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+/* multiroots/test_funcs.c
+ *
+ * Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
+ *
+ * This program is free software; you can redistribute it and/or modify
+ * it under the terms of the GNU General Public License as published by
+ * the Free Software Foundation; either version 2 of the License, or (at
+ * your option) any later version.
+ *
+ * This program is distributed in the hope that it will be useful, but
+ * WITHOUT ANY WARRANTY; without even the implied warranty of
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
+ * General Public License for more details.
+ *
+ * You should have received a copy of the GNU General Public License
+ * along with this program; if not, write to the Free Software
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
+ */
+
+#include <config.h>
+#include <math.h>
+#include <gsl/gsl_vector.h>
+#include <gsl/gsl_matrix.h>
+#include <gsl/gsl_multiroots.h>
+
+#include "test_funcs.h"
+
+/* For information on testing see the following paper,
+
+ J.J More, B.S. Garbow, K.E. Hillstrom, "Testing Unconstrained
+ Optimization Software", ACM Transactions on Mathematical Software,
+ Vol 7, No 1, (1981) p 17-41
+
+ */
+
+/* Rosenbrock Function */
+
+gsl_multiroot_function_fdf rosenbrock =
+{&rosenbrock_f,
+ &rosenbrock_df,
+ &rosenbrock_fdf,
+ 2, 0};
+
+void
+rosenbrock_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, -1.2);
+ gsl_vector_set (x, 1, 1.0);
+}
+
+int
+rosenbrock_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double y0 = 1 - x0;
+ double y1 = 10 * (x1 - x0 * x0);
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+rosenbrock_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+
+ double df00 = -1;
+ double df01 = 0;
+ double df10 = -20 * x0;
+ double df11 = 10;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+rosenbrock_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ rosenbrock_f (x, params, f);
+ rosenbrock_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Freudenstein and Roth function */
+
+gsl_multiroot_function_fdf roth =
+{&roth_f,
+ &roth_df,
+ &roth_fdf,
+ 2, 0};
+
+void
+roth_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, 4.5); /* changed from the value in the paper */
+ gsl_vector_set (x, 1, 3.5); /* otherwise the problem is too hard */
+}
+
+int
+roth_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double y0 = -13.0 + x0 + ((5.0 - x1)*x1 - 2.0)*x1;
+ double y1 = -29.0 + x0 + ((x1 + 1.0)*x1 - 14.0)*x1;
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+roth_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x1 = gsl_vector_get (x, 1);
+
+ double df00 = 1;
+ double df01 = -3 * x1 * x1 + 10 * x1 - 2;
+ double df10 = 1;
+ double df11 = 3 * x1 * x1 + 2 * x1 - 14;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+roth_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ roth_f (x, params, f);
+ roth_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+
+/* Powell badly scaled function */
+
+gsl_multiroot_function_fdf powellscal =
+{&powellscal_f,
+ &powellscal_df,
+ &powellscal_fdf,
+ 2, 0};
+
+void
+powellscal_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, 0.0);
+ gsl_vector_set (x, 1, 1.0);
+}
+
+int
+powellscal_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double y0 = 10000.0 * x0 * x1 - 1.0;
