1 /* specfunc/bessel_Ynu.c
2 *
3 * Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman, 2017 Konrad Griessinger
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
18 */
19
20 /* Author: G. Jungman */
21
22 #include <config.h>
23 #include <gsl/gsl_math.h>
24 #include <gsl/gsl_errno.h>
25 #include <gsl/gsl_sf_bessel.h>
26 #include <gsl/gsl_sf_sincos_pi.h>
27
28 #include "error.h"
29
30 #include "bessel.h"
31 #include "bessel_olver.h"
32 #include "bessel_temme.h"
33
34 /* Perform forward recurrence for Y_nu(x) and Y'_nu(x)
35 *
36 * Y_{nu+1} = nu/x Y_nu - Y'_nu
37 * Y'_{nu+1} = -(nu+1)/x Y_{nu+1} + Y_nu
38 */
39 #if 0
40 static
41 int
42 bessel_Y_recur(const double nu_min, const double x, const int kmax,
43 const double Y_start, const double Yp_start,
44 double * Y_end, double * Yp_end)
45 {
46 double x_inv = 1.0/x;
47 double nu = nu_min;
48 double Y_nu = Y_start;
49 double Yp_nu = Yp_start;
50 int k;
51
52 for(k=1; k<=kmax; k++) {
53 double nuox = nu*x_inv;
54 double Y_nu_save = Y_nu;
55 Y_nu = -Yp_nu + nuox * Y_nu;
56 Yp_nu = Y_nu_save - (nuox+x_inv) * Y_nu;
57 nu += 1.0;
58 }
59 *Y_end = Y_nu;
60 *Yp_end = Yp_nu;
61 return GSL_SUCCESS;
62 }
63 #endif
64
65
66 /*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
67
68 int
gsl_sf_bessel_Ynupos_e(double nu,double x,gsl_sf_result * result)69 gsl_sf_bessel_Ynupos_e(double nu, double x, gsl_sf_result * result)
70 {
71 /* CHECK_POINTER(result) */
72 if(nu > 50.0) {
73 return gsl_sf_bessel_Ynu_asymp_Olver_e(nu, x, result);
74 }
75 else {
76 /* -1/2 <= mu <= 1/2 */
77 int N = (int)(nu + 0.5);
78 double mu = nu - N;
79
80 gsl_sf_result Y_mu, Y_mup1;
81 int stat_mu;
82 double Ynm1;
83 double Yn;
84 double Ynp1;
85 int n;
86
87 if(x < 2.0) {
88 /* Determine Ymu, Ymup1 directly. This is really
89 * an optimization since this case could as well
90 * be handled by a call to gsl_sf_bessel_JY_mu_restricted(),
91 * as below.
92 */
93 stat_mu = gsl_sf_bessel_Y_temme(mu, x, &Y_mu, &Y_mup1);
94 }
95 else {
96 /* Determine Ymu, Ymup1 and Jmu, Jmup1.
97 */
98 gsl_sf_result J_mu, J_mup1;
99 stat_mu = gsl_sf_bessel_JY_mu_restricted(mu, x, &J_mu, &J_mup1, &Y_mu, &Y_mup1);
100 }
101
102 /* Forward recursion to get Ynu, Ynup1.
103 */
104 Ynm1 = Y_mu.val;
105 Yn = Y_mup1.val;
106 for(n=1; n<=N; n++) {
107 Ynp1 = 2.0*(mu+n)/x * Yn - Ynm1;
108 Ynm1 = Yn;
109 Yn = Ynp1;
110 }
111
112 result->val = Ynm1; /* Y_nu */
113 result->err = (N + 1.0) * fabs(Ynm1) * (fabs(Y_mu.err/Y_mu.val) + fabs(Y_mup1.err/Y_mup1.val));
114 result->err += 2.0 * GSL_DBL_EPSILON * fabs(Ynm1);
115
116 return stat_mu;
117 }
118 }
119
120 int
gsl_sf_bessel_Ynu_e(double nu,double x,gsl_sf_result * result)121 gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result)
122 {
123 /* CHECK_POINTER(result) */
124
125 if(x <= 0.0) {
126 DOMAIN_ERROR(result);
127 }
128 else if (nu < 0.0) {
129 int Jstatus = gsl_sf_bessel_Jnupos_e(-nu, x, result);
130 double Jval = result->val;
131 double Jerr = result->err;
132 int Ystatus = gsl_sf_bessel_Ynupos_e(-nu, x, result);
133 double Yval = result->val;
134 double Yerr = result->err;
135 /* double s = sin(M_PI*nu), c = cos(M_PI*nu); */
136 int sinstatus = gsl_sf_sin_pi_e(nu, result);
137 double s = result->val;
138 double serr = result->err;
139 int cosstatus = gsl_sf_cos_pi_e(nu, result);
140 double c = result->val;
141 double cerr = result->err;
142 result->val = c*Yval - s*Jval;
143 result->err = fabs(c*Yerr) + fabs(s*Jerr) + fabs(cerr*Yval) + fabs(serr*Jval);
144 return GSL_ERROR_SELECT_4(Jstatus, Ystatus, sinstatus, cosstatus);
145 }
146 else return gsl_sf_bessel_Ynupos_e(nu, x, result);
147 }
148
149 /*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
150
151 #include "eval.h"
152
gsl_sf_bessel_Ynu(const double nu,const double x)153 double gsl_sf_bessel_Ynu(const double nu, const double x)
154 {
155 EVAL_RESULT(gsl_sf_bessel_Ynu_e(nu, x, &result));
156 }
157