/* integration/gsl_integration.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 Brian Gough
*
* 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.
*/
#ifndef __GSL_INTEGRATION_H__
#define __GSL_INTEGRATION_H__
#include <stdlib.h>
#include <gsl/gsl_math.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
/* Workspace for adaptive integrators */
typedef struct
{
size_t limit;
size_t size;
size_t nrmax;
size_t i;
size_t maximum_level;
double *alist;
double *blist;
double *rlist;
double *elist;
size_t *order;
size_t *level;
}
gsl_integration_workspace;
gsl_integration_workspace *
gsl_integration_workspace_alloc (const size_t n);
void
gsl_integration_workspace_free (gsl_integration_workspace * w);
/* Workspace for QAWS integrator */
typedef struct
{
double alpha;
double beta;
int mu;
int nu;
double ri[25];
double rj[25];
double rg[25];
double rh[25];
}
gsl_integration_qaws_table;
gsl_integration_qaws_table *
gsl_integration_qaws_table_alloc (double alpha, double beta, int mu, int nu);
int
gsl_integration_qaws_table_set (gsl_integration_qaws_table * t,
double alpha, double beta, int mu, int nu);
void
gsl_integration_qaws_table_free (gsl_integration_qaws_table * t);
/* Workspace for QAWO integrator */
enum gsl_integration_qawo_enum { GSL_INTEG_COSINE, GSL_INTEG_SINE };
typedef struct
{
size_t n;
double omega;
double L;
double par;
enum gsl_integration_qawo_enum sine;
double *chebmo;
}
gsl_integration_qawo_table;
gsl_integration_qawo_table *
gsl_integration_qawo_table_alloc (double omega, double L,
enum gsl_integration_qawo_enum sine,
size_t n);
int
gsl_integration_qawo_table_set (gsl_integration_qawo_table * t,
double omega, double L,
enum gsl_integration_qawo_enum sine);
int
gsl_integration_qawo_table_set_length (gsl_integration_qawo_table * t,
double L);
void
gsl_integration_qawo_table_free (gsl_integration_qawo_table * t);
/* Definition of an integration rule */
typedef void gsl_integration_rule (const gsl_function * f,
double a, double b,
double *result, double *abserr,
double *defabs, double *resabs);
void gsl_integration_qk15 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qk21 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qk31 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qk41 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qk51 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qk61 (const gsl_function * f, double a, double b,
double *result, double *abserr,
double *resabs, double *resasc);
void gsl_integration_qcheb (gsl_function * f, double a, double b,
double *cheb12, double *cheb24);
/* The low-level integration rules in QUADPACK are identified by small
integers (1-6). We'll use symbolic constants to refer to them. */
enum
{
GSL_INTEG_GAUSS15 = 1, /* 15 point Gauss-Kronrod rule */
GSL_INTEG_GAUSS21 = 2, /* 21 point Gauss-Kronrod rule */
GSL_INTEG_GAUSS31 = 3, /* 31 point Gauss-Kronrod rule */
GSL_INTEG_GAUSS41 = 4, /* 41 point Gauss-Kronrod rule */
GSL_INTEG_GAUSS51 = 5, /* 51 point Gauss-Kronrod rule */
GSL_INTEG_GAUSS61 = 6 /* 61 point Gauss-Kronrod rule */
};
void
gsl_integration_qk (const int n, const double xgk[],
const double wg[], const double wgk[],
double fv1[], double fv2[],
const gsl_function *f, double a, double b,
double * result, double * abserr,
double * resabs, double * resasc);
int gsl_integration_qng (const gsl_function * f,
double a, double b,
double epsabs, double epsrel,
double *result, double *abserr,
size_t * neval);
int gsl_integration_qag (const gsl_function * f,
double a, double b,
double epsabs, double epsrel, size_t limit,
int key,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qagi (gsl_function * f,
double epsabs, double epsrel, size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qagiu (gsl_function * f,
double a,
double epsabs, double epsrel, size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qagil (gsl_function * f,
double b,
double epsabs, double epsrel, size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qags (const gsl_function * f,
double a, double b,
double epsabs, double epsrel, size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qagp (const gsl_function * f,
double *pts, size_t npts,
double epsabs, double epsrel, size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qawc (gsl_function *f,
const double a, const double b, const double c,
const double epsabs, const double epsrel, const size_t limit,
gsl_integration_workspace * workspace,
double * result, double * abserr);
int gsl_integration_qaws (gsl_function * f,
const double a, const double b,
gsl_integration_qaws_table * t,
const double epsabs, const double epsrel,
const size_t limit,
gsl_integration_workspace * workspace,