+ double y1 = exp (-x0) + exp (-x1) - 1.0001;
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+powellscal_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double df00 = 10000.0 * x1, df01 = 10000.0 * x0;
+ double df10 = -exp (-x0), df11 = -exp (-x1);
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+powellscal_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ powellscal_f (x, params, f);
+ powellscal_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Brown badly scaled function */
+
+gsl_multiroot_function_fdf brownscal =
+{&brownscal_f,
+ &brownscal_df,
+ &brownscal_fdf,
+ 2, 0};
+
+void
+brownscal_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, 1.0);
+ gsl_vector_set (x, 1, 1.0);
+}
+
+int
+brownscal_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double y0 = x0 - 1e6;
+ double y1 = x0 * x1 - 2;
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+brownscal_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double df00 = 1.0, df01 = 0.0;
+ double df10 = x1, df11 = x0;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+brownscal_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ brownscal_f (x, params, f);
+ brownscal_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Powell Singular Function */
+
+gsl_multiroot_function_fdf powellsing =
+{&powellsing_f,
+ &powellsing_df,
+ &powellsing_fdf,
+ 4, 0};
+
+void
+powellsing_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, 3.0);
+ gsl_vector_set (x, 1, -1.0);
+ gsl_vector_set (x, 2, 0.0);
+ gsl_vector_set (x, 3, 1.0);
+}
+
+int
+powellsing_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+ double x2 = gsl_vector_get (x, 2);
+ double x3 = gsl_vector_get (x, 3);
+
+ double y0 = x0 + 10 * x1;
+ double y1 = sqrt (5.0) * (x2 - x3);
+ double y2 = pow (x1 - 2 * x2, 2.0);
+ double y3 = sqrt (10.0) * pow (x0 - x3, 2.0);
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+ gsl_vector_set (f, 2, y2);
+ gsl_vector_set (f, 3, y3);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+powellsing_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+ double x2 = gsl_vector_get (x, 2);
+ double x3 = gsl_vector_get (x, 3);
+
+ double df00 = 1, df01 = 10, df02 = 0, df03 = 0;
+ double df10 = 0, df11 = 0, df12 = sqrt (5.0), df13 = -df12;
+ double df20 = 0, df21 = 2 * (x1 - 2 * x2), df22 = -2 * df21, df23 = 0;
+ double df30 = 2 * sqrt (10.0) * (x0 - x3), df31 = 0, df32 = 0, df33 = -df30;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 0, 2, df02);
+ gsl_matrix_set (df, 0, 3, df03);
+
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+ gsl_matrix_set (df, 1, 2, df12);
+ gsl_matrix_set (df, 1, 3, df13);
+
+ gsl_matrix_set (df, 2, 0, df20);
+ gsl_matrix_set (df, 2, 1, df21);
+ gsl_matrix_set (df, 2, 2, df22);
+ gsl_matrix_set (df, 2, 3, df23);
+
+ gsl_matrix_set (df, 3, 0, df30);
+ gsl_matrix_set (df, 3, 1, df31);
+ gsl_matrix_set (df, 3, 2, df32);
+ gsl_matrix_set (df, 3, 3, df33);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+powellsing_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ powellsing_f (x, params, f);
+ powellsing_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Wood function */
+
+gsl_multiroot_function_fdf wood =
+{&wood_f,
+ &wood_df,
+ &wood_fdf,
+ 4, 0};
+
