#define penalty2_N         8 /* 2*p */

#define penalty2_P         4

static double penalty2_x0[penalty2_P] = { 0.5, 0.5, 0.5, 0.5 };

static double penalty2_epsrel = 1.0e-12;

static void

penalty2_checksol(const double x[], const double sumsq,

                  const double epsrel, const char *sname,

                  const char *pname)

{

  const double sumsq_exact = 9.37629300735544219e-06;

  gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",

               sname, pname);

  (void)x; /* avoid unused parameter warning */

}

static int

penalty2_f (const gsl_vector * x, void *params, gsl_vector * f)

{

  const double alpha = 1.0e-5;

  const double sqrt_alpha = sqrt(alpha);

  double x1 = gsl_vector_get(x, 0);

  size_t i;

  double sum = penalty2_P * x1 * x1;

  gsl_vector_set(f, 0, x1 - 0.2);

  /* rows [2:p] */

  for (i = 1; i < penalty2_P; ++i)

    {

      double xi = gsl_vector_get(x, i);

      double xim1 = gsl_vector_get(x, i - 1);

      double yi = exp(0.1*(i + 1.0)) + exp(0.1*i);

      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) + exp(0.1*xim1) - yi));

      sum += (penalty2_P - i) * xi * xi;

    }

  /* rows [p+1:2p-1] */

  for (i = penalty2_P; i < penalty2_N - 1; ++i)

    {

      double xi = gsl_vector_get(x, i - penalty2_P + 1);

      gsl_vector_set(f, i, sqrt_alpha*(exp(0.1*xi) - exp(-0.1)));

    }

  /* row 2p */

  gsl_vector_set(f, penalty2_N - 1, sum - 1.0);

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

penalty2_df (const gsl_vector * x, void *params, gsl_matrix * J)

{

  const double alpha = 1.0e-5;

  const double sqrt_alpha = sqrt(alpha);

  size_t i, j;

  for (j = 0; j < penalty2_P; ++j)

    {

      double xj = gsl_vector_get(x, j);

      double delta1j = (j == 0) ? 1.0 : 0.0;

      /* first and last rows */

      gsl_matrix_set(J, 0, j, delta1j);

      gsl_matrix_set(J, penalty2_N - 1, j, 2.0 * (penalty2_P - j) * xj);

      /* rows [2:p] */

      for (i = 1; i < penalty2_P; ++i)

        {

          double xi = gsl_vector_get(x, i);

          double xim1 = gsl_vector_get(x, i - 1);

          double Jij;

          if (i == j)

            Jij = exp(0.1 * xi);

          else if (i - 1 == j)

            Jij = exp(0.1 * xim1);

          else

            Jij = 0.0;

          Jij *= 0.1 * sqrt_alpha;

          gsl_matrix_set(J, i, j, Jij);

        }

      /* rows [p+1:2p-1] */

      for (i = penalty2_P; i < penalty2_N - 1; ++i)

        {

          double xi = gsl_vector_get(x, i - penalty2_P + 1);

          if (i - penalty2_P + 1 == j)

            gsl_matrix_set(J, i, j, 0.1 * sqrt_alpha * exp(0.1*xi));

          else

            gsl_matrix_set(J, i, j, 0.0);

        }

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static int

penalty2_fvv (const gsl_vector * x, const gsl_vector * v,

              void *params, gsl_vector * fvv)

{

  const double alpha = 1.0e-5;

  const double sqrt_alpha = sqrt(alpha);

  double v1 = gsl_vector_get(v, 0);

  double sum = penalty2_P * v1 * v1;

  size_t i;

  /* first row */

  gsl_vector_set(fvv, 0, 0.0);

  /* rows [2:p] */

  for (i = 1; i < penalty2_P; ++i)

    {

      double xi = gsl_vector_get(x, i);

      double xim1 = gsl_vector_get(x, i - 1);

      double vi = gsl_vector_get(v, i);

      double vim1 = gsl_vector_get(v, i - 1);

      double term1 = exp(xi / 10.0);

      double term2 = exp(xim1 / 10.0);

      gsl_vector_set(fvv, i,

        sqrt_alpha / 100.0 * (term1 * vi * vi + term2 * vim1 * vim1));

      sum += (penalty2_P - i) * vi * vi;

    }

  /* last row */

  gsl_vector_set(fvv, penalty2_N - 1, 2.0 * sum);

  /* rows [p+1:2p-1] */

  for (i = penalty2_P; i < penalty2_N - 1; ++i)

    {

      double xi = gsl_vector_get(x, i - penalty2_P + 1);

      double vi = gsl_vector_get(v, i - penalty2_P + 1);

      gsl_vector_set(fvv, i, sqrt_alpha / 100.0 * exp(xi / 10.0) * vi * vi);

    }

  (void)params; /* avoid unused parameter warning */

  return GSL_SUCCESS;

}

static gsl_multifit_nlinear_fdf penalty2_func =

{

  penalty2_f,

  penalty2_df,

  penalty2_fvv,

  penalty2_N,

  penalty2_P,

  NULL,

  0,

  0,

  0

};

static test_fdf_problem penalty2_problem =

{

  "penalty2",

  penalty2_x0,

  NULL,

  NULL,

  &penalty2_epsrel,

  &penalty2_checksol,

  &penalty2_func

};