#define biggs_N         6  /* >= p */

#define biggs_P         6

/* dogleg method has trouble converging from recommended starting point,

 * so we use an x0 which is a little closer to the true solution */

/*static double biggs_x0[biggs_P] = { 1.0, 2.0, 1.0, 1.0, 1.0, 1.0 };*/

static double biggs_x0[biggs_P] = { 1.0, 8.0, 1.0, 2.0, 3.0, 2.0 };

static double biggs_epsrel = 1.0e-9;

static double biggs_J[biggs_N * biggs_P];

static void

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

               const double epsrel, const char *sname,

               const char *pname)

{

#if 0

  const double sumsq_exact = 0.0;

#endif

  const double biggs_x[biggs_P] = { 1.0, 10.0, 1.0, 5.0, 4.0, 3.0 };

  const double norm_exact = 12.3288280059380;

  gsl_vector_const_view v = gsl_vector_const_view_array(biggs_x, biggs_P);

  double norm = gsl_blas_dnrm2(&v.vector);

#if 0

  /* some solvers have difficulty reaching sumsq = 0 to sufficient

   * decimal places */

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

               sname, pname);

#endif

  /*

   * the solution vector is not unique due to permutations, so test

   * the norm instead of individual elements

   */

  gsl_test_rel(norm, norm_exact, epsrel, "%s/%s norm",

               sname, pname);

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

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

}

static int

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

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  double x6 = gsl_vector_get(x, 5);

  size_t i;

  for (i = 0; i < biggs_N; ++i)

    {

      double ti = 0.1 * (i + 1.0);

      double yi = exp(-ti) - 5*exp(-10*ti) + 3*exp(-4*ti);

      double fi = x3*exp(-ti*x1) - x4*exp(-ti*x2) + x6*exp(-ti*x5) - yi;

      gsl_vector_set(f, i, fi);

    }

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

  return GSL_SUCCESS;

}

static int

biggs_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,

          const gsl_vector * u, void * params, gsl_vector * v,

          gsl_matrix * JTJ)

{

  gsl_matrix_view J = gsl_matrix_view_array(biggs_J, biggs_N, biggs_P);

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  double x6 = gsl_vector_get(x, 5);

  size_t i;

  for (i = 0; i < biggs_N; ++i)

    {

      double ti = 0.1 * (i + 1.0);

      gsl_matrix_set(&J.matrix, i, 0, -ti*x3*exp(-ti*x1));

      gsl_matrix_set(&J.matrix, i, 1, ti*x4*exp(-ti*x2));

      gsl_matrix_set(&J.matrix, i, 2, exp(-ti*x1));

      gsl_matrix_set(&J.matrix, i, 3, -exp(-ti*x2));

      gsl_matrix_set(&J.matrix, i, 4, -ti*x6*exp(-ti*x5));

      gsl_matrix_set(&J.matrix, i, 5, exp(-ti*x5));

    }

  if (v)

    gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);

  if (JTJ)

    gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);

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

  return GSL_SUCCESS;

}

static int

biggs_fvv (const gsl_vector * x, const gsl_vector * v,

           void *params, gsl_vector * fvv)

{

  double x1 = gsl_vector_get(x, 0);

  double x2 = gsl_vector_get(x, 1);

  double x3 = gsl_vector_get(x, 2);

  double x4 = gsl_vector_get(x, 3);

  double x5 = gsl_vector_get(x, 4);

  double x6 = gsl_vector_get(x, 5);

  double v1 = gsl_vector_get(v, 0);

  double v2 = gsl_vector_get(v, 1);

  double v3 = gsl_vector_get(v, 2);

  double v4 = gsl_vector_get(v, 3);

  double v5 = gsl_vector_get(v, 4);

  double v6 = gsl_vector_get(v, 5);

  size_t i;

  for (i = 0; i < biggs_N; ++i)

    {

      double ti = 0.1 * (i + 1.0);

      double term1 = exp(-ti * x1);

      double term2 = exp(-ti * x2);

      double term3 = exp(-ti * x5);

      gsl_vector_set(fvv, i, ti * term1 * term2 * term3 *

                             (v1/(term2*term3)*(-2*v3 + ti*v1*x3) -

                              v2/(term1*term3)*(-2*v4 + ti*v2*x4) +

                              v5/(term1*term2)*(-2*v6 + ti*v5*x6)));

    }

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

  return GSL_SUCCESS;

}

static gsl_multilarge_nlinear_fdf biggs_func =

{

  biggs_f,

  biggs_df,

  biggs_fvv,

  biggs_N,

  biggs_P,

  NULL,

  0,

  0,

  0,

  0

};

static test_fdf_problem biggs_problem =

{

  "biggs",

  biggs_x0,

  NULL,

  &biggs_epsrel,

  &biggs_checksol,

  &biggs_func

};