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- /* 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 3 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 "gsl__config.h"
- #include "gsl_math.h"
- #include "gsl_errno.h"
- #include "gsl_sf_bessel.h"
- #include "gsl_specfunc__error.h"
- #include "gsl_specfunc__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 "gsl_specfunc__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));
- }
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