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/* ode-initval/gsl_odeiv.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 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
/* Author: G. Jungman
*/
#ifndef __GSL_ODEIV_H__
#define __GSL_ODEIV_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_odeiv_system;
#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)
/* General 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_odeiv_system * dydt);
int (*reset) (void * state, size_t dim);
unsigned int (*order) (void * state);
void (*free) (void * state);
}
gsl_odeiv_step_type;
typedef struct {
const gsl_odeiv_step_type * type;
size_t dimension;
void * state;
}
gsl_odeiv_step;
/* Available stepper types.
*
* rk2 : embedded 2nd(3rd) Runge-Kutta
* rk4 : 4th order (classical) Runge-Kutta
* rkck : embedded 4th(5th) Runge-Kutta, Cash-Karp
* rk8pd : embedded 8th(9th) Runge-Kutta, Prince-Dormand
* rk2imp : implicit 2nd order Runge-Kutta at Gaussian points
* rk4imp : implicit 4th order Runge-Kutta at Gaussian points
* gear1 : M=1 implicit Gear method
* gear2 : M=2 implicit Gear method
*/
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk4;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rkf45;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rkck;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk8pd;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2imp;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk4imp;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_bsimp;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_gear1;
GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_gear2;
/* Constructor for specialized stepper objects.
*/
gsl_odeiv_step * gsl_odeiv_step_alloc(const gsl_odeiv_step_type * T, size_t dim);
int gsl_odeiv_step_reset(gsl_odeiv_step * s);
void gsl_odeiv_step_free(gsl_odeiv_step * s);
/* General stepper object methods.
*/
const char * gsl_odeiv_step_name(const gsl_odeiv_step *);
unsigned int gsl_odeiv_step_order(const gsl_odeiv_step * s);
int gsl_odeiv_step_apply(gsl_odeiv_step *, double t, double h, double y[], double yerr[], const double dydt_in[], double dydt_out[], const gsl_odeiv_system * dydt);
/* General step size control object.
*
* 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.
*
* The general data can be used by specializations
* to store state and control their heuristics.
*/
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);
void (*free) (void * state);
}
gsl_odeiv_control_type;
typedef struct
{
const gsl_odeiv_control_type * type;
void * state;
}
gsl_odeiv_control;
/* 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 */
gsl_odeiv_control * gsl_odeiv_control_alloc(const gsl_odeiv_control_type * T);
int gsl_odeiv_control_init(gsl_odeiv_control * c, double eps_abs, double eps_rel, double a_y, double a_dydt);
void gsl_odeiv_control_free(gsl_odeiv_control * c);
int gsl_odeiv_control_hadjust (gsl_odeiv_control * c, gsl_odeiv_step * s, const double y[], const double yerr[], const double dydt[], double * h);
const char * gsl_odeiv_control_name(const gsl_odeiv_control * c);
/* 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_odeiv_control * gsl_odeiv_control_standard_new(double eps_abs, double eps_rel, double a_y, double a_dydt);
gsl_odeiv_control * gsl_odeiv_control_y_new(double eps_abs, double eps_rel);
gsl_odeiv_control * gsl_odeiv_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_odeiv_control * gsl_odeiv_control_scaled_new(double eps_abs, double eps_rel, double a_y, double a_dydt, const double scale_abs[], size_t dim);
/* General evolution object.
*/
typedef 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;
}
gsl_odeiv_evolve;
/* Evolution object methods.
*/
gsl_odeiv_evolve * gsl_odeiv_evolve_alloc(size_t dim);
int gsl_odeiv_evolve_apply(gsl_odeiv_evolve *, gsl_odeiv_control * con, gsl_odeiv_step * step, const gsl_odeiv_system * dydt, double * t, double t1, double * h, double y[]);
int gsl_odeiv_evolve_reset(gsl_odeiv_evolve *);
void gsl_odeiv_evolve_free(gsl_odeiv_evolve *);
__END_DECLS
#endif /* __GSL_ODEIV_H__ */
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