/* specfunc/mathieu_radfunc.c

 * 

 * Copyright (C) 2002 Lowell Johnson

 * 

 * 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., 675 Mass Ave, Cambridge, MA 02139, USA.

 */

/* Author:  L. Johnson */

#include <config.h>

#include <stdlib.h>

#include <math.h>

#include <gsl/gsl_math.h>

#include <gsl/gsl_sf.h>

#include <gsl/gsl_sf_mathieu.h>

int gsl_sf_mathieu_Mc_e(int kind, int order, double qq, double zz,

                      gsl_sf_result *result)

{

  int even_odd, kk, mm, status;

  double maxerr = 1e-14, amax, pi = M_PI, fn, factor;

  double coeff[GSL_SF_MATHIEU_COEFF], fc;

  double j1c, z2c, j1pc, z2pc;

  double u1, u2;

  gsl_sf_result aa;

  /* Check for out of bounds parameters. */

  if (qq <= 0.0)

  {

      GSL_ERROR("q must be greater than zero", GSL_EINVAL);

  }

  if (kind < 1 || kind > 2)

  {

      GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);

  }

  mm = 0;

  amax = 0.0;

  fn = 0.0;

  u1 = sqrt(qq)*exp(-1.0*zz);

  u2 = sqrt(qq)*exp(zz);

  even_odd = 0;

  if (order % 2 != 0)

      even_odd = 1;

  /* Compute the characteristic value. */

  status = gsl_sf_mathieu_a_e(order, qq, &aa);

  if (status != GSL_SUCCESS)

  {

      return status;

  }

  /* Compute the series coefficients. */

  status = gsl_sf_mathieu_a_coeff(order, qq, aa.val, coeff);

  if (status != GSL_SUCCESS)

  {

      return status;

  }

  if (even_odd == 0)

  {

      for (kk=0; kk

      {

          amax = GSL_MAX(amax, fabs(coeff[kk]));

          if (fabs(coeff[kk])/amax < maxerr)

              break;

          j1c = gsl_sf_bessel_Jn(kk, u1);

          if (kind == 1)

          {

              z2c = gsl_sf_bessel_Jn(kk, u2);

          }

          else /* kind = 2 */

          {

              z2c = gsl_sf_bessel_Yn(kk, u2);

          }

          fc = pow(-1.0, 0.5*order+kk)*coeff[kk];

          fn += fc*j1c*z2c;

      }

      fn *= sqrt(pi/2.0)/coeff[0];

  }

  else

  {

      for (kk=0; kk

      {

          amax = GSL_MAX(amax, fabs(coeff[kk]));

          if (fabs(coeff[kk])/amax < maxerr)

              break;

          j1c = gsl_sf_bessel_Jn(kk, u1);

          j1pc = gsl_sf_bessel_Jn(kk+1, u1);

          if (kind == 1)

          {

              z2c = gsl_sf_bessel_Jn(kk, u2);

              z2pc = gsl_sf_bessel_Jn(kk+1, u2);

          }

          else /* kind = 2 */

          {

              z2c = gsl_sf_bessel_Yn(kk, u2);

              z2pc = gsl_sf_bessel_Yn(kk+1, u2);

          }

          fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];

          fn += fc*(j1c*z2pc + j1pc*z2c);

      }

      fn *= sqrt(pi/2.0)/coeff[0];

  }

  result->val = fn;

  result->err = 2.0*GSL_DBL_EPSILON;

  factor = fabs(fn);

  if (factor > 1.0)

      result->err *= factor;

  return GSL_SUCCESS;

}

int gsl_sf_mathieu_Ms_e(int kind, int order, double qq, double zz,

                      gsl_sf_result *result)

{

  int even_odd, kk, mm, status;

  double maxerr = 1e-14, amax, pi = M_PI, fn, factor;

  double coeff[GSL_SF_MATHIEU_COEFF], fc;

  double j1c, z2c, j1mc, z2mc, j1pc, z2pc;

  double u1, u2;

  gsl_sf_result aa;

  /* Check for out of bounds parameters. */

  if (qq <= 0.0)

  {

      GSL_ERROR("q must be greater than zero", GSL_EINVAL);

  }

  if (kind < 1 || kind > 2)

  {

      GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);

  }

  /* Handle the trivial cases where order = 0. */

  if (order == 0)

  {

      result->val = 0.0;

      result->err = 0.0;

      return GSL_SUCCESS;

  }

  mm = 0;

  amax = 0.0;

  fn = 0.0;

  u1 = sqrt(qq)*exp(-1.0*zz);

  u2 = sqrt(qq)*exp(zz);

  even_odd = 0;

  if (order % 2 != 0)

      even_odd = 1;

  /* Compute the characteristic value. */

  status = gsl_sf_mathieu_b_e(order, qq, &aa);

  if (status != GSL_SUCCESS)

