void AnalyticJacob 
                      // a function that codes the analytic expression...
                      // ...of the forcing function and its Jacobian matrix...
                      // ...for the sample problem

           (double x_ [],   // argument of the sample forcing function
            int    dim,     // dimension of the sample problem
            double J [MAX_DIM][MAX_DIM], // value of Jacobian matrix and...
            double F  []);  // ...value of the sample forcing function at x_ []




void AnalyticJacob 
            (double x_ [], int dim, double J [MAX_DIM][MAX_DIM], double F [])
{
  double beta1 = 1.0e+3;
  double beta2 = 1.0e-3;
  
  
  if (dim != 2) abort ();


// Dx0 / Dt = (1 - x0) - beta1 x0 x1
// Dx1 / Dt = -beta2 x0 x1

  F [0] = (1 - x_ [0]) - beta1 * x_[1] * x_ [0];
  F [1] = -(x_[1] * x_ [0]) * beta2;
    
  J [0][0] = -1 - beta1 * x_ [1];
  J [0][1] = -beta1 * x_ [0];
  J [1][0] = -beta2 * x_ [1];
  J [1][1] = -beta2 * x_ [0];
}