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#define powell1_N 4
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#define powell1_P 4
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static double powell1_x0[powell1_P] = { 3.0, -1.0, 0.0, 1.0 };
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static double powell1_epsrel = 1.0e-4;
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static double powell1_J[powell1_N * powell1_P];
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static void
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powell1_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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size_t i;
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const double sumsq_exact = 0.0;
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gsl_test_rel(sumsq, sumsq_exact, epsrel, "%s/%s sumsq",
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sname, pname);
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for (i = 0; i < powell1_P; ++i)
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{
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gsl_test_rel(x[i], 0.0, epsrel, "%s/%s i=%zu",
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sname, pname, i);
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}
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}
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static int
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powell1_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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double x4 = gsl_vector_get (x, 3);
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gsl_vector_set(f, 0, x1 + 10.0*x2);
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gsl_vector_set(f, 1, sqrt(5.0) * (x3 - x4));
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gsl_vector_set(f, 2, pow(x2 - 2.0*x3, 2.0));
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gsl_vector_set(f, 3, sqrt(10.0) * pow((x1 - x4), 2.0));
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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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powell1_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(powell1_J, powell1_N, powell1_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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double x3 = gsl_vector_get (x, 2);
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double x4 = gsl_vector_get (x, 3);
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double term1 = x2 - 2.0*x3;
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double term2 = x1 - x4;
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gsl_matrix_set(&J.matrix, 0, 0, 1.0);
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gsl_matrix_set(&J.matrix, 0, 1, 10.0);
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gsl_matrix_set(&J.matrix, 0, 2, 0.0);
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gsl_matrix_set(&J.matrix, 0, 3, 0.0);
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gsl_matrix_set(&J.matrix, 1, 0, 0.0);
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gsl_matrix_set(&J.matrix, 1, 1, 0.0);
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gsl_matrix_set(&J.matrix, 1, 2, sqrt(5.0));
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gsl_matrix_set(&J.matrix, 1, 3, -sqrt(5.0));
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gsl_matrix_set(&J.matrix, 2, 0, 0.0);
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gsl_matrix_set(&J.matrix, 2, 1, 2.0*term1);
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gsl_matrix_set(&J.matrix, 2, 2, -4.0*term1);
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gsl_matrix_set(&J.matrix, 2, 3, 0.0);
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gsl_matrix_set(&J.matrix, 3, 0, 2.0*sqrt(10.0)*term2);
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gsl_matrix_set(&J.matrix, 3, 1, 0.0);
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gsl_matrix_set(&J.matrix, 3, 2, 0.0);
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gsl_matrix_set(&J.matrix, 3, 3, -2.0*sqrt(10.0)*term2);
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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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powell1_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 v1 = gsl_vector_get(v, 0);
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double v2 = gsl_vector_get(v, 1);
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double v3 = gsl_vector_get(v, 2);
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double v4 = gsl_vector_get(v, 3);
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gsl_vector_set(fvv, 0, 0.0);
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gsl_vector_set(fvv, 1, 0.0);
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gsl_vector_set(fvv, 2, 2.0 * pow(v2 - 2.0*v3, 2.0));
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gsl_vector_set(fvv, 3, 2.0 * sqrt(10.0) * pow(v1 - v4, 2.0));
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(void)x; /* avoid unused parameter warning */
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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 powell1_func =
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{
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powell1_f,
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powell1_df,
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powell1_fvv,
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powell1_N,
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powell1_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 powell1_problem =
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{
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"powell_singular",
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powell1_x0,
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NULL,
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&powell1_epsrel,
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&powell1_checksol,
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&powell1_func
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};
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