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#define kowalik_N 11
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#define kowalik_P 4
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static double kowalik_x0[kowalik_P] = { 0.25, 0.39, 0.415, 0.39 };
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static double kowalik_epsrel = 1.0e-6;
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static double kowalik_J[kowalik_N * kowalik_P];
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static double kowalik_Y[kowalik_N] = {
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0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
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0.0456, 0.0342, 0.0323, 0.0235, 0.0246
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};
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static double kowalik_U[kowalik_N] = {
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4.0000, 2.0000, 1.0000, 0.5000, 0.2500, 0.1670,
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0.1250, 0.1000, 0.0833, 0.0714, 0.0625
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};
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static void
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kowalik_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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gsl_vector_const_view v = gsl_vector_const_view_array(x, kowalik_P);
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const double norm = gsl_blas_dnrm2(&v.vector);
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const double sumsq_exact1 = 3.075056038492370e-04;
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const double kowalik_x1[kowalik_P] = { 1.928069345723978e-01,
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1.912823290344599e-01,
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1.230565070690708e-01,
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1.360623308065148e-01 };
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const double sumsq_exact2 = 0.00102734304869549252;
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double kowalik_x2[kowalik_P] = { 0.0, /* inf */
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-14.0758834005984603,
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0.0, /* -inf */
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0.0 }; /* -inf */
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const double *kowalik_x;
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double sumsq_exact;
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kowalik_x2[0] = GSL_NAN;
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kowalik_x2[2] = GSL_NAN;
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kowalik_x2[3] = GSL_NAN;
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if (norm < 10.0)
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{
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kowalik_x = kowalik_x1;
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sumsq_exact = sumsq_exact1;
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}
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else
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{
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kowalik_x = kowalik_x2;
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sumsq_exact = sumsq_exact2;
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}
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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 < kowalik_P; ++i)
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{
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if (!gsl_finite(kowalik_x[i]))
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continue;
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gsl_test_rel(x[i], kowalik_x[i], 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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kowalik_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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size_t i;
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for (i = 0; i < kowalik_N; ++i)
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{
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double yi = kowalik_Y[i];
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double ui = kowalik_U[i];
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double fi = yi - (x1*ui*(ui+x2)) / (x4 + ui*(ui + x3));
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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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kowalik_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(kowalik_J, kowalik_N, kowalik_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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size_t i;
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for (i = 0; i < kowalik_N; ++i)
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{
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double ui = kowalik_U[i];
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double term1 = ui*(ui + x2);
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double term2 = ui*(ui + x3) + x4;
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gsl_matrix_set(&J.matrix, i, 0, -term1 / term2);
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gsl_matrix_set(&J.matrix, i, 1, -ui*x1/term2);
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gsl_matrix_set(&J.matrix, i, 2, ui*term1*x1 / (term2*term2));
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gsl_matrix_set(&J.matrix, i, 3, term1*x1 / (term2*term2));
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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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kowalik_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 x3 = gsl_vector_get(x, 2);
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double x4 = gsl_vector_get(x, 3);
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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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size_t i;
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for (i = 0; i < kowalik_N; ++i)
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{
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double ui = kowalik_U[i];
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double term2 = ui*(ui + x3) + x4;
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double term3 = ui*ui*v1 - ui*v3*x1 - v4*x1 +
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ui*v1*x3 + v1*x4;
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double term4 = ui*ui*(v3-v2) + v4*x2 +
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ui*(v4 + v3*x2 - v2*x3) - v2*x4;
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gsl_vector_set(fvv, i, 2.0*ui*term3*term4 / pow(term2, 3.0));
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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 kowalik_func =
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{
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kowalik_f,
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kowalik_df,
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kowalik_fvv,
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kowalik_N,
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kowalik_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 kowalik_problem =
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{
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"kowalik",
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kowalik_x0,
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NULL,
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&kowalik_epsrel,
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&kowalik_checksol,
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&kowalik_func
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};
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