double *result, double *abserr);
int gsl_integration_qawo (gsl_function * f,
const double a,
const double epsabs, const double epsrel,
const size_t limit,
gsl_integration_workspace * workspace,
gsl_integration_qawo_table * wf,
double *result, double *abserr);
int gsl_integration_qawf (gsl_function * f,
const double a,
const double epsabs,
const size_t limit,
gsl_integration_workspace * workspace,
gsl_integration_workspace * cycle_workspace,
gsl_integration_qawo_table * wf,
double *result, double *abserr);
/* Workspace for fixed-order Gauss-Legendre integration */
typedef struct
{
size_t n; /* number of points */
double *x; /* Gauss abscissae/points */
double *w; /* Gauss weights for each abscissae */
int precomputed; /* high precision abscissae/weights precomputed? */
}
gsl_integration_glfixed_table;
gsl_integration_glfixed_table * gsl_integration_glfixed_table_alloc (size_t n);
void gsl_integration_glfixed_table_free (gsl_integration_glfixed_table * t);
/* Routine for fixed-order Gauss-Legendre integration */
double gsl_integration_glfixed (const gsl_function *f,
double a,
double b,
const gsl_integration_glfixed_table * t);
/* Routine to retrieve the i-th Gauss-Legendre point and weight from t */
int gsl_integration_glfixed_point (double a,
double b,
size_t i,
double *xi,
double *wi,
const gsl_integration_glfixed_table * t);
/* Cquad integration - Pedro Gonnet */
/* Data of a single interval */
typedef struct
{
double a, b;
double c[64];
double fx[33];
double igral, err;
int depth, rdepth, ndiv;
} gsl_integration_cquad_ival;
/* The workspace is just a collection of intervals */
typedef struct
{
size_t size;
gsl_integration_cquad_ival *ivals;
size_t *heap;
} gsl_integration_cquad_workspace;
gsl_integration_cquad_workspace *
gsl_integration_cquad_workspace_alloc (const size_t n);
void
gsl_integration_cquad_workspace_free (gsl_integration_cquad_workspace * w);
int
gsl_integration_cquad (const gsl_function * f, double a, double b,
double epsabs, double epsrel,
gsl_integration_cquad_workspace * ws,
double *result, double *abserr, size_t * nevals);
/* Romberg integration workspace and routines */
typedef struct
{
size_t n; /* maximum number of steps */
double *work1; /* workspace for a row of R matrix, size n */
double *work2; /* workspace for a row of R matrix, size n */
} gsl_integration_romberg_workspace;
gsl_integration_romberg_workspace *gsl_integration_romberg_alloc(const size_t n);
void gsl_integration_romberg_free(gsl_integration_romberg_workspace * w);
int gsl_integration_romberg(const gsl_function * f, const double a, const double b,
const double epsabs, const double epsrel, double * result,
size_t * neval, gsl_integration_romberg_workspace * w);
/* IQPACK related structures and routines */
typedef struct
{
double alpha;
double beta;
double a;
double b;
double zemu;
double shft;
double slp;
double al;
double be;
} gsl_integration_fixed_params;
typedef struct
{
int (*check)(const size_t n, const gsl_integration_fixed_params * params);
int (*init)(const size_t n, double * diag, double * subdiag, gsl_integration_fixed_params * params);
} gsl_integration_fixed_type;
typedef struct
{
size_t n; /* number of nodes/weights */
double *weights; /* quadrature weights */
double *x; /* quadrature nodes */
double *diag; /* diagonal of Jacobi matrix */
double *subdiag; /* subdiagonal of Jacobi matrix */
const gsl_integration_fixed_type * type;
} gsl_integration_fixed_workspace;
/* IQPACK integral types */
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_legendre;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_chebyshev;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_gegenbauer;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_jacobi;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_laguerre;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_hermite;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_exponential;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_rational;
GSL_VAR const gsl_integration_fixed_type * gsl_integration_fixed_chebyshev2;
gsl_integration_fixed_workspace *
gsl_integration_fixed_alloc(const gsl_integration_fixed_type * type, const size_t n,
const double a, const double b, const double alpha, const double beta);
void gsl_integration_fixed_free(gsl_integration_fixed_workspace * w);
size_t gsl_integration_fixed_n(const gsl_integration_fixed_workspace * w);
double *gsl_integration_fixed_nodes(const gsl_integration_fixed_workspace * w);
double *gsl_integration_fixed_weights(const gsl_integration_fixed_workspace * w);
int gsl_integration_fixed(const gsl_function * func, double * result,
const gsl_integration_fixed_workspace * w);
__END_DECLS
#endif /* __GSL_INTEGRATION_H__ */