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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__ */