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daubechies.c

/* wavelet/daubechies.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 for Daubechies wavelets of extremal phase are from
 * I. Daubechies, "Orthonormal Bases of Compactly Supported Wavelets",
 * Communications on Pure and Applied Mathematics, 41 (1988) 909--996
 * (table 1).
 * Additional digits have been obtained using the Mathematica package
 * Daubechies.m by Tong Chen & Meng Xu available at
 * http://www.cwp.mines.edu/wavelets/.
 */

#include <config.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_wavelet.h>

static const double h_4[4] = { 0.48296291314453414337487159986,
  0.83651630373780790557529378092,
  0.22414386804201338102597276224,
  -0.12940952255126038117444941881
};

static const double g_4[4] = { -0.12940952255126038117444941881,
  -0.22414386804201338102597276224,
  0.83651630373780790557529378092,
  -0.48296291314453414337487159986
};

static const double h_6[6] = { 0.33267055295008261599851158914,
  0.80689150931109257649449360409,
  0.45987750211849157009515194215,
  -0.13501102001025458869638990670,
  -0.08544127388202666169281916918,
  0.03522629188570953660274066472
};

static const double g_6[6] = { 0.03522629188570953660274066472,
  0.08544127388202666169281916918,
  -0.13501102001025458869638990670,
  -0.45987750211849157009515194215,
  0.80689150931109257649449360409,
  -0.33267055295008261599851158914
};

static const double h_8[8] = { 0.23037781330889650086329118304,
  0.71484657055291564708992195527,
  0.63088076792985890788171633830,
  -0.02798376941685985421141374718,
  -0.18703481171909308407957067279,
  0.03084138183556076362721936253,
  0.03288301166688519973540751355,
  -0.01059740178506903210488320852
};

static const double g_8[8] = { -0.01059740178506903210488320852,
  -0.03288301166688519973540751355,
  0.03084138183556076362721936253,
  0.18703481171909308407957067279,
  -0.02798376941685985421141374718,
  -0.63088076792985890788171633830,
  0.71484657055291564708992195527,
  -0.23037781330889650086329118304
};

static const double h_10[10] = { 0.16010239797419291448072374802,
  0.60382926979718967054011930653,
  0.72430852843777292772807124410,
  0.13842814590132073150539714634,
  -0.24229488706638203186257137947,
  -0.03224486958463837464847975506,
  0.07757149384004571352313048939,
  -0.00624149021279827427419051911,
  -0.01258075199908199946850973993,
  0.00333572528547377127799818342
};

static const double g_10[10] = { 0.00333572528547377127799818342,
  0.01258075199908199946850973993,
  -0.00624149021279827427419051911,
  -0.07757149384004571352313048939,
  -0.03224486958463837464847975506,
  0.24229488706638203186257137947,
  0.13842814590132073150539714634,
  -0.72430852843777292772807124410,
  0.60382926979718967054011930653,
  -0.16010239797419291448072374802
};

static const double h_12[12] = { 0.11154074335010946362132391724,
  0.49462389039845308567720417688,
  0.75113390802109535067893449844,
  0.31525035170919762908598965481,
  -0.22626469396543982007631450066,
  -0.12976686756726193556228960588,
  0.09750160558732304910234355254,
  0.02752286553030572862554083950,
  -0.03158203931748602956507908070,
  0.00055384220116149613925191840,
  0.00477725751094551063963597525,
  -0.00107730108530847956485262161
};

static const double g_12[12] = { -0.00107730108530847956485262161,
  -0.00477725751094551063963597525,
  0.00055384220116149613925191840,
  0.03158203931748602956507908070,
  0.02752286553030572862554083950,
  -0.09750160558732304910234355254,
  -0.12976686756726193556228960588,
  0.22626469396543982007631450066,
  0.31525035170919762908598965481,
  -0.75113390802109535067893449844,
  0.49462389039845308567720417688,
  -0.11154074335010946362132391724
};

static const double h_14[14] = { 0.07785205408500917901996352196,
  0.39653931948191730653900039094,
  0.72913209084623511991694307034,
  0.46978228740519312247159116097,
  -0.14390600392856497540506836221,
  -0.22403618499387498263814042023,
  0.07130921926683026475087657050,
  0.08061260915108307191292248036,
  -0.03802993693501441357959206160,
  -0.01657454163066688065410767489,
  0.01255099855609984061298988603,
  0.00042957797292136652113212912,
  -0.00180164070404749091526826291,
  0.00035371379997452024844629584
};

