/* ode-initval/odeiv2.h
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
*
* 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.
*/
/* Author: G. Jungman */
/* Modified by Tuomo Keskitalo */
#ifndef __GSL_ODEIV2_H__
#define __GSL_ODEIV2_H__
#include <stdio.h>
#include <stdlib.h>
#include <gsl/gsl_types.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
/* Description of a system of ODEs.
*
* y' = f(t,y) = dydt(t, y)
*
* The system is specified by giving the right-hand-side
* of the equation and possibly a jacobian function.
*
* Some methods require the jacobian function, which calculates
* the matrix dfdy and the vector dfdt. The matrix dfdy conforms
* to the GSL standard, being a continuous range of floating point
* values, in row-order.
*
* As with GSL function objects, user-supplied parameter
* data is also present.
*/
typedef struct
{
int (*function) (double t, const double y[], double dydt[], void *params);
int (*jacobian) (double t, const double y[], double *dfdy, double dfdt[],
void *params);
size_t dimension;
void *params;
}
gsl_odeiv2_system;
/* Function evaluation macros */
#define GSL_ODEIV_FN_EVAL(S,t,y,f) (*((S)->function))(t,y,f,(S)->params)
#define GSL_ODEIV_JA_EVAL(S,t,y,dfdy,dfdt) (*((S)->jacobian))(t,y,dfdy,dfdt,(S)->params)
/* Type definitions */
typedef struct gsl_odeiv2_step_struct gsl_odeiv2_step;
typedef struct gsl_odeiv2_control_struct gsl_odeiv2_control;
typedef struct gsl_odeiv2_evolve_struct gsl_odeiv2_evolve;
typedef struct gsl_odeiv2_driver_struct gsl_odeiv2_driver;
/* Stepper object
*
* Opaque object for stepping an ODE system from t to t+h.
* In general the object has some state which facilitates
* iterating the stepping operation.
*/
typedef struct
{
const char *name;
int can_use_dydt_in;
int gives_exact_dydt_out;
void *(*alloc) (size_t dim);
int (*apply) (void *state, size_t dim, double t, double h, double y[],
double yerr[], const double dydt_in[], double dydt_out[],
const gsl_odeiv2_system * dydt);
int (*set_driver) (void *state, const gsl_odeiv2_driver * d);
int (*reset) (void *state, size_t dim);
unsigned int (*order) (void *state);
void (*free) (void *state);
}
gsl_odeiv2_step_type;
struct gsl_odeiv2_step_struct
{
const gsl_odeiv2_step_type *type;
size_t dimension;
void *state;
};
/* Available stepper types */
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk2;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk4;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rkf45;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rkck;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk8pd;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk2imp;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk4imp;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_bsimp;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_rk1imp;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_msadams;
GSL_VAR const gsl_odeiv2_step_type *gsl_odeiv2_step_msbdf;
/* Stepper object methods */
gsl_odeiv2_step *gsl_odeiv2_step_alloc (const gsl_odeiv2_step_type * T,
size_t dim);
int gsl_odeiv2_step_reset (gsl_odeiv2_step * s);
void gsl_odeiv2_step_free (gsl_odeiv2_step * s);
const char *gsl_odeiv2_step_name (const gsl_odeiv2_step * s);
unsigned int gsl_odeiv2_step_order (const gsl_odeiv2_step * s);
int gsl_odeiv2_step_apply (gsl_odeiv2_step * s, double t, double h,
double y[], double yerr[], const double dydt_in[],
double dydt_out[], const gsl_odeiv2_system * dydt);
int gsl_odeiv2_step_set_driver (gsl_odeiv2_step * s,
const gsl_odeiv2_driver * d);
/* Step size control object. */
typedef struct
{
const char *name;
void *(*alloc) (void);
int (*init) (void *state, double eps_abs, double eps_rel, double a_y,
double a_dydt);
int (*hadjust) (void *state, size_t dim, unsigned int ord, const double y[],
const double yerr[], const double yp[], double *h);
int (*errlevel) (void *state, const double y, const double dydt,
const double h, const size_t ind, double *errlev);
int (*set_driver) (void *state, const gsl_odeiv2_driver * d);
void (*free) (void *state);
}
gsl_odeiv2_control_type;
struct gsl_odeiv2_control_struct
{
const gsl_odeiv2_control_type *type;
void *state;
};
/* Possible return values for an hadjust() evolution method */
#define GSL_ODEIV_HADJ_INC 1 /* step was increased */
#define GSL_ODEIV_HADJ_NIL 0 /* step unchanged */
#define GSL_ODEIV_HADJ_DEC (-1) /* step decreased */
/* General step size control methods.
*
* The hadjust() method controls the adjustment of
* step size given the result of a step and the error.
* Valid hadjust() methods must return one of the codes below.
* errlevel function calculates the desired error level D0.
*
* The general data can be used by specializations
* to store state and control their heuristics.
*/
gsl_odeiv2_control *gsl_odeiv2_control_alloc (const gsl_odeiv2_control_type *
T);
int gsl_odeiv2_control_init (gsl_odeiv2_control * c, double eps_abs,
double eps_rel, double a_y, double a_dydt);
void gsl_odeiv2_control_free (gsl_odeiv2_control * c);
int gsl_odeiv2_control_hadjust (gsl_odeiv2_control * c, gsl_odeiv2_step * s,
const double y[], const double yerr[],
const double dydt[], double *h);
const char *gsl_odeiv2_control_name (const gsl_odeiv2_control * c);
int gsl_odeiv2_control_errlevel (gsl_odeiv2_control * c, const double y,
const double dydt, const double h,
const size_t ind, double *errlev);
int gsl_odeiv2_control_set_driver (gsl_odeiv2_control * c,
const gsl_odeiv2_driver * d);
/* Available control object constructors.
