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/* ode-initval/gsl_odeiv.h
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000 Gerard Jungman
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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/* Author: G. Jungman
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*/
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#ifndef __GSL_ODEIV_H__
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#define __GSL_ODEIV_H__
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#include <stdio.h>
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#include <stdlib.h>
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#include <gsl/gsl_types.h>
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#undef __BEGIN_DECLS
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#undef __END_DECLS
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#ifdef __cplusplus
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# define __BEGIN_DECLS extern "C" {
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# define __END_DECLS }
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#else
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# define __BEGIN_DECLS /* empty */
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# define __END_DECLS /* empty */
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#endif
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__BEGIN_DECLS
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/* Description of a system of ODEs.
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*
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* y' = f(t,y) = dydt(t, y)
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*
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* The system is specified by giving the right-hand-side
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* of the equation and possibly a jacobian function.
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*
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* Some methods require the jacobian function, which calculates
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* the matrix dfdy and the vector dfdt. The matrix dfdy conforms
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* to the GSL standard, being a continuous range of floating point
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* values, in row-order.
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*
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* As with GSL function objects, user-supplied parameter
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* data is also present.
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*/
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typedef struct
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{
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int (* function) (double t, const double y[], double dydt[], void * params);
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int (* jacobian) (double t, const double y[], double * dfdy, double dfdt[], void * params);
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size_t dimension;
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void * params;
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}
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gsl_odeiv_system;
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#define GSL_ODEIV_FN_EVAL(S,t,y,f) (*((S)->function))(t,y,f,(S)->params)
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#define GSL_ODEIV_JA_EVAL(S,t,y,dfdy,dfdt) (*((S)->jacobian))(t,y,dfdy,dfdt,(S)->params)
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/* General stepper object.
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*
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* Opaque object for stepping an ODE system from t to t+h.
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* In general the object has some state which facilitates
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* iterating the stepping operation.
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*/
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typedef struct
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{
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const char * name;
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int can_use_dydt_in;
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int gives_exact_dydt_out;
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void * (*alloc) (size_t dim);
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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);
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int (*reset) (void * state, size_t dim);
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unsigned int (*order) (void * state);
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void (*free) (void * state);
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}
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gsl_odeiv_step_type;
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typedef struct {
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const gsl_odeiv_step_type * type;
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size_t dimension;
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void * state;
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}
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gsl_odeiv_step;
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/* Available stepper types.
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*
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* rk2 : embedded 2nd(3rd) Runge-Kutta
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* rk4 : 4th order (classical) Runge-Kutta
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* rkck : embedded 4th(5th) Runge-Kutta, Cash-Karp
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* rk8pd : embedded 8th(9th) Runge-Kutta, Prince-Dormand
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* rk2imp : implicit 2nd order Runge-Kutta at Gaussian points
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* rk4imp : implicit 4th order Runge-Kutta at Gaussian points
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* gear1 : M=1 implicit Gear method
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* gear2 : M=2 implicit Gear method
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*/
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk4;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rkf45;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rkck;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk8pd;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2imp;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk2simp;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_rk4imp;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_bsimp;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_gear1;
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GSL_VAR const gsl_odeiv_step_type *gsl_odeiv_step_gear2;
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/* Constructor for specialized stepper objects.
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*/
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gsl_odeiv_step * gsl_odeiv_step_alloc(const gsl_odeiv_step_type * T, size_t dim);
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int gsl_odeiv_step_reset(gsl_odeiv_step * s);
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void gsl_odeiv_step_free(gsl_odeiv_step * s);
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/* General stepper object methods.
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*/
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const char * gsl_odeiv_step_name(const gsl_odeiv_step * s);
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unsigned int gsl_odeiv_step_order(const gsl_odeiv_step * s);
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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);
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/* General step size control object.
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*
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* The hadjust() method controls the adjustment of
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* step size given the result of a step and the error.
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* Valid hadjust() methods must return one of the codes below.
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*
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* The general data can be used by specializations
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* to store state and control their heuristics.
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*/
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typedef struct
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{
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const char * name;
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void * (*alloc) (void);
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int (*init) (void * state, double eps_abs, double eps_rel, double a_y, double a_dydt);
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int (*hadjust) (void * state, size_t dim, unsigned int ord, const double y[], const double yerr[], const double yp[], double * h);
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void (*free) (void * state);
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}
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gsl_odeiv_control_type;
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typedef struct
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{
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const gsl_odeiv_control_type * type;
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void * state;
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}
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gsl_odeiv_control;
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/* Possible return values for an hadjust() evolution method.
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*/
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#define GSL_ODEIV_HADJ_INC 1 /* step was increased */
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#define GSL_ODEIV_HADJ_NIL 0 /* step unchanged */
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#define GSL_ODEIV_HADJ_DEC (-1) /* step decreased */
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gsl_odeiv_control * gsl_odeiv_control_alloc(const gsl_odeiv_control_type * T);
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int gsl_odeiv_control_init(gsl_odeiv_control * c, double eps_abs, double eps_rel, double a_y, double a_dydt);
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void gsl_odeiv_control_free(gsl_odeiv_control * c);
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int gsl_odeiv_control_hadjust (gsl_odeiv_control * c, gsl_odeiv_step * s, const double y[], const double yerr[], const double dydt[], double * h);
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const char * gsl_odeiv_control_name(const gsl_odeiv_control * c);
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/* Available control object constructors.
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*
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* The standard control object is a four parameter heuristic
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* defined as follows:
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* D0 = eps_abs + eps_rel * (a_y |y| + a_dydt h |y'|)
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* D1 = |yerr|
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* q = consistency order of method (q=4 for 4(5) embedded RK)
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* S = safety factor (0.9 say)
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*
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* / (D0/D1)^(1/(q+1)) D0 >= D1
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* h_NEW = S h_OLD * |
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* \ (D0/D1)^(1/q) D0 < D1
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*
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* This encompasses all the standard error scaling methods.
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*
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* The y method is the standard method with a_y=1, a_dydt=0.
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* The yp method is the standard method with a_y=0, a_dydt=1.
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*/
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gsl_odeiv_control * gsl_odeiv_control_standard_new(double eps_abs, double eps_rel, double a_y, double a_dydt);
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gsl_odeiv_control * gsl_odeiv_control_y_new(double eps_abs, double eps_rel);
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gsl_odeiv_control * gsl_odeiv_control_yp_new(double eps_abs, double eps_rel);
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/* This controller computes errors using different absolute errors for
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* each component
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*
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* D0 = eps_abs * scale_abs[i] + eps_rel * (a_y |y| + a_dydt h |y'|)
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*/
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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);
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/* General evolution object.
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*/
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typedef struct {
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size_t dimension;
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double * y0;
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double * yerr;
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double * dydt_in;
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double * dydt_out;
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double last_step;
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unsigned long int count;
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unsigned long int failed_steps;
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}
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gsl_odeiv_evolve;
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/* Evolution object methods.
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*/
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gsl_odeiv_evolve * gsl_odeiv_evolve_alloc(size_t dim);
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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[]);
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int gsl_odeiv_evolve_reset(gsl_odeiv_evolve * e);
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void gsl_odeiv_evolve_free(gsl_odeiv_evolve * e);
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__END_DECLS
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#endif /* __GSL_ODEIV_H__ */
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