bspline.c

This library is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY without ev

/* 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 2 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 Apllied 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,