diff options
Diffstat (limited to 'gsl-1.9/specfunc/gegenbauer.c')
| -rw-r--r-- | gsl-1.9/specfunc/gegenbauer.c | 194 |
1 files changed, 194 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/gegenbauer.c b/gsl-1.9/specfunc/gegenbauer.c new file mode 100644 index 0000000..7d3dfb4 --- /dev/null +++ b/gsl-1.9/specfunc/gegenbauer.c @@ -0,0 +1,194 @@ +/* specfunc/gegenbauer.c + * + * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman + * + * 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. + */ + +/* Author: G. Jungman */ + +#include <config.h> +#include <gsl/gsl_math.h> +#include <gsl/gsl_errno.h> +#include <gsl/gsl_sf_gegenbauer.h> + +#include "error.h" + +/* See: [Thompson, Atlas for Computing Mathematical Functions] */ + + +int +gsl_sf_gegenpoly_1_e(double lambda, double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(lambda == 0.0) { + result->val = 2.0*x; + result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else { + result->val = 2.0*lambda*x; + result->err = 4.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } +} + +int +gsl_sf_gegenpoly_2_e(double lambda, double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(lambda == 0.0) { + const double txx = 2.0*x*x; + result->val = -1.0 + txx; + result->err = 2.0 * GSL_DBL_EPSILON * fabs(txx); + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + return GSL_SUCCESS; + } + else { + result->val = lambda*(-1.0 + 2.0*(1.0+lambda)*x*x); + result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda)); + return GSL_SUCCESS; + } +} + +int +gsl_sf_gegenpoly_3_e(double lambda, double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(lambda == 0.0) { + result->val = x*(-2.0 + 4.0/3.0*x*x); + result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(x)); + return GSL_SUCCESS; + } + else { + double c = 4.0 + lambda*(6.0 + 2.0*lambda); + result->val = 2.0*lambda * x * ( -1.0 - lambda + c*x*x/3.0 ); + result->err = GSL_DBL_EPSILON * (2.0 * fabs(result->val) + fabs(lambda * x)); + return GSL_SUCCESS; + } +} + + +int +gsl_sf_gegenpoly_n_e(int n, double lambda, double x, gsl_sf_result * result) +{ + /* CHECK_POINTER(result) */ + + if(lambda <= -0.5 || n < 0) { + DOMAIN_ERROR(result); + } + else if(n == 0) { + result->val = 1.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else if(n == 1) { + return gsl_sf_gegenpoly_1_e(lambda, x, result); + } + else if(n == 2) { + return gsl_sf_gegenpoly_2_e(lambda, x, result); + } + else if(n == 3) { + return gsl_sf_gegenpoly_3_e(lambda, x, result); + } + else { + if(lambda == 0.0 && (x >= -1.0 || x <= 1.0)) { + /* 2 T_n(x)/n */ + const double z = n * acos(x); + result->val = 2.0 * cos(z) / n; + result->err = 2.0 * GSL_DBL_EPSILON * fabs(z * result->val); + return GSL_SUCCESS; + } + else { + int k; + gsl_sf_result g2; + gsl_sf_result g3; + int stat_g2 = gsl_sf_gegenpoly_2_e(lambda, x, &g2); + int stat_g3 = gsl_sf_gegenpoly_3_e(lambda, x, &g3); + int stat_g = GSL_ERROR_SELECT_2(stat_g2, stat_g3); + double gkm2 = g2.val; + double gkm1 = g3.val; + double gk = 0.0; + for(k=4; k<=n; k++) { + gk = (2.0*(k+lambda-1.0)*x*gkm1 - (k+2.0*lambda-2.0)*gkm2) / k; + gkm2 = gkm1; + gkm1 = gk; + } + result->val = gk; + result->err = 2.0 * GSL_DBL_EPSILON * 0.5 * n * fabs(gk); + return stat_g; + } + } +} + + +int +gsl_sf_gegenpoly_array(int nmax, double lambda, double x, double * result_array) +{ + int k; + + /* CHECK_POINTER(result_array) */ + + if(lambda <= -0.5 || nmax < 0) { + GSL_ERROR("domain error", GSL_EDOM); + } + + /* n == 0 */ + result_array[0] = 1.0; + if(nmax == 0) return GSL_SUCCESS; + + /* n == 1 */ + if(lambda == 0.0) + result_array[1] = 2.0*x; + else + result_array[1] = 2.0*lambda*x; + + /* n <= nmax */ + for(k=2; k<=nmax; k++) { + double term1 = 2.0*(k+lambda-1.0) * x * result_array[k-1]; + double term2 = (k+2.0*lambda-2.0) * result_array[k-2]; + result_array[k] = (term1 - term2) / k; + } + + return GSL_SUCCESS; +} + + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_gegenpoly_1(double lambda, double x) +{ + EVAL_RESULT(gsl_sf_gegenpoly_1_e(lambda, x, &result)); +} + +double gsl_sf_gegenpoly_2(double lambda, double x) +{ + EVAL_RESULT(gsl_sf_gegenpoly_2_e(lambda, x, &result)); +} + +double gsl_sf_gegenpoly_3(double lambda, double x) +{ + EVAL_RESULT(gsl_sf_gegenpoly_3_e(lambda, x, &result)); +} + +double gsl_sf_gegenpoly_n(int n, double lambda, double x) +{ + EVAL_RESULT(gsl_sf_gegenpoly_n_e(n, lambda, x, &result)); +} |