621048,
0.3535533905932737622004221810524,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
};
static const double g1_2[18] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-0.3535533905932737622004221810524,
0.7071067811865475244008443621048,
-0.3535533905932737622004221810524,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
};
static const double h1_301[4] = { -0.3535533905932737622004221810524,
1.0606601717798212866012665431573,
1.0606601717798212866012665431573,
-0.3535533905932737622004221810524
};
static const double g2_301[4] = { 0.3535533905932737622004221810524,
1.0606601717798212866012665431573,
-1.0606601717798212866012665431573,
-0.3535533905932737622004221810524
};
static const double h1_303[8] = { 0.0662912607362388304125791589473,
-0.1988737822087164912377374768420,
-0.1546796083845572709626847042104,
0.9943689110435824561886873842099,
0.9943689110435824561886873842099,
-0.1546796083845572709626847042104,
-0.1988737822087164912377374768420,
0.0662912607362388304125791589473
};
static const double g2_303[8] = { -0.0662912607362388304125791589473,
-0.1988737822087164912377374768420,
0.1546796083845572709626847042104,
0.9943689110435824561886873842099,
-0.9943689110435824561886873842099,
-0.1546796083845572709626847042104,
0.1988737822087164912377374768420,
0.0662912607362388304125791589473
};
static const double h1_305[12] = { -0.0138106793200497563359539914474,
0.0414320379601492690078619743421,
0.0524805814161890740766251675000,
-0.2679271788089652729175074340788,
-0.0718155324642587329469607555263,
0.9667475524034829435167794013152,
0.9667475524034829435167794013152,
-0.0718155324642587329469607555263,
-0.2679271788089652729175074340788,
0.0524805814161890740766251675000,
0.0414320379601492690078619743421,
-0.0138106793200497563359539914474
};
static const double g2_305[12] = { 0.0138106793200497563359539914474,
0.0414320379601492690078619743421,
-0.0524805814161890740766251675000,
-0.2679271788089652729175074340788,
0.0718155324642587329469607555263,
0.9667475524034829435167794013152,
-0.9667475524034829435167794013152,
-0.0718155324642587329469607555263,
0.2679271788089652729175074340788,
0.0524805814161890740766251675000,
-0.0414320379601492690078619743421,
-0.0138106793200497563359539914474
};
static const double h1_307[16] = { 0.0030210861012608841984899356291,
-0.0090632583037826525954698068873,
-0.0168317654213106405344439270765,
0.0746639850740189951912512662623,
0.0313329787073628846871956180962,
-0.3011591259228349991008967259990,
-0.0264992409453454699696117210896,
0.9516421218971785225243297231697,
0.9516421218971785225243297231697,
-0.0264992409453454699696117210896,
-0.3011591259228349991008967259990,
0.0313329787073628846871956180962,
0.0746639850740189951912512662623,
-0.0168317654213106405344439270765,
-0.0090632583037826525954698068873,
0.0030210861012608841984899356291
};
static const double g2_307[16] = { -0.0030210861012608841984899356291,
-0.0090632583037826525954698068873,
0.0168317654213106405344439270765,
0.0746639850740189951912512662623,
-0.0313329787073628846871956180962,
-0.3011591259228349991008967259990,
0.0264992409453454699696117210896,
0.9516421218971785225243297231697,
-0.9516421218971785225243297231697,
-0.0264992409453454699696117210896,
0.3011591259228349991008967259990,
0.0313329787073628846871956180962,
-0.0746639850740189951912512662623,
-0.0168317654213106405344439270765,
0.0090632583037826525954698068873,
0.0030210861012608841984899356291
};
static const double h1_309[20] = { -0.0006797443727836989446602355165,
0.0020392331183510968339807065496,
0.0050603192196119810324706421788,
-0.0206189126411055346546938106687,
-0.0141127879301758447558029850103,
0.0991347824942321571990197448581,
0.0123001362694193142367090236328,
-0.3201919683607785695513833204624,
0.0020500227115698857061181706055,
0.9421257006782067372990864259380,
0.9421257006782067372990864259380,
0.0020500227115698857061181706055,
-0.3201919683607785695513833204624,
0.0123001362694193142367090236328,
0.0991347824942321571990197448581,
-0.0141127879301758447558029850103,
-0.0206189126411055346546938106687,
