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#define box_N 10 /* can be >= p */
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#define box_P 3
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/* dogleg method fails with recommended starting point, so use
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* a slightly easier x0 */
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/*static double box_x0[box_P] = { 0.0, 10.0, 20.0 };*/
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static double box_x0[box_P] = { 5.0, 10.0, 2.0 };
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static double box_epsrel = 1.0e-12;
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static double box_J[box_N * box_P];
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static void
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box_checksol(const double x[], const double sumsq,
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const double epsrel, const char *sname,
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const char *pname)
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{
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const double sumsq_exact = 0.0;
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const double eps = 1.0e-6;
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gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
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sname, pname);
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/* there are 3 possible solution vectors */
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if (fabs(x[2] - 1.0) < eps)
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{
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/* case 1: x* = [ 1; 10; 1 ] */
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gsl_test_rel(x[0], 1.0, epsrel, "%s/%s i=0",
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sname, pname);
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gsl_test_rel(x[1], 10.0, epsrel, "%s/%s i=1",
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sname, pname);
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gsl_test_rel(x[2], 1.0, epsrel, "%s/%s i=2",
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sname, pname);
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}
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else if (fabs(x[2] + 1.0) < eps)
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{
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/* case 2: x* = [ 10; 1; -1 ] */
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gsl_test_rel(x[0], 10.0, epsrel, "%s/%s i=0",
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sname, pname);
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gsl_test_rel(x[1], 1.0, epsrel, "%s/%s i=1",
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sname, pname);
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gsl_test_rel(x[2], -1.0, epsrel, "%s/%s i=2",
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sname, pname);
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}
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else
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{
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/* case 3: x* = [ a; a; 0 ] for any a */
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gsl_test_rel(x[0], x[1], epsrel, "%s/%s i=0,1",
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sname, pname);
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gsl_test_rel(x[2], 0.0, epsrel, "%s/%s i=2",
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sname, pname);
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}
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}
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static int
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box_f (const gsl_vector * x, void *params, gsl_vector * f)
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{
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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double x3 = gsl_vector_get(x, 2);
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size_t i;
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for (i = 0; i < box_N; ++i)
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{
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double ti = (i + 1.0) / 10.0;
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double fi = exp(-x1*ti) - exp(-x2*ti) - x3*(exp(-ti) - exp(-10.0*ti));
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gsl_vector_set(f, i, fi);
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}
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(void)params; /* avoid unused parameter warning */
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return GSL_SUCCESS;
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}
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static int
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box_df (CBLAS_TRANSPOSE_t TransJ, const gsl_vector * x,
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const gsl_vector * u, void * params, gsl_vector * v,
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gsl_matrix * JTJ)
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{
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gsl_matrix_view J = gsl_matrix_view_array(box_J, box_N, box_P);
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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size_t i;
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for (i = 0; i < box_N; ++i)
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{
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double ti = (i + 1.0) / 10.0;
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double term1 = exp(-x1*ti);
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double term2 = exp(-x2*ti);
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double term3 = exp(-10.0*ti) - exp(-ti);
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gsl_matrix_set(&J.matrix, i, 0, -ti*term1);
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gsl_matrix_set(&J.matrix, i, 1, ti*term2);
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gsl_matrix_set(&J.matrix, i, 2, term3);
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}
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if (v)
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gsl_blas_dgemv(TransJ, 1.0, &J.matrix, u, 0.0, v);
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if (JTJ)
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gsl_blas_dsyrk(CblasLower, CblasTrans, 1.0, &J.matrix, 0.0, JTJ);
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(void)params; /* avoid unused parameter warning */
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return GSL_SUCCESS;
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}
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static int
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box_fvv (const gsl_vector * x, const gsl_vector * v,
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void *params, gsl_vector * fvv)
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{
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double x1 = gsl_vector_get(x, 0);
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double x2 = gsl_vector_get(x, 1);
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double v1 = gsl_vector_get(v, 0);
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double v2 = gsl_vector_get(v, 1);
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size_t i;
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for (i = 0; i < box_N; ++i)
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{
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double ti = (i + 1.0) / 10.0;
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double term1 = exp(-x1*ti);
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double term2 = exp(-x2*ti);
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gsl_vector_set(fvv, i, ti * ti * (v1*v1*term1 - v2*v2*term2));
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}
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(void)params; /* avoid unused parameter warning */
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return GSL_SUCCESS;
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}
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static gsl_multilarge_nlinear_fdf box_func =
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{
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box_f,
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box_df,
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box_fvv,
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box_N,
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box_P,
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NULL,
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0,
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0,
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0,
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0
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};
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static test_fdf_problem box_problem =
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{
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"box3d",
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box_x0,
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NULL,
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&box_epsrel,
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&box_checksol,
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&box_func
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};
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