/* specfunc/gsl_sf_mathieu.h

 * 

 * 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 */

#ifndef __GSL_SF_MATHIEU_H__

#define __GSL_SF_MATHIEU_H__

#include <gsl/gsl_sf_result.h>

#include <gsl/gsl_eigen.h>

#undef __BEGIN_DECLS

#undef __END_DECLS

#ifdef __cplusplus

# define __BEGIN_DECLS extern "C" {

# define __END_DECLS }

#else

# define __BEGIN_DECLS /* empty */

# define __END_DECLS /* empty */

#endif

__BEGIN_DECLS

#define GSL_SF_MATHIEU_COEFF 100

typedef struct 

{

  size_t size;

  size_t even_order;

  size_t odd_order;

  int extra_values;

  double qa;   /* allow for caching of results: not implemented yet */

  double qb;   /* allow for caching of results: not implemented yet */

  double *aa;

  double *bb;

  double *dd;

  double *ee;

  double *tt;

  double *e2;

  double *zz;

  gsl_vector *eval;

  gsl_matrix *evec;

  gsl_eigen_symmv_workspace *wmat;

} gsl_sf_mathieu_workspace;

/* Compute an array of characteristic (eigen) values from the recurrence

   matrices for the Mathieu equations. */

int gsl_sf_mathieu_a_array(int order_min, int order_max, double qq, gsl_sf_mathieu_workspace *work, double result_array[]);

int gsl_sf_mathieu_b_array(int order_min, int order_max, double qq,  gsl_sf_mathieu_workspace *work, double result_array[]);

/* Compute the characteristic value for a Mathieu function of order n and

   type ntype. */

int gsl_sf_mathieu_a_e(int order, double qq, gsl_sf_result *result);

double gsl_sf_mathieu_a(int order, double qq);

int gsl_sf_mathieu_b_e(int order, double qq, gsl_sf_result *result);

double gsl_sf_mathieu_b(int order, double qq);

/* Compute the Fourier coefficients for a Mathieu function. */

int gsl_sf_mathieu_a_coeff(int order, double qq, double aa, double coeff[]);

int gsl_sf_mathieu_b_coeff(int order, double qq, double aa, double coeff[]);

/* Allocate computational storage space for eigenvalue solution. */

gsl_sf_mathieu_workspace *gsl_sf_mathieu_alloc(const size_t nn,

                                               const double qq);

void gsl_sf_mathieu_free(gsl_sf_mathieu_workspace *workspace);

/* Compute an angular Mathieu function. */

int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result);

double gsl_sf_mathieu_ce(int order, double qq, double zz);

int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result);

double gsl_sf_mathieu_se(int order, double qq, double zz);

int gsl_sf_mathieu_ce_array(int nmin, int nmax, double qq, double zz,

                            gsl_sf_mathieu_workspace *work,

                            double result_array[]);

int gsl_sf_mathieu_se_array(int nmin, int nmax, double qq, double zz,

                            gsl_sf_mathieu_workspace *work,

                            double result_array[]);

/* Compute a radial Mathieu function. */

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

                      gsl_sf_result *result);

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

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

                      gsl_sf_result *result);

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

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

                            double zz, gsl_sf_mathieu_workspace *work,

                            double result_array[]);

__END_DECLS

#endif /* !__GSL_SF_MATHIEU_H__ */