static const double g_14[14] = { 0.00035371379997452024844629584,
  0.00180164070404749091526826291,
  0.00042957797292136652113212912,
  -0.01255099855609984061298988603,
  -0.01657454163066688065410767489,
  0.03802993693501441357959206160,
  0.08061260915108307191292248036,
  -0.07130921926683026475087657050,
  -0.22403618499387498263814042023,
  0.14390600392856497540506836221,
  0.46978228740519312247159116097,
  -0.72913209084623511991694307034,
  0.39653931948191730653900039094,
  -0.07785205408500917901996352196
};

static const double h_16[16] = { 0.05441584224310400995500940520,
  0.31287159091429997065916237551,
  0.67563073629728980680780076705,
  0.58535468365420671277126552005,
  -0.01582910525634930566738054788,
  -0.28401554296154692651620313237,
  0.00047248457391328277036059001,
  0.12874742662047845885702928751,
  -0.01736930100180754616961614887,
  -0.04408825393079475150676372324,
  0.01398102791739828164872293057,
  0.00874609404740577671638274325,
  -0.00487035299345157431042218156,
  -0.00039174037337694704629808036,
  0.00067544940645056936636954757,
  -0.00011747678412476953373062823
};

static const double g_16[16] = { -0.00011747678412476953373062823,
  -0.00067544940645056936636954757,
  -0.00039174037337694704629808036,
  0.00487035299345157431042218156,
  0.00874609404740577671638274325,
  -0.01398102791739828164872293057,
  -0.04408825393079475150676372324,
  0.01736930100180754616961614887,
  0.12874742662047845885702928751,
  -0.00047248457391328277036059001,
  -0.28401554296154692651620313237,
  0.01582910525634930566738054788,
  0.58535468365420671277126552005,
  -0.67563073629728980680780076705,
  0.31287159091429997065916237551,
  -0.05441584224310400995500940520
};

static const double h_18[18] = { 0.03807794736387834658869765888,
  0.24383467461259035373204158165,
  0.60482312369011111190307686743,
  0.65728807805130053807821263905,
  0.13319738582500757619095494590,
  -0.29327378327917490880640319524,
  -0.09684078322297646051350813354,
  0.14854074933810638013507271751,
  0.03072568147933337921231740072,
  -0.06763282906132997367564227483,
  0.00025094711483145195758718975,
  0.02236166212367909720537378270,
  -0.00472320475775139727792570785,
  -0.00428150368246342983449679500,
  0.00184764688305622647661912949,
  0.00023038576352319596720521639,
  -0.00025196318894271013697498868,
  0.00003934732031627159948068988
};

static const double g_18[18] = { 0.00003934732031627159948068988,
  0.00025196318894271013697498868,
  0.00023038576352319596720521639,
  -0.00184764688305622647661912949,
  -0.00428150368246342983449679500,
  0.00472320475775139727792570785,
  0.02236166212367909720537378270,
  -0.00025094711483145195758718975,
  -0.06763282906132997367564227483,
  -0.03072568147933337921231740072,
  0.14854074933810638013507271751,
  0.09684078322297646051350813354,
  -0.29327378327917490880640319524,
  -0.13319738582500757619095494590,
  0.65728807805130053807821263905,
  -0.60482312369011111190307686743,
  0.24383467461259035373204158165,
  -0.03807794736387834658869765888
};

static const double h_20[20] = { 0.02667005790055555358661744877,
  0.18817680007769148902089297368,
  0.52720118893172558648174482796,
  0.68845903945360356574187178255,
  0.28117234366057746074872699845,
  -0.24984642432731537941610189792,
  -0.19594627437737704350429925432,
  0.12736934033579326008267723320,
  0.09305736460357235116035228984,
  -0.07139414716639708714533609308,
  -0.02945753682187581285828323760,
  0.03321267405934100173976365318,
  0.00360655356695616965542329142,
  -0.01073317548333057504431811411,
  0.00139535174705290116578931845,
  0.00199240529518505611715874224,
  -0.00068585669495971162656137098,
  -0.00011646685512928545095148097,
  0.00009358867032006959133405013,
  -0.00001326420289452124481243668
};