+void
+wood_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, -3.0);
+ gsl_vector_set (x, 1, -1.0);
+ gsl_vector_set (x, 2, -3.0);
+ gsl_vector_set (x, 3, -1.0);
+}
+
+int
+wood_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+ double x2 = gsl_vector_get (x, 2);
+ double x3 = gsl_vector_get (x, 3);
+
+ double t1 = x1 - x0 * x0;
+ double t2 = x3 - x2 * x2;
+
+ double y0 = -200.0 * x0 * t1 - (1 - x0);
+ double y1 = 200.0 * t1 + 20.2 * (x1 - 1) + 19.8 * (x3 - 1);
+ double y2 = -180.0 * x2 * t2 - (1 - x2);
+ double y3 = 180.0 * t2 + 20.2 * (x3 - 1) + 19.8 * (x1 - 1);
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+ gsl_vector_set (f, 2, y2);
+ gsl_vector_set (f, 3, y3);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+wood_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+ double x2 = gsl_vector_get (x, 2);
+ double x3 = gsl_vector_get (x, 3);
+
+ double t1 = x1 - 3 * x0 * x0;
+ double t2 = x3 - 3 * x2 * x2;
+
+ double df00 = -200.0 * t1 + 1, df01 = -200.0 * x0, df02 = 0, df03 = 0;
+ double df10 = -400.0*x0, df11 = 200.0 + 20.2, df12 = 0, df13 = 19.8;
+ double df20 = 0, df21 = 0, df22 = -180.0 * t2 + 1, df23 = -180.0 * x2;
+ double df30 = 0, df31 = 19.8, df32 = -2 * 180 * x2, df33 = 180.0 + 20.2;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 0, 2, df02);
+ gsl_matrix_set (df, 0, 3, df03);
+
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+ gsl_matrix_set (df, 1, 2, df12);
+ gsl_matrix_set (df, 1, 3, df13);
+
+ gsl_matrix_set (df, 2, 0, df20);
+ gsl_matrix_set (df, 2, 1, df21);
+ gsl_matrix_set (df, 2, 2, df22);
+ gsl_matrix_set (df, 2, 3, df23);
+
+ gsl_matrix_set (df, 3, 0, df30);
+ gsl_matrix_set (df, 3, 1, df31);
+ gsl_matrix_set (df, 3, 2, df32);
+ gsl_matrix_set (df, 3, 3, df33);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+wood_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ wood_f (x, params, f);
+ wood_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Helical Valley Function */
+
+gsl_multiroot_function_fdf helical =
+{&helical_f,
+ &helical_df,
+ &helical_fdf,
+ 3, 0};
+
+void
+helical_initpt (gsl_vector * x)
+{
+ gsl_vector_set (x, 0, -1.0);
+ gsl_vector_set (x, 1, 0.0);
+ gsl_vector_set (x, 2, 0.0);
+}
+
+int
+helical_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+ double x2 = gsl_vector_get (x, 2);
+
+ double t1, t2;
+ double y0, y1, y2;
+
+ if (x0 > 0)
+ {
+ t1 = atan(x1/x0) / (2.0 * M_PI);
+ }
+ else if (x0 < 0)
+ {
+ t1 = 0.5 + atan(x1/x0) / (2.0 * M_PI);
+ }
+ else
+ {
+ t1 = 0.25 * (x1 > 0 ? +1 : -1);
+ }
+
+ t2 = sqrt(x0*x0 + x1*x1) ;
+
+ y0 = 10 * (x2 - 10 * t1);
+ y1 = 10 * (t2 - 1);
+ y2 = x2 ;
+
+ gsl_vector_set (f, 0, y0);
+ gsl_vector_set (f, 1, y1);
+ gsl_vector_set (f, 2, y2);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+helical_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ double x0 = gsl_vector_get (x, 0);
+ double x1 = gsl_vector_get (x, 1);
+
+ double t = x0 * x0 + x1 * x1 ;
+ double t1 = 2 * M_PI * t ;
+ double t2 = sqrt(t) ;
+
+ double df00 = 100*x1/t1, df01 = -100.0 * x0/t1, df02 = 10.0;
+ double df10 = 10*x0/t2, df11 = 10*x1/t2, df12 = 0;
+ double df20 = 0, df21 = 0, df22 = 1.0;
+
+ gsl_matrix_set (df, 0, 0, df00);
+ gsl_matrix_set (df, 0, 1, df01);
+ gsl_matrix_set (df, 0, 2, df02);
+
+ gsl_matrix_set (df, 1, 0, df10);
