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Diffstat (limited to 'gsl-1.9/integration/qmomof.c')
-rw-r--r-- | gsl-1.9/integration/qmomof.c | 389 |
1 files changed, 389 insertions, 0 deletions
diff --git a/gsl-1.9/integration/qmomof.c b/gsl-1.9/integration/qmomof.c new file mode 100644 index 0000000..b0026dc --- /dev/null +++ b/gsl-1.9/integration/qmomof.c @@ -0,0 +1,389 @@ +/* integration/qmomof.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough + * + * 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. + */ + +#include <config.h> +#include <stdlib.h> +#include <gsl/gsl_integration.h> +#include <gsl/gsl_errno.h> + +static void +compute_moments (double par, double * cheb); + +static int +dgtsl (size_t n, double *c, double *d, double *e, double *b); + +gsl_integration_qawo_table * +gsl_integration_qawo_table_alloc (double omega, double L, + enum gsl_integration_qawo_enum sine, + size_t n) +{ + gsl_integration_qawo_table *t; + double * chebmo; + + if (n == 0) + { + GSL_ERROR_VAL ("table length n must be positive integer", + GSL_EDOM, 0); + } + + t = (gsl_integration_qawo_table *) + malloc (sizeof (gsl_integration_qawo_table)); + + if (t == 0) + { + GSL_ERROR_VAL ("failed to allocate space for qawo_table struct", + GSL_ENOMEM, 0); + } + + chebmo = (double *) malloc (25 * n * sizeof (double)); + + if (chebmo == 0) + { + free (t); + GSL_ERROR_VAL ("failed to allocate space for chebmo block", + GSL_ENOMEM, 0); + } + + t->n = n; + t->sine = sine; + t->omega = omega; + t->L = L; + t->par = 0.5 * omega * L; + t->chebmo = chebmo; + + /* precompute the moments */ + + { + size_t i; + double scale = 1.0; + + for (i = 0 ; i < t->n; i++) + { + compute_moments (t->par * scale, t->chebmo + 25*i); + scale *= 0.5; + } + } + + return t; +} + +int +gsl_integration_qawo_table_set (gsl_integration_qawo_table * t, + double omega, double L, + enum gsl_integration_qawo_enum sine) +{ + t->omega = omega; + t->sine = sine; + t->L = L; + t->par = 0.5 * omega * L; + + /* recompute the moments */ + + { + size_t i; + double scale = 1.0; + + for (i = 0 ; i < t->n; i++) + { + compute_moments (t->par * scale, t->chebmo + 25*i); + scale *= 0.5; + } + } + + return GSL_SUCCESS; +} + + +int +gsl_integration_qawo_table_set_length (gsl_integration_qawo_table * t, + double L) +{ + /* return immediately if the length is the same as the old length */ + + if (L == t->L) + return GSL_SUCCESS; + + /* otherwise reset the table and compute the new parameters */ + + t->L = L; + t->par = 0.5 * t->omega * L; + + /* recompute the moments */ + + { + size_t i; + double scale = 1.0; + + for (i = 0 ; i < t->n; i++) + { + compute_moments (t->par * scale, t->chebmo + 25*i); + scale *= 0.5; + } + } + + return GSL_SUCCESS; +} + + +void +gsl_integration_qawo_table_free (gsl_integration_qawo_table * t) +{ + free (t->chebmo); + free (t); +} + +static void +compute_moments (double par, double *chebmo) +{ + double v[28], d[25], d1[25], d2[25]; + + const size_t noeq = 25; + + const double par2 = par * par; + const double par4 = par2 * par2; + const double par22 = par2 + 2.0; + + const double sinpar = sin (par); + const double cospar = cos (par); + + size_t i; + + /* compute the chebyschev moments with respect to cosine */ + + double ac = 8 * cospar; + double as = 24 * par * sinpar; + + v[0] = 2 * sinpar / par; + v[1] = (8 * cospar + (2 * par2 - 8) * sinpar / par) / par2; + v[2] = (32 * (par2 - 12) * cospar + + (2 * ((par2 - 80) * par2 + 192) * sinpar) / par) / par4; + + if (fabs (par) <= 24) + { + /* compute the moments as the solution of a boundary value + problem using the asyptotic expansion as an endpoint */ + + double an2, ass, asap; + double an = 6; + size_t k; + + for (k = 0; k < noeq - 1; k++) + { + an2 = an * an; + d[k] = -2 * (an2 - 4) * (par22 - 2 * an2); + d2[k] = (an - 1) * (an - 2) * par2; + d1[k + 1] = (an + 3) * (an + 4) * par2; + v[k + 3] = as - (an2 - 4) * ac; + an = an + 2.0; + } + + an2 = an * an; + + d[noeq - 1] = -2 * (an2 - 4) * (par22 - 2 * an2); + v[noeq + 2] = as - (an2 - 4) * ac; + v[3] = v[3] - 56 * par2 * v[2]; + + ass = par * sinpar; + asap = (((((210 * par2 - 1) * cospar - (105 * par2 - 63) * ass) / an2 + - (1 - 15 * par2) * cospar + 15 * ass) / an2 + - cospar + 3 * ass) / an2 + - cospar) / an2; + v[noeq + 2] = v[noeq + 2] - 2 * asap * par2 * (an - 1) * (an - 2); + + dgtsl (noeq, d1, d, d2, v + 3); + + } + else + { + /* compute the moments by forward recursion */ + size_t k; + double an = 4; + + for (k = 3; k < 13; k++) + { + double an2 = an * an; + v[k] = ((an2 - 4) * (2 * (par22 - 2 * an2) * v[k - 1] - ac) + + as - par2 * (an + 1) * (an + 2) * v[k - 2]) + / (par2 * (an - 1) * (an - 2)); + an = an + 2.0; + } + } + + + for (i = 0; i < 13; i++) + { + chebmo[2 * i] = v[i]; + } + + /* compute the chebyschev moments with respect to sine */ + + v[0] = 2 * (sinpar - par * cospar) / par2; + v[1] = (18 - 48 / par2) * sinpar / par2 + (-2 + 48 / par2) * cospar / par; + + ac = -24 * par * cospar; + as = -8 * sinpar; + + if (fabs (par) <= 24) + { + /* compute the moments as the solution of a boundary value + problem using the asyptotic expansion as an endpoint */ + + size_t k; + double an2, ass, asap; + double an = 5; + + for (k = 0; k < noeq - 1; k++) + { + an2 = an * an; + d[k] = -2 * (an2 - 4) * (par22 - 2 * an2); + d2[k] = (an - 1) * (an - 2) * par2; + d1[k + 1] = (an + 3) * (an + 4) * par2; + v[k + 2] = ac + (an2 - 4) * as; + an = an + 2.0; + } + + an2 = an * an; + + d[noeq - 1] = -2 * (an2 - 4) * (par22 - 2 * an2); + v[noeq + 1] = ac + (an2 - 4) * as; + v[2] = v[2] - 42 * par2 * v[1]; + + ass = par * cospar; + asap = (((((105 * par2 - 63) * ass - (210 * par2 - 1) * sinpar) / an2 + + (15 * par2 - 1) * sinpar + - 15 * ass) / an2 - sinpar - 3 * ass) / an2 - sinpar) / an2; + v[noeq + 1] = v[noeq + 1] - 2 * asap * par2 * (an - 1) * (an - 2); + + dgtsl (noeq, d1, d, d2, v + 2); + + } + else + { + /* compute the moments by forward recursion */ + size_t k; + double an = 3; + for (k = 2; k < 12; k++) + { + double an2 = an * an; + v[k] = ((an2 - 4) * (2 * (par22 - 2 * an2) * v[k - 1] + as) + + ac - par2 * (an + 1) * (an + 2) * v[k - 2]) + / (par2 * (an - 1) * (an - 2)); + an = an + 2.0; + } + } + + for (i = 0; i < 12; i++) + { + chebmo[2 * i + 1] = v[i]; + } + +} + +static int +dgtsl (size_t n, double *c, double *d, double *e, double *b) +{ + /* solves a tridiagonal matrix A x = b + + c[1 .. n - 1] subdiagonal of the matrix A + d[0 .. n - 1] diagonal of the matrix A + e[0 .. n - 2] superdiagonal of the matrix A + + b[0 .. n - 1] right hand side, replaced by the solution vector x */ + + size_t k; + + c[0] = d[0]; + + if (n == 0) + { + return GSL_SUCCESS; + } + + if (n == 1) + { + b[0] = b[0] / d[0] ; + return GSL_SUCCESS; + } + + d[0] = e[0]; + e[0] = 0; + e[n - 1] = 0; + + for (k = 0; k < n - 1; k++) + { + size_t k1 = k + 1; + + if (fabs (c[k1]) >= fabs (c[k])) + { + { + double t = c[k1]; + c[k1] = c[k]; + c[k] = t; + }; + { + double t = d[k1]; + d[k1] = d[k]; + d[k] = t; + }; + { + double t = e[k1]; + e[k1] = e[k]; + e[k] = t; + }; + { + double t = b[k1]; + b[k1] = b[k]; + b[k] = t; + }; + } + + if (c[k] == 0) + { + return GSL_FAILURE ; + } + + { + double t = -c[k1] / c[k]; + + c[k1] = d[k1] + t * d[k]; + d[k1] = e[k1] + t * e[k]; + e[k1] = 0; + b[k1] = b[k1] + t * b[k]; + } + + } + + if (c[n - 1] == 0) + { + return GSL_FAILURE; + } + + + b[n - 1] = b[n - 1] / c[n - 1]; + + b[n - 2] = (b[n - 2] - d[n - 2] * b[n - 1]) / c[n - 2]; + + for (k = n ; k > 2; k--) + { + size_t kb = k - 3; + b[kb] = (b[kb] - d[kb] * b[kb + 1] - e[kb] * b[kb + 2]) / c[kb]; + } + + return GSL_SUCCESS; +} |