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#define lin2_N 20 /* can be anything >= p */
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#define lin2_P 5
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static double lin2_x0[lin2_P] = { 1.0, 1.0, 1.0, 1.0, 1.0 };
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static double lin2_epsrel = 1.0e-8;
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static double lin2_J[lin2_N * lin2_P];
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static void
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lin2_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 n = (double) lin2_N;
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const double sumsq_exact = 0.5 * (n*(n - 1.0)) / (2.0*n + 1.0);
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const double sum_exact = 3.0 / (2.0*n + 1.0);
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double sum = 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 < lin2_P; ++i)
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sum += (i + 1.0) * x[i];
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gsl_test_rel(sum, sum_exact, epsrel, "%s/%s coeff sum",
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sname, pname);
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}
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static int
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lin2_f (const gsl_vector * x, void *params, gsl_vector * f)
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{
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size_t i, j;
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for (i = 0; i < lin2_N; ++i)
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{
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double fi = 0.0;
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for (j = 0; j < lin2_P; ++j)
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{
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double xj = gsl_vector_get(x, j);
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fi += (j + 1) * xj;
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}
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fi = (i + 1) * fi - 1.0;
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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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lin2_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(lin2_J, lin2_N, lin2_P);
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size_t i, j;
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for (i = 0; i < lin2_N; ++i)
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{
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for (j = 0; j < lin2_P; ++j)
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{
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gsl_matrix_set(&J.matrix, i, j, (i + 1.0) * (j + 1.0));
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}
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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)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 int
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lin2_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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(void)x; /* avoid unused parameter warnings */
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(void)v;
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(void)params;
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gsl_vector_set_zero(fvv);
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return GSL_SUCCESS;
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}
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static gsl_multilarge_nlinear_fdf lin2_func =
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{
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lin2_f,
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lin2_df,
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lin2_fvv,
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lin2_N,
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lin2_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 lin2_problem =
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{
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"linear_rank1",
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lin2_x0,
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NULL,
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&lin2_epsrel,
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&lin2_checksol,
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&lin2_func
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};
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