diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_Jn.c')
| -rw-r--r-- | gsl-1.9/specfunc/bessel_Jn.c | 199 |
1 files changed, 199 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_Jn.c b/gsl-1.9/specfunc/bessel_Jn.c new file mode 100644 index 0000000..a79ded4 --- /dev/null +++ b/gsl-1.9/specfunc/bessel_Jn.c @@ -0,0 +1,199 @@ +/* specfunc/bessel_Jn.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_pow_int.h> +#include "bessel.h" +#include "bessel_amp_phase.h" +#include "bessel_olver.h" +#include <gsl/gsl_sf_bessel.h> + + + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + + +int gsl_sf_bessel_Jn_e(int n, double x, gsl_sf_result * result) +{ + int sign = 1; + + if(n < 0) { + /* reduce to case n >= 0 */ + n = -n; + if(GSL_IS_ODD(n)) sign = -sign; + } + + if(x < 0.0) { + /* reduce to case x >= 0. */ + x = -x; + if(GSL_IS_ODD(n)) sign = -sign; + } + + /* CHECK_POINTER(result) */ + + if(n == 0) { + gsl_sf_result b0; + int stat_J0 = gsl_sf_bessel_J0_e(x, &b0); + result->val = sign * b0.val; + result->err = b0.err; + return stat_J0; + } + else if(n == 1) { + gsl_sf_result b1; + int stat_J1 = gsl_sf_bessel_J1_e(x, &b1); + result->val = sign * b1.val; + result->err = b1.err; + return stat_J1; + } + else { + if(x == 0.0) { + result->val = 0.0; + result->err = 0.0; + return GSL_SUCCESS; + } + else if(x*x < 10.0*(n+1.0)*GSL_ROOT5_DBL_EPSILON) { + gsl_sf_result b; + int status = gsl_sf_bessel_IJ_taylor_e((double)n, x, -1, 50, GSL_DBL_EPSILON, &b); + result->val = sign * b.val; + result->err = b.err; + result->err += GSL_DBL_EPSILON * fabs(result->val); + return status; + } + else if(GSL_ROOT4_DBL_EPSILON * x > (n*n+1.0)) { + int status = gsl_sf_bessel_Jnu_asympx_e((double)n, x, result); + result->val *= sign; + return status; + } + else if(n > 50) { + int status = gsl_sf_bessel_Jnu_asymp_Olver_e((double)n, x, result); + result->val *= sign; + return status; + } + else if(x > 1000.0) + { + /* We need this to avoid feeding large x to CF1; note that + * due to the above check, we know that n <= 50. + */ + int status = gsl_sf_bessel_Jnu_asympx_e((double)n, x, result); + result->val *= sign; + return status; + } + else { + double ans; + double err; + double ratio; + double sgn; + int stat_b; + int stat_CF1 = gsl_sf_bessel_J_CF1((double)n, x, &ratio, &sgn); + + /* backward recurrence */ + double Jkp1 = GSL_SQRT_DBL_MIN * ratio; + double Jk = GSL_SQRT_DBL_MIN; + double Jkm1; + int k; + + for(k=n; k>0; k--) { + Jkm1 = 2.0*k/x * Jk - Jkp1; + Jkp1 = Jk; + Jk = Jkm1; + } + + if(fabs(Jkp1) > fabs(Jk)) { + gsl_sf_result b1; + stat_b = gsl_sf_bessel_J1_e(x, &b1); + ans = b1.val/Jkp1 * GSL_SQRT_DBL_MIN; + err = b1.err/Jkp1 * GSL_SQRT_DBL_MIN; + } + else { + gsl_sf_result b0; + stat_b = gsl_sf_bessel_J0_e(x, &b0); + ans = b0.val/Jk * GSL_SQRT_DBL_MIN; + err = b0.err/Jk * GSL_SQRT_DBL_MIN; + } + + result->val = sign * ans; + result->err = fabs(err); + return GSL_ERROR_SELECT_2(stat_CF1, stat_b); + } + } +} + + +int +gsl_sf_bessel_Jn_array(int nmin, int nmax, double x, double * result_array) +{ + /* CHECK_POINTER(result_array) */ + + if(nmin < 0 || nmax < nmin) { + int n; + for(n=nmax; n>=nmin; n--) { + result_array[n-nmin] = 0.0; + } + GSL_ERROR ("domain error", GSL_EDOM); + } + else if(x == 0.0) { + int n; + for(n=nmax; n>=nmin; n--) { + result_array[n-nmin] = 0.0; + } + if(nmin == 0) result_array[0] = 1.0; + return GSL_SUCCESS; + } + else { + gsl_sf_result r_Jnp1; + gsl_sf_result r_Jn; + int stat_np1 = gsl_sf_bessel_Jn_e(nmax+1, x, &r_Jnp1); + int stat_n = gsl_sf_bessel_Jn_e(nmax, x, &r_Jn); + int stat = GSL_ERROR_SELECT_2(stat_np1, stat_n); + + double Jnp1 = r_Jnp1.val; + double Jn = r_Jn.val; + double Jnm1; + int n; + + if(stat == GSL_SUCCESS) { + for(n=nmax; n>=nmin; n--) { + result_array[n-nmin] = Jn; + Jnm1 = -Jnp1 + 2.0*n/x * Jn; + Jnp1 = Jn; + Jn = Jnm1; + } + } + else { + for(n=nmax; n>=nmin; n--) { + result_array[n-nmin] = 0.0; + } + } + + return stat; + } +} + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_bessel_Jn(const int n, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_Jn_e(n, x, &result)); +} |