/* 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 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

 */

#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 * s);

unsigned int gsl_odeiv_step_order(const gsl_odeiv_step * s);

int  gsl_odeiv_step_apply(gsl_odeiv_step * s, 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 * e, 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 * e);

void gsl_odeiv_evolve_free(gsl_odeiv_evolve * e);

__END_DECLS

#endif /* __GSL_ODEIV_H__ */