test_funcs.c

该文件为c++的数学函数库!是一个非常有用的编程工具.它含有各种数学函数,为科学计算、工程应用等程序编写提供方便！

/* 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., 675 Mass Ave, Cambridge, MA 02139, 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;
}