#include <stdio.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_matrix.h>
#include <gsl/gsl_odeiv.h>


int func (double t, const double y[], double f[], void *params)
{
  double mu = *(double *)params;
  f[0] = y[1];
  f[1] = -y[0] - mu*y[1]*(y[0]*y[0] - 1);
  return GSL_SUCCESS;
}


int jac (double t, const double y[], double *dfdy, double dfdt[], void *params)
{
  double mu = *(double *)params;
  gsl_matrix_view dfdy_mat
    = gsl_matrix_view_array (dfdy, 2, 2);
  gsl_matrix * m = &dfdy_mat.matrix;
  gsl_matrix_set (m, 0, 0, 0.0);
  gsl_matrix_set (m, 0, 1, 1.0);
  gsl_matrix_set (m, 1, 0, -2.0*mu*y[0]*y[1] - 1.0);
  gsl_matrix_set (m, 1, 1, -mu*(y[0]*y[0] - 1.0));
  dfdt[0] = 0.0;
  dfdt[1] = 0.0;
  return GSL_SUCCESS;
}


int main (void)
{
  const gsl_odeiv_step_type * T
    = gsl_odeiv_step_rk8pd;
  gsl_odeiv_step * s
    = gsl_odeiv_step_alloc (T, 2);
  gsl_odeiv_control * c
    = gsl_odeiv_control_y_new (1e-6, 0.0);
  gsl_odeiv_evolve * e
    = gsl_odeiv_evolve_alloc (2);
  double mu = 10;
  gsl_odeiv_system sys = {func, jac, 2, &mu};
  double t = 0.0, t1 = 100.0;
  double h = 1e-6;
  double y[2] = { 1.0, 0.0 };
  while (t < t1)
    {
      int status = gsl_odeiv_evolve_apply (e, c, s, &sys, &t, t1, &h, y);
      if (status != GSL_SUCCESS)
	break;
      printf ("%.5e %.5e %.5e\n", t, y[0], y[1]);
    }
  gsl_odeiv_evolve_free (e);
  gsl_odeiv_control_free (c);
  gsl_odeiv_step_free (s);
  return 0;
}