| /* 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)); |
| } |