0.0050603192196119810324706421788,
0.0020392331183510968339807065496,
-0.0006797443727836989446602355165
};
static const double g2_309[20] = { 0.0006797443727836989446602355165,
0.0020392331183510968339807065496,
-0.0050603192196119810324706421788,
-0.0206189126411055346546938106687,
0.0141127879301758447558029850103,
0.0991347824942321571990197448581,
-0.0123001362694193142367090236328,
-0.3201919683607785695513833204624,
-0.0020500227115698857061181706055,
0.9421257006782067372990864259380,
-0.9421257006782067372990864259380,
0.0020500227115698857061181706055,
0.3201919683607785695513833204624,
0.0123001362694193142367090236328,
-0.0991347824942321571990197448581,
-0.0141127879301758447558029850103,
0.0206189126411055346546938106687,
0.0050603192196119810324706421788,
-0.0020392331183510968339807065496,
-0.0006797443727836989446602355165
};
static const double h2_3[20] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
0.1767766952966368811002110905262,
0.5303300858899106433006332715786,
0.5303300858899106433006332715786,
0.1767766952966368811002110905262,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
};
static const double g1_3[20] = { 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0,
-0.1767766952966368811002110905262,
0.5303300858899106433006332715786,
-0.5303300858899106433006332715786,
0.1767766952966368811002110905262,
0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0, 0.0
};
static int
bspline_init (const double **h1, const double **g1,
const double **h2, const double **g2, size_t * nc,
size_t * offset, size_t member)
{
switch (member)
{
case 103:
*nc = 6;
*h1 = h1_103;
*g1 = &g1_1[2];
*h2 = &h2_1[2];
*g2 = g2_103;
break;
case 105:
*nc = 10;
*h1 = h1_105;
*g1 = g1_1;
*h2 = h2_1;
*g2 = g2_105;
break;
case 202:
*nc = 6;
*h1 = h1_202;
*g1 = &g1_2[6];
*h2 = &h2_2[6];
*g2 = g2_202;
break;
case 204:
*nc = 10;
*h1 = h1_204;
*g1 = &g1_2[4];
*h2 = &h2_2[4];
*g2 = g2_204;
break;
case 206:
*nc = 14;
*h1 = h1_206;
*g1 = &g1_2[2];
*h2 = &h2_2[2];
*g2 = g2_206;
break;
case 208:
*nc = 18;
*h1 = h1_208;
*g1 = g1_2;
*h2 = h2_2;
*g2 = g2_208;
break;
case 301:
*nc = 4;
*h1 = h1_301;
*g1 = &g1_3[8];
*h2 = &h2_3[8];
*g2 = g2_301;
break;
case 303:
*nc = 8;
*h1 = h1_303;
*g1 = &g1_3[6];
*h2 = &h2_3[6];
*g2 = g2_303;
break;
case 305:
*nc = 12;
*h1 = h1_305;
*g1 = &g1_3[4];
*h2 = &h2_3[4];
*g2 = g2_305;
break;
case 307:
*nc = 16;
*h1 = h1_307;
*g1 = &g1_3[2];
*h2 = &h2_3[2];
*g2 = g2_307;
break;
case 309:
*nc = 20;
*h1 = h1_309;
*g1 = g1_3;
*h2 = h2_3;
*g2 = g2_309;
break;
default:
return GSL_FAILURE;
}
*offset = 0;
return GSL_SUCCESS;
}
static int
bspline_centered_init (const double **h1, const double **g1,
const double **h2, const double **g2, size_t * nc,
size_t * offset, size_t member)
{
switch (member)
{
case 103:
*nc = 6;
*h1 = h1_103;
*g1 = &g1_1[2];
*h2 = &h2_1[2];
*g2 = g2_103;
break;
case 105:
*nc = 10;
*h1 = h1_105;
*g1 = g1_1;
*h2 = h2_1;
*g2 = g2_105;
break;
case 202:
*nc = 6;
*h1 = h1_202;
*g1 = &g1_2[6];
*h2 = &h2_2[6];
*g2 = g2_202;
break;
case 204:
*nc = 10;
*h1 = h1_204;
*g1 = &g1_2[4];
*h2 = &h2_2[4];
*g2 = g2_204;
break;
case 206:
*nc = 14;
*h1 = h1_206;
*g1 = &g1_2[2];
*h2 = &h2_2[2];
*g2 = g2_206;
break;
case 208:
*nc = 18;
*h1 = h1_208;
*g1 = g1_2;
*h2 = h2_2;
*g2 = g2_208;
break;
case 301:
*nc = 4;
*h1 = h1_301;
*g1 = &g1_3[8];
*h2 = &h2_3[8];
*g2 = g2_301;
break;
case 303:
*nc = 8;
*h1 = h1_303;
*g1 = &g1_3[6];
*h2 = &h2_3[6];
*g2 = g2_303;
break;
case 305:
*nc = 12;
*h1 = h1_305;
*g1 = &g1_3[4];
*h2 = &h2_3[4];
*g2 = g2_305;
break;
case 307:
*nc = 16;
*h1 = h1_307;
*g1 = &g1_3[2];
*h2 = &h2_3[2];
*g2 = g2_307;
break;
case 309:
*nc = 20;
*h1 = h1_309;
*g1 = g1_3;
*h2 = h2_3;
*g2 = g2_309;
break;
default:
return GSL_FAILURE;
}
*offset = ((*nc) >> 1);
return GSL_SUCCESS;
}
static const gsl_wavelet_type bspline_type = {
"bspline",
&bspline_init
};
static const gsl_wavelet_type bspline_centered_type = {
"bspline-centered",
&bspline_centered_init
};
const gsl_wavelet_type *gsl_wavelet_bspline = &bspline_type;
const gsl_wavelet_type *gsl_wavelet_bspline_centered = &bspline_centered_type;