| /* 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)); |
| } |