  {

      return status;

  }

  /* Compute the series coefficients. */

  status = gsl_sf_mathieu_b_coeff(order, qq, aa.val, coeff);

  if (status != GSL_SUCCESS)

  {

      return status;

  }

  if (even_odd == 0)

  {

      for (kk=0; kk

      {

          amax = GSL_MAX(amax, fabs(coeff[kk]));

          if (fabs(coeff[kk])/amax < maxerr)

              break;

          j1mc = gsl_sf_bessel_Jn(kk, u1);

          j1pc = gsl_sf_bessel_Jn(kk+2, u1);

          if (kind == 1)

          {

              z2mc = gsl_sf_bessel_Jn(kk, u2);

              z2pc = gsl_sf_bessel_Jn(kk+2, u2);

          }

          else /* kind = 2 */

          {

              z2mc = gsl_sf_bessel_Yn(kk, u2);

              z2pc = gsl_sf_bessel_Yn(kk+2, u2);

          }

          fc = pow(-1.0, 0.5*order+kk+1)*coeff[kk];

          fn += fc*(j1mc*z2pc - j1pc*z2mc);

      }

      fn *= sqrt(pi/2.0)/coeff[0];

  }

  else

  {

      for (kk=0; kk

      {

          amax = GSL_MAX(amax, fabs(coeff[kk]));

          if (fabs(coeff[kk])/amax < maxerr)

              break;

          j1c = gsl_sf_bessel_Jn(kk, u1);

          j1pc = gsl_sf_bessel_Jn(kk+1, u1);

          if (kind == 1)

          {

              z2c = gsl_sf_bessel_Jn(kk, u2);

              z2pc = gsl_sf_bessel_Jn(kk+1, u2);

          }

          else /* kind = 2 */

          {

              z2c = gsl_sf_bessel_Yn(kk, u2);

              z2pc = gsl_sf_bessel_Yn(kk+1, u2);

          }

          fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];

          fn += fc*(j1c*z2pc - j1pc*z2c);

      }

      fn *= sqrt(pi/2.0)/coeff[0];

  }

  result->val = fn;

  result->err = 2.0*GSL_DBL_EPSILON;

  factor = fabs(fn);

  if (factor > 1.0)

      result->err *= factor;

  return GSL_SUCCESS;

}

int gsl_sf_mathieu_Mc_array(int kind, int nmin, int nmax, double qq,

                            double zz, gsl_sf_mathieu_workspace *work,

                            double result_array[])

{

  int even_odd, order, ii, kk, mm, status;

  double maxerr = 1e-14, amax, pi = M_PI, fn;

  double coeff[GSL_SF_MATHIEU_COEFF], fc;

  double j1c, z2c, j1pc, z2pc;

  double u1, u2;

  double *aa = work->aa;

  /* Initialize the result array to zeroes. */

  for (ii=0; ii

      result_array[ii] = 0.0;

  /* Check for out of bounds parameters. */

  if (qq <= 0.0)

  {

      GSL_ERROR("q must be greater than zero", GSL_EINVAL);

  }

  if (kind < 1 || kind > 2)

  {

      GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);

  }

  mm = 0;

  amax = 0.0;

  u1 = sqrt(qq)*exp(-1.0*zz);

  u2 = sqrt(qq)*exp(zz);

  /* Compute all eigenvalues up to nmax. */

  gsl_sf_mathieu_a_array(0, nmax, qq, work, aa);

  for (ii=0, order=nmin; order<=nmax; ii++, order++)

  {

      fn = 0.0;

      even_odd = 0;

      if (order % 2 != 0)

          even_odd = 1;

      /* Compute the series coefficients. */

      status = gsl_sf_mathieu_a_coeff(order, qq, aa[order], coeff);

      if (status != GSL_SUCCESS)

      {

          return status;

      }

      if (even_odd == 0)

      {

          for (kk=0; kk

          {

              amax = GSL_MAX(amax, fabs(coeff[kk]));

              if (fabs(coeff[kk])/amax < maxerr)

                  break;

              j1c = gsl_sf_bessel_Jn(kk, u1);

              if (kind == 1)

              {

                  z2c = gsl_sf_bessel_Jn(kk, u2);

              }

              else /* kind = 2 */

              {

                  z2c = gsl_sf_bessel_Yn(kk, u2);

              }

              fc = pow(-1.0, 0.5*order+kk)*coeff[kk];

              fn += fc*j1c*z2c;

          }

          fn *= sqrt(pi/2.0)/coeff[0];

      }

      else

      {

          for (kk=0; kk

          {

              amax = GSL_MAX(amax, fabs(coeff[kk]));

              if (fabs(coeff[kk])/amax < maxerr)

                  break;

              j1c = gsl_sf_bessel_Jn(kk, u1);

              j1pc = gsl_sf_bessel_Jn(kk+1, u1);

              if (kind == 1)

