/* 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));

}