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/* specfunc/bessel_Ynu.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman, 2017 Konrad Griessinger
*
* 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_bessel.h>
#include <gsl/gsl_sf_sincos_pi.h>
#include "error.h"
#include "bessel.h"
#include "bessel_olver.h"
#include "bessel_temme.h"
/* Perform forward recurrence for Y_nu(x) and Y'_nu(x)
*
* Y_{nu+1} = nu/x Y_nu - Y'_nu
* Y'_{nu+1} = -(nu+1)/x Y_{nu+1} + Y_nu
*/
#if 0
static
int
bessel_Y_recur(const double nu_min, const double x, const int kmax,
const double Y_start, const double Yp_start,
double * Y_end, double * Yp_end)
{
double x_inv = 1.0/x;
double nu = nu_min;
double Y_nu = Y_start;
double Yp_nu = Yp_start;
int k;
for(k=1; k<=kmax; k++) {
double nuox = nu*x_inv;
double Y_nu_save = Y_nu;
Y_nu = -Yp_nu + nuox * Y_nu;
Yp_nu = Y_nu_save - (nuox+x_inv) * Y_nu;
nu += 1.0;
}
*Y_end = Y_nu;
*Yp_end = Yp_nu;
return GSL_SUCCESS;
}
#endif
/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/
int
gsl_sf_bessel_Ynupos_e(double nu, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(nu > 50.0) {
return gsl_sf_bessel_Ynu_asymp_Olver_e(nu, x, result);
}
else {
/* -1/2 <= mu <= 1/2 */
int N = (int)(nu + 0.5);
double mu = nu - N;
gsl_sf_result Y_mu, Y_mup1;
int stat_mu;
double Ynm1;
double Yn;
double Ynp1;
int n;
if(x < 2.0) {
/* Determine Ymu, Ymup1 directly. This is really
* an optimization since this case could as well
* be handled by a call to gsl_sf_bessel_JY_mu_restricted(),
* as below.
*/
stat_mu = gsl_sf_bessel_Y_temme(mu, x, &Y_mu, &Y_mup1);
}
else {
/* Determine Ymu, Ymup1 and Jmu, Jmup1.
*/
gsl_sf_result J_mu, J_mup1;
stat_mu = gsl_sf_bessel_JY_mu_restricted(mu, x, &J_mu, &J_mup1, &Y_mu, &Y_mup1);
}
/* Forward recursion to get Ynu, Ynup1.
*/
Ynm1 = Y_mu.val;
Yn = Y_mup1.val;
for(n=1; n<=N; n++) {
Ynp1 = 2.0*(mu+n)/x * Yn - Ynm1;
Ynm1 = Yn;
Yn = Ynp1;
}
result->val = Ynm1; /* Y_nu */
result->err = (N + 1.0) * fabs(Ynm1) * (fabs(Y_mu.err/Y_mu.val) + fabs(Y_mup1.err/Y_mup1.val));
result->err += 2.0 * GSL_DBL_EPSILON * fabs(Ynm1);
return stat_mu;
}
}
int
gsl_sf_bessel_Ynu_e(double nu, double x, gsl_sf_result * result)
{
/* CHECK_POINTER(result) */
if(x <= 0.0) {
DOMAIN_ERROR(result);
}
else if (nu < 0.0) {
int Jstatus = gsl_sf_bessel_Jnupos_e(-nu, x, result);
double Jval = result->val;
double Jerr = result->err;
int Ystatus = gsl_sf_bessel_Ynupos_e(-nu, x, result);
double Yval = result->val;
double Yerr = result->err;
/* double s = sin(M_PI*nu), c = cos(M_PI*nu); */
int sinstatus = gsl_sf_sin_pi_e(nu, result);
double s = result->val;
double serr = result->err;
int cosstatus = gsl_sf_cos_pi_e(nu, result);
double c = result->val;
double cerr = result->err;
result->val = c*Yval - s*Jval;
result->err = fabs(c*Yerr) + fabs(s*Jerr) + fabs(cerr*Yval) + fabs(serr*Jval);
return GSL_ERROR_SELECT_4(Jstatus, Ystatus, sinstatus, cosstatus);
}
else return gsl_sf_bessel_Ynupos_e(nu, x, result);
}
/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/
#include "eval.h"
double gsl_sf_bessel_Ynu(const double nu, const double x)
{
EVAL_RESULT(gsl_sf_bessel_Ynu_e(nu, x, &result));
}
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