              {

                  z2c = gsl_sf_bessel_Jn(kk, u2);

                  z2pc = gsl_sf_bessel_Jn(kk+1, u2);

              }

              else /* kind = 2 */

              {

                  z2c = gsl_sf_bessel_Yn(kk, u2);

                  z2pc = gsl_sf_bessel_Yn(kk+1, u2);

              }

              fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];

              fn += fc*(j1c*z2pc + j1pc*z2c);

          }

          fn *= sqrt(pi/2.0)/coeff[0];

      }

      result_array[ii] = fn;

  } /* order loop */

  return GSL_SUCCESS;

}

int gsl_sf_mathieu_Ms_array(int kind, int nmin, int nmax, double qq,

                            double zz, gsl_sf_mathieu_workspace *work,

                            double result_array[])

{

  int even_odd, order, ii, kk, mm, status;

  double maxerr = 1e-14, amax, pi = M_PI, fn;

  double coeff[GSL_SF_MATHIEU_COEFF], fc;

  double j1c, z2c, j1mc, z2mc, j1pc, z2pc;

  double u1, u2;

  double *bb = work->bb;

  /* Initialize the result array to zeroes. */

  for (ii=0; ii

      result_array[ii] = 0.0;

  /* Check for out of bounds parameters. */

  if (qq <= 0.0)

  {

      GSL_ERROR("q must be greater than zero", GSL_EINVAL);

  }

  if (kind < 1 || kind > 2)

  {

      GSL_ERROR("kind must be 1 or 2", GSL_EINVAL);

  }

  mm = 0;

  amax = 0.0;

  u1 = sqrt(qq)*exp(-1.0*zz);

  u2 = sqrt(qq)*exp(zz);

  /* Compute all eigenvalues up to nmax. */

  gsl_sf_mathieu_b_array(0, nmax, qq, work, bb);

  for (ii=0, order=nmin; order<=nmax; ii++, order++)

  {

      fn = 0.0;

      even_odd = 0;

      if (order % 2 != 0)

          even_odd = 1;

      /* Handle the trivial cases where order = 0. */

      if (order == 0)

      {

          result_array[ii] = 0.0;

          continue;

      }

      /* Compute the series coefficients. */

      status = gsl_sf_mathieu_b_coeff(order, qq, bb[order], coeff);

      if (status != GSL_SUCCESS)

      {

          return status;

      }

      if (even_odd == 0)

      {

          for (kk=0; kk

          {

              amax = GSL_MAX(amax, fabs(coeff[kk]));

              if (fabs(coeff[kk])/amax < maxerr)

                  break;

              j1mc = gsl_sf_bessel_Jn(kk, u1);

              j1pc = gsl_sf_bessel_Jn(kk+2, u1);

              if (kind == 1)

              {

                  z2mc = gsl_sf_bessel_Jn(kk, u2);

                  z2pc = gsl_sf_bessel_Jn(kk+2, u2);

              }

              else /* kind = 2 */

              {

                  z2mc = gsl_sf_bessel_Yn(kk, u2);

                  z2pc = gsl_sf_bessel_Yn(kk+2, u2);

              }

              fc = pow(-1.0, 0.5*order+kk+1)*coeff[kk];

              fn += fc*(j1mc*z2pc - j1pc*z2mc);

          }

          fn *= sqrt(pi/2.0)/coeff[0];

      }

      else

      {

          for (kk=0; kk

          {

              amax = GSL_MAX(amax, fabs(coeff[kk]));

              if (fabs(coeff[kk])/amax < maxerr)

                  break;

              j1c = gsl_sf_bessel_Jn(kk, u1);

              j1pc = gsl_sf_bessel_Jn(kk+1, u1);

              if (kind == 1)

              {

                  z2c = gsl_sf_bessel_Jn(kk, u2);

                  z2pc = gsl_sf_bessel_Jn(kk+1, u2);

              }

              else /* kind = 2 */

              {

                  z2c = gsl_sf_bessel_Yn(kk, u2);

                  z2pc = gsl_sf_bessel_Yn(kk+1, u2);

              }

              fc = pow(-1.0, 0.5*(order-1)+kk)*coeff[kk];

              fn += fc*(j1c*z2pc - j1pc*z2c);

          }

          fn *= sqrt(pi/2.0)/coeff[0];

      }

      result_array[ii] = fn;

  } /* order loop */

  return GSL_SUCCESS;

}

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

#include "eval.h"                                                           

double gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz)

{

	EVAL_RESULT(gsl_sf_mathieu_Mc_e(kind, order, qq, zz, &result));

}

double gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz)

{

	EVAL_RESULT(gsl_sf_mathieu_Ms_e(kind, order, qq, zz, &result));

}