/* specfunc/coulomb_bound.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_exp.h>

#include <gsl/gsl_sf_gamma.h>

#include <gsl/gsl_sf_pow_int.h>

#include <gsl/gsl_sf_laguerre.h>

#include <gsl/gsl_sf_coulomb.h>

#include "error.h"

#include "check.h"

/* normalization for hydrogenic wave functions */

static

int

R_norm(const int n, const int l, const double Z, gsl_sf_result * result)

{

  double A   = 2.0*Z/n;

  double pre = sqrt(A*A*A /(2.0*n));

  gsl_sf_result ln_a, ln_b;

  gsl_sf_result ex;

  int stat_a = gsl_sf_lnfact_e(n+l, &ln_a);

  int stat_b = gsl_sf_lnfact_e(n-l-1, &ln_b);

  double diff_val = 0.5*(ln_b.val - ln_a.val);

  double diff_err = 0.5*(ln_b.err + ln_a.err) + GSL_DBL_EPSILON * fabs(diff_val);

  int stat_e = gsl_sf_exp_err_e(diff_val, diff_err, &ex);

  result->val  = pre * ex.val;

  result->err  = pre * ex.err;

  result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

  return GSL_ERROR_SELECT_3(stat_e, stat_a, stat_b);

}

/*-*-*-*-*-*-*-*-*-*-*-* Functions with Error Codes *-*-*-*-*-*-*-*-*-*-*-*/

int

gsl_sf_hydrogenicR_1_e(const double Z, const double r, gsl_sf_result * result)

{

  if(Z > 0.0 && r >= 0.0) {

    double A = 2.0*Z;

    double norm = A*sqrt(Z);

    double ea = exp(-Z*r);

    result->val = norm*ea;

    result->err = 2.0 * GSL_DBL_EPSILON * fabs(result->val) * fabs(Z*r);

    CHECK_UNDERFLOW(result);

    return GSL_SUCCESS;

  }

  else {

    DOMAIN_ERROR(result);

  }

}

int

gsl_sf_hydrogenicR_e(const int n, const int l,

                        const double Z, const double r,

                        gsl_sf_result * result)

{

  if(n < 1 || l > n-1 || Z <= 0.0 || r < 0.0) {

    DOMAIN_ERROR(result);

  }

  else {

    double A = 2.0*Z/n;

    gsl_sf_result norm;

    int stat_norm = R_norm(n, l, Z, &norm);

    double rho = A*r;

    double ea = exp(-0.5*rho);

    double pp = gsl_sf_pow_int(rho, l);

    gsl_sf_result lag;

    int stat_lag = gsl_sf_laguerre_n_e(n-l-1, 2*l+1, rho, &lag);

    double W_val = norm.val * ea * pp;

    double W_err = norm.err * ea * pp;

    W_err += norm.val * ((0.5*rho + 1.0) * GSL_DBL_EPSILON) * ea * pp;

    W_err += norm.val * ea * ((l+1.0) * GSL_DBL_EPSILON) * pp;

    result->val  = W_val * lag.val;

    result->err  = W_val * lag.err + W_err * fabs(lag.val);

    result->err += 2.0 * GSL_DBL_EPSILON * fabs(result->val);

    if ((l == 0 || (r > 0 && l > 0)) && lag.val != 0.0 

        && stat_lag == GSL_SUCCESS && stat_norm == GSL_SUCCESS) {

      CHECK_UNDERFLOW(result);

    };

    return GSL_ERROR_SELECT_2(stat_lag, stat_norm);

  }

}

/*-*-*-*-*-*-*-*-*-* Functions w/ Natural Prototypes *-*-*-*-*-*-*-*-*-*-*/

#include "eval.h"

double gsl_sf_hydrogenicR_1(const double Z, const double r)

{

  EVAL_RESULT(gsl_sf_hydrogenicR_1_e(Z, r, &result));

}

double gsl_sf_hydrogenicR(const int n, const int l, const double Z, const double r)

{

  EVAL_RESULT(gsl_sf_hydrogenicR_e(n, l, Z, r, &result));

}