+ gsl_matrix_set (df, 1, 1, df11);
+ gsl_matrix_set (df, 1, 2, df12);
+
+ gsl_matrix_set (df, 2, 0, df20);
+ gsl_matrix_set (df, 2, 1, df21);
+ gsl_matrix_set (df, 2, 2, df22);
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+helical_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ helical_f (x, params, f);
+ helical_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+
+/* Discrete Boundary Value Function */
+
+#define N 10
+
+gsl_multiroot_function_fdf dbv =
+{&dbv_f,
+ &dbv_df,
+ &dbv_fdf,
+ N, 0};
+
+void
+dbv_initpt (gsl_vector * x)
+{
+ size_t i;
+ double h = 1.0 / (N + 1.0);
+
+ for (i = 0; i < N; i++)
+ {
+ double t = (i + 1) * h;
+ double z = t * (t - 1);
+ gsl_vector_set (x, i, z);
+ }
+}
+
+int
+dbv_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ size_t i;
+
+ double h = 1.0 / (N + 1.0);
+
+ for (i = 0; i < N; i++)
+ {
+ double z, ti = (i + 1) * h;
+ double xi = 0, xim1 = 0, xip1 = 0;
+
+ xi = gsl_vector_get (x, i);
+
+ if (i > 0)
+ xim1 = gsl_vector_get (x, i - 1);
+
+ if (i < N - 1)
+ xip1 = gsl_vector_get (x, i + 1);
+
+ z = 2 * xi - xim1 - xip1 + h * h * pow(xi + ti + 1, 3.0) / 2.0;
+
+ gsl_vector_set (f, i, z);
+
+ }
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+dbv_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ size_t i, j;
+
+ double h = 1.0 / (N + 1.0);
+
+ for (i = 0; i < N; i++)
+ for (j = 0; j < N; j++)
+ gsl_matrix_set (df, i, j, 0.0);
+
+ for (i = 0; i < N; i++)
+ {
+ double dz_dxi, ti = (i + 1) * h;
+
+ double xi = gsl_vector_get (x, i);
+
+ dz_dxi = 2.0 + (3.0 / 2.0) * h * h * pow(xi + ti + 1, 2.0) ;
+
+ gsl_matrix_set (df, i, i, dz_dxi);
+
+ if (i > 0)
+ gsl_matrix_set (df, i, i-1, -1.0);
+
+ if (i < N - 1)
+ gsl_matrix_set (df, i, i+1, -1.0);
+
+ }
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+dbv_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ dbv_f (x, params, f);
+ dbv_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
+
+/* Trigonometric Function */
+
+gsl_multiroot_function_fdf trig =
+{&trig_f,
+ &trig_df,
+ &trig_fdf,
+ N, 0};
+
+void
+trig_initpt (gsl_vector * x)
+{
+ size_t i;
+
+ for (i = 0; i < N; i++) /* choose an initial point which converges */
+ {
+ gsl_vector_set (x, i, 0.05);
+ }
+}
+
+int
+trig_f (const gsl_vector * x, void *params, gsl_vector * f)
+{
+ size_t i;
+ double sum = 0;
+
+ for (i = 0; i < N; i++)
+ {
+ sum += cos(gsl_vector_get(x,i));
+ }
+
+ for (i = 0; i < N; i++)
+ {
+ double xi = gsl_vector_get (x,i);
+ double z = N - sum + (i + 1) * (1 - cos(xi)) - sin(xi);
+
+ gsl_vector_set (f, i, z);
+ }
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+trig_df (const gsl_vector * x, void *params, gsl_matrix * df)
+{
+ size_t i, j;
+
+ for (i = 0; i < N; i++)
+ {
+ for (j = 0; j < N; j++)
+ {
+ double dz;
+ double xi = gsl_vector_get(x, i);
+ double xj = gsl_vector_get(x, j);
+
+ if (j == i)
+ dz = sin(xi) + (i + 1) * sin(xi) - cos(xi);
+ else
+ dz = sin(xj);
+
+ gsl_matrix_set(df, i, j, dz);
+ }
+ }
+
+ params = 0; /* avoid warning about unused parameters */
+
+ return GSL_SUCCESS;
+}
+
+int
+trig_fdf (const gsl_vector * x, void *params,
+ gsl_vector * f, gsl_matrix * df)
+{
+ trig_f (x, params, f);
+ trig_df (x, params, df);
+
+ return GSL_SUCCESS;
+}
generated by cgit v1.2.3 (git 2.25.1) at 2024-05-01 11:41:31 +0000