diff options
Diffstat (limited to 'gsl-1.9/specfunc/bessel_In.c')
-rw-r--r-- | gsl-1.9/specfunc/bessel_In.c | 225 |
1 files changed, 225 insertions, 0 deletions
diff --git a/gsl-1.9/specfunc/bessel_In.c b/gsl-1.9/specfunc/bessel_In.c new file mode 100644 index 0000000..ea4e18b --- /dev/null +++ b/gsl-1.9/specfunc/bessel_In.c @@ -0,0 +1,225 @@ +/* specfunc/bessel_In.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_bessel.h> + +#include "error.h" + +#include "bessel.h" + +/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/ + + +int +gsl_sf_bessel_In_scaled_e(int n, const double x, gsl_sf_result * result) +{ + const double ax = fabs(x); + + n = abs(n); /* I(-n, z) = I(n, z) */ + + /* CHECK_POINTER(result) */ + + if(n == 0) { + return gsl_sf_bessel_I0_scaled_e(x, result); + } + else if(n == 1) { + return gsl_sf_bessel_I1_scaled_e(x, result); + } + 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)/M_E) { + gsl_sf_result t; + double ex = exp(-ax); + int stat_In = gsl_sf_bessel_IJ_taylor_e((double)n, ax, 1, 50, GSL_DBL_EPSILON, &t); + result->val = t.val * ex; + result->err = t.err * ex; + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val; + return stat_In; + } + else if(n < 150 && ax < 1e7) { + gsl_sf_result I0_scaled; + int stat_I0 = gsl_sf_bessel_I0_scaled_e(ax, &I0_scaled); + double rat; + int stat_CF1 = gsl_sf_bessel_I_CF1_ser((double)n, ax, &rat); + double Ikp1 = rat * GSL_SQRT_DBL_MIN; + double Ik = GSL_SQRT_DBL_MIN; + double Ikm1; + int k; + for(k=n; k >= 1; k--) { + Ikm1 = Ikp1 + 2.0*k/ax * Ik; + Ikp1 = Ik; + Ik = Ikm1; + } + result->val = I0_scaled.val * (GSL_SQRT_DBL_MIN / Ik); + result->err = I0_scaled.err * (GSL_SQRT_DBL_MIN / Ik); + result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val); + if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val; + return GSL_ERROR_SELECT_2(stat_I0, stat_CF1); + } + else if( GSL_MIN( 0.29/(n*n), 0.5/(n*n + x*x) ) < 0.5*GSL_ROOT3_DBL_EPSILON) { + int stat_as = gsl_sf_bessel_Inu_scaled_asymp_unif_e((double)n, ax, result); + if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val; + return stat_as; + } + else { + const int nhi = 2 + (int) (1.2 / GSL_ROOT6_DBL_EPSILON); + gsl_sf_result r_Ikp1; + gsl_sf_result r_Ik; + int stat_a1 = gsl_sf_bessel_Inu_scaled_asymp_unif_e(nhi+1.0, ax, &r_Ikp1); + int stat_a2 = gsl_sf_bessel_Inu_scaled_asymp_unif_e((double)nhi, ax, &r_Ik); + double Ikp1 = r_Ikp1.val; + double Ik = r_Ik.val; + double Ikm1; + int k; + for(k=nhi; k > n; k--) { + Ikm1 = Ikp1 + 2.0*k/ax * Ik; + Ikp1 = Ik; + Ik = Ikm1; + } + result->val = Ik; + result->err = Ik * (r_Ikp1.err/r_Ikp1.val + r_Ik.err/r_Ik.val); + if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val; + return GSL_ERROR_SELECT_2(stat_a1, stat_a2); + } +} + + +int +gsl_sf_bessel_In_scaled_array(const int nmin, const int nmax, const double x, double * result_array) +{ + /* CHECK_POINTER(result_array) */ + + if(nmax < nmin || nmin < 0) { + int j; + for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0; + GSL_ERROR ("domain error", GSL_EDOM); + } + else if(x == 0.0) { + int j; + for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0; + if(nmin == 0) result_array[0] = 1.0; + return GSL_SUCCESS; + } + else if(nmax == 0) { + gsl_sf_result I0_scaled; + int stat = gsl_sf_bessel_I0_scaled_e(x, &I0_scaled); + result_array[0] = I0_scaled.val; + return stat; + } + else { + const double ax = fabs(x); + const double two_over_x = 2.0/ax; + + /* starting values */ + gsl_sf_result r_Inp1; + gsl_sf_result r_In; + int stat_0 = gsl_sf_bessel_In_scaled_e(nmax+1, ax, &r_Inp1); + int stat_1 = gsl_sf_bessel_In_scaled_e(nmax, ax, &r_In); + double Inp1 = r_Inp1.val; + double In = r_In.val; + double Inm1; + int n; + + for(n=nmax; n>=nmin; n--) { + result_array[n-nmin] = In; + Inm1 = Inp1 + n * two_over_x * In; + Inp1 = In; + In = Inm1; + } + + /* deal with signs */ + if(x < 0.0) { + for(n=nmin; n<=nmax; n++) { + if(GSL_IS_ODD(n)) result_array[n-nmin] = -result_array[n-nmin]; + } + } + + return GSL_ERROR_SELECT_2(stat_0, stat_1); + } +} + + +int +gsl_sf_bessel_In_e(const int n_in, const double x, gsl_sf_result * result) +{ + const double ax = fabs(x); + const int n = abs(n_in); /* I(-n, z) = I(n, z) */ + gsl_sf_result In_scaled; + const int stat_In_scaled = gsl_sf_bessel_In_scaled_e(n, ax, &In_scaled); + + /* In_scaled is always less than 1, + * so this overflow check is conservative. + */ + if(ax > GSL_LOG_DBL_MAX - 1.0) { + OVERFLOW_ERROR(result); + } + else { + const double ex = exp(ax); + result->val = ex * In_scaled.val; + result->err = ex * In_scaled.err; + result->err += ax * GSL_DBL_EPSILON * fabs(result->val); + if(x < 0.0 && GSL_IS_ODD(n)) result->val = -result->val; + return stat_In_scaled; + } +} + + +int +gsl_sf_bessel_In_array(const int nmin, const int nmax, const double x, double * result_array) +{ + double ax = fabs(x); + + /* CHECK_POINTER(result_array) */ + + if(ax > GSL_LOG_DBL_MAX - 1.0) { + int j; + for(j=0; j<=nmax-nmin; j++) result_array[j] = 0.0; /* FIXME: should be Inf */ + GSL_ERROR ("overflow", GSL_EOVRFLW); + } + else { + int j; + double eax = exp(ax); + int status = gsl_sf_bessel_In_scaled_array(nmin, nmax, x, result_array); + for(j=0; j<=nmax-nmin; j++) result_array[j] *= eax; + return status; + } +} + +/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/ + +#include "eval.h" + +double gsl_sf_bessel_In_scaled(const int n, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_In_scaled_e(n, x, &result)); +} + +double gsl_sf_bessel_In(const int n, const double x) +{ + EVAL_RESULT(gsl_sf_bessel_In_e(n, x, &result)); +} |