| /* 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 2 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(int order, double qq, gsl_sf_result *result); |
| int gsl_sf_mathieu_b(int order, double qq, gsl_sf_result *result); |
| |
| /* 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(int order, double qq, double zz, gsl_sf_result *result); |
| int gsl_sf_mathieu_se(int order, double qq, double zz, gsl_sf_result *result); |
| 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(int kind, int order, double qq, double zz, |
| gsl_sf_result *result); |
| int gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz, |
| gsl_sf_result *result); |
| 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__ */ |
