1/* specfunc/gsl_sf_mathieu.h
2 *
3 * Copyright (C) 2002 Lowell Johnson
4 *
5 * This program is free software; you can redistribute it and/or modify
6 * it under the terms of the GNU General Public License as published by
7 * the Free Software Foundation; either version 3 of the License, or (at
8 * your option) any later version.
9 *
10 * This program is distributed in the hope that it will be useful, but
11 * WITHOUT ANY WARRANTY; without even the implied warranty of
12 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 * General Public License for more details.
14 *
15 * You should have received a copy of the GNU General Public License
16 * along with this program; if not, write to the Free Software
17 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
18 */
19
20/* Author: L. Johnson */
21
22#ifndef __GSL_SF_MATHIEU_H__
23#define __GSL_SF_MATHIEU_H__
24
25#include <gsl/gsl_sf_result.h>
26#include <gsl/gsl_eigen.h>
27
28#undef __BEGIN_DECLS
29#undef __END_DECLS
30#ifdef __cplusplus
31# define __BEGIN_DECLS extern "C" {
32# define __END_DECLS }
33#else
34# define __BEGIN_DECLS /* empty */
35# define __END_DECLS /* empty */
36#endif
37
38__BEGIN_DECLS
39
40#define GSL_SF_MATHIEU_COEFF 100
41
42typedef struct
43{
44 size_t size;
45 size_t even_order;
46 size_t odd_order;
47 int extra_values;
48 double qa; /* allow for caching of results: not implemented yet */
49 double qb; /* allow for caching of results: not implemented yet */
50 double *aa;
51 double *bb;
52 double *dd;
53 double *ee;
54 double *tt;
55 double *e2;
56 double *zz;
57 gsl_vector *eval;
58 gsl_matrix *evec;
59 gsl_eigen_symmv_workspace *wmat;
60} gsl_sf_mathieu_workspace;
61
62
63/* Compute an array of characteristic (eigen) values from the recurrence
64 matrices for the Mathieu equations. */
65int gsl_sf_mathieu_a_array(int order_min, int order_max, double qq, gsl_sf_mathieu_workspace *work, double result_array[]);
66int gsl_sf_mathieu_b_array(int order_min, int order_max, double qq, gsl_sf_mathieu_workspace *work, double result_array[]);
67
68/* Compute the characteristic value for a Mathieu function of order n and
69 type ntype. */
70int gsl_sf_mathieu_a_e(int order, double qq, gsl_sf_result *result);
71double gsl_sf_mathieu_a(int order, double qq);
72int gsl_sf_mathieu_b_e(int order, double qq, gsl_sf_result *result);
73double gsl_sf_mathieu_b(int order, double qq);
74
75/* Compute the Fourier coefficients for a Mathieu function. */
76int gsl_sf_mathieu_a_coeff(int order, double qq, double aa, double coeff[]);
77int gsl_sf_mathieu_b_coeff(int order, double qq, double aa, double coeff[]);
78
79/* Allocate computational storage space for eigenvalue solution. */
80gsl_sf_mathieu_workspace *gsl_sf_mathieu_alloc(const size_t nn,
81 const double qq);
82void gsl_sf_mathieu_free(gsl_sf_mathieu_workspace *workspace);
83
84/* Compute an angular Mathieu function. */
85int gsl_sf_mathieu_ce_e(int order, double qq, double zz, gsl_sf_result *result);
86double gsl_sf_mathieu_ce(int order, double qq, double zz);
87int gsl_sf_mathieu_se_e(int order, double qq, double zz, gsl_sf_result *result);
88double gsl_sf_mathieu_se(int order, double qq, double zz);
89int gsl_sf_mathieu_ce_array(int nmin, int nmax, double qq, double zz,
90 gsl_sf_mathieu_workspace *work,
91 double result_array[]);
92int gsl_sf_mathieu_se_array(int nmin, int nmax, double qq, double zz,
93 gsl_sf_mathieu_workspace *work,
94 double result_array[]);
95
96/* Compute a radial Mathieu function. */
97int gsl_sf_mathieu_Mc_e(int kind, int order, double qq, double zz,
98 gsl_sf_result *result);
99double gsl_sf_mathieu_Mc(int kind, int order, double qq, double zz);
100int gsl_sf_mathieu_Ms_e(int kind, int order, double qq, double zz,
101 gsl_sf_result *result);
102double gsl_sf_mathieu_Ms(int kind, int order, double qq, double zz);
103int gsl_sf_mathieu_Mc_array(int kind, int nmin, int nmax, double qq,
104 double zz, gsl_sf_mathieu_workspace *work,
105 double result_array[]);
106int gsl_sf_mathieu_Ms_array(int kind, int nmin, int nmax, double qq,
107 double zz, gsl_sf_mathieu_workspace *work,
108 double result_array[]);
109
110
111__END_DECLS
112
113#endif /* !__GSL_SF_MATHIEU_H__ */
114