1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
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 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 <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));
}
|