static const double g_20[20] = { -0.00001326420289452124481243668,
  -0.00009358867032006959133405013,
  -0.00011646685512928545095148097,
  0.00068585669495971162656137098,
  0.00199240529518505611715874224,
  -0.00139535174705290116578931845,
  -0.01073317548333057504431811411,
  -0.00360655356695616965542329142,
  0.03321267405934100173976365318,
  0.02945753682187581285828323760,
  -0.07139414716639708714533609308,
  -0.09305736460357235116035228984,
  0.12736934033579326008267723320,
  0.19594627437737704350429925432,
  -0.24984642432731537941610189792,
  -0.28117234366057746074872699845,
  0.68845903945360356574187178255,
  -0.52720118893172558648174482796,
  0.18817680007769148902089297368,
  -0.02667005790055555358661744877
};

static int
daubechies_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 4:
      *h1 = h_4;
      *g1 = g_4;
      *h2 = h_4;
      *g2 = g_4;
      break;

    case 6:
      *h1 = h_6;
      *g1 = g_6;
      *h2 = h_6;
      *g2 = g_6;
      break;

    case 8:
      *h1 = h_8;
      *g1 = g_8;
      *h2 = h_8;
      *g2 = g_8;
      break;

    case 10:
      *h1 = h_10;
      *g1 = g_10;
      *h2 = h_10;
      *g2 = g_10;
      break;

    case 12:
      *h1 = h_12;
      *g1 = g_12;
      *h2 = h_12;
      *g2 = g_12;
      break;

    case 14:
      *h1 = h_14;
      *g1 = g_14;
      *h2 = h_14;
      *g2 = g_14;
      break;

    case 16:
      *h1 = h_16;
      *g1 = g_16;
      *h2 = h_16;
      *g2 = g_16;
      break;

    case 18:
      *h1 = h_18;
      *g1 = g_18;
      *h2 = h_18;
      *g2 = g_18;
      break;

    case 20:
      *h1 = h_20;
      *g1 = g_20;
      *h2 = h_20;
      *g2 = g_20;
      break;

    default:
      return GSL_FAILURE;
    }

  *nc = member;
  *offset = 0;

  return GSL_SUCCESS;
}

static int
daubechies_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 4:
      *h1 = h_4;
      *g1 = g_4;
      *h2 = h_4;
      *g2 = g_4;
      break;

    case 6:
      *h1 = h_6;
      *g1 = g_6;
      *h2 = h_6;
      *g2 = g_6;
      break;

    case 8:
      *h1 = h_8;
      *g1 = g_8;
      *h2 = h_8;
      *g2 = g_8;
      break;

    case 10:
      *h1 = h_10;
      *g1 = g_10;
      *h2 = h_10;
      *g2 = g_10;
      break;

    case 12:
      *h1 = h_12;
      *g1 = g_12;
      *h2 = h_12;
      *g2 = g_12;
      break;

    case 14:
      *h1 = h_14;
      *g1 = g_14;
      *h2 = h_14;
      *g2 = g_14;
      break;

    case 16:
      *h1 = h_16;
      *g1 = g_16;
      *h2 = h_16;
      *g2 = g_16;
      break;

    case 18:
      *h1 = h_18;
      *g1 = g_18;
      *h2 = h_18;
      *g2 = g_18;
      break;

    case 20:
      *h1 = h_20;
      *g1 = g_20;
      *h2 = h_20;
      *g2 = g_20;
      break;

    default:
      return GSL_FAILURE;
    }

  *nc = member;
  *offset = (member >> 1);

  return GSL_SUCCESS;
}

static const gsl_wavelet_type daubechies_type = {
  "daubechies",
  &daubechies_init
};

static const gsl_wavelet_type daubechies_centered_type = { 
  "daubechies-centered",
  &daubechies_centered_init
};

const gsl_wavelet_type *gsl_wavelet_daubechies = &daubechies_type;
const gsl_wavelet_type *gsl_wavelet_daubechies_centered =
  &daubechies_centered_type;

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