*
* The standard control object is a four parameter heuristic
* defined as follows:
* D0 = eps_abs + eps_rel * (a_y |y| + a_dydt h |y'|)
* D1 = |yerr|
* q = consistency order of method (q=4 for 4(5) embedded RK)
* S = safety factor (0.9 say)
*
* / (D0/D1)^(1/(q+1)) D0 >= D1
* h_NEW = S h_OLD * |
* \ (D0/D1)^(1/q) D0 < D1
*
* This encompasses all the standard error scaling methods.
*
* The y method is the standard method with a_y=1, a_dydt=0.
* The yp method is the standard method with a_y=0, a_dydt=1.
*/
gsl_odeiv2_control *gsl_odeiv2_control_standard_new (double eps_abs,
double eps_rel,
double a_y,
double a_dydt);
gsl_odeiv2_control *gsl_odeiv2_control_y_new (double eps_abs, double eps_rel);
gsl_odeiv2_control *gsl_odeiv2_control_yp_new (double eps_abs,
double eps_rel);
/* This controller computes errors using different absolute errors for
* each component
*
* D0 = eps_abs * scale_abs[i] + eps_rel * (a_y |y| + a_dydt h |y'|)
*/
gsl_odeiv2_control *gsl_odeiv2_control_scaled_new (double eps_abs,
double eps_rel, double a_y,
double a_dydt,
const double scale_abs[],
size_t dim);
/* Evolution object */
struct gsl_odeiv2_evolve_struct
{
size_t dimension;
double *y0;
double *yerr;
double *dydt_in;
double *dydt_out;
double last_step;
unsigned long int count;
unsigned long int failed_steps;
const gsl_odeiv2_driver *driver;
};
/* Evolution object methods */
gsl_odeiv2_evolve *gsl_odeiv2_evolve_alloc (size_t dim);
int gsl_odeiv2_evolve_apply (gsl_odeiv2_evolve * e, gsl_odeiv2_control * con,
gsl_odeiv2_step * step,
const gsl_odeiv2_system * dydt, double *t,
double t1, double *h, double y[]);
int gsl_odeiv2_evolve_apply_fixed_step (gsl_odeiv2_evolve * e,
gsl_odeiv2_control * con,
gsl_odeiv2_step * step,
const gsl_odeiv2_system * dydt,
double *t, const double h0,
double y[]);
int gsl_odeiv2_evolve_reset (gsl_odeiv2_evolve * e);
void gsl_odeiv2_evolve_free (gsl_odeiv2_evolve * e);
int gsl_odeiv2_evolve_set_driver (gsl_odeiv2_evolve * e,
const gsl_odeiv2_driver * d);
/* Driver object
*
* This is a high level wrapper for step, control and
* evolve objects.
*/
struct gsl_odeiv2_driver_struct
{
const gsl_odeiv2_system *sys; /* ODE system */
gsl_odeiv2_step *s; /* stepper object */
gsl_odeiv2_control *c; /* control object */
gsl_odeiv2_evolve *e; /* evolve object */
double h; /* step size */
double hmin; /* minimum step size allowed */
double hmax; /* maximum step size allowed */
unsigned long int n; /* number of steps taken */
unsigned long int nmax; /* Maximum number of steps allowed */
};
/* Driver object methods */
gsl_odeiv2_driver *gsl_odeiv2_driver_alloc_y_new (const gsl_odeiv2_system *
sys,
const gsl_odeiv2_step_type *
T, const double hstart,
const double epsabs,
const double epsrel);
gsl_odeiv2_driver *gsl_odeiv2_driver_alloc_yp_new (const gsl_odeiv2_system *
sys,
const gsl_odeiv2_step_type
* T, const double hstart,
const double epsabs,
const double epsrel);
gsl_odeiv2_driver *gsl_odeiv2_driver_alloc_scaled_new (const gsl_odeiv2_system
* sys,
const
gsl_odeiv2_step_type *
T, const double hstart,
const double epsabs,
const double epsrel,
const double a_y,
const double a_dydt,
const double
scale_abs[]);
gsl_odeiv2_driver *gsl_odeiv2_driver_alloc_standard_new (const
gsl_odeiv2_system *
sys,
const
gsl_odeiv2_step_type
* T,
const double hstart,
const double epsabs,
const double epsrel,
const double a_y,
const double a_dydt);
int gsl_odeiv2_driver_set_hmin (gsl_odeiv2_driver * d, const double hmin);
int gsl_odeiv2_driver_set_hmax (gsl_odeiv2_driver * d, const double hmax);
int gsl_odeiv2_driver_set_nmax (gsl_odeiv2_driver * d,
const unsigned long int nmax);
int gsl_odeiv2_driver_apply (gsl_odeiv2_driver * d, double *t,
const double t1, double y[]);
int gsl_odeiv2_driver_apply_fixed_step (gsl_odeiv2_driver * d, double *t,
const double h,
const unsigned long int n,
double y[]);
int gsl_odeiv2_driver_reset (gsl_odeiv2_driver * d);
int gsl_odeiv2_driver_reset_hstart (gsl_odeiv2_driver * d, const double hstart);
void gsl_odeiv2_driver_free (gsl_odeiv2_driver * state);
__END_DECLS
#endif /* __GSL_ODEIV2_H__ */