void test01 ( )
/******************************************************************************/
/*
Purpose:
TEST01 tests P00_PROBLEM_NUM and P00_TITLE.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
*/
{
int problem;
int problem_num;
char *title;
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " P00_PROBLEM_NUM returns the number of problems.\n" );
printf ( " P00_TITLE returns the title of a problem.\n" );
problem_num = p00_problem_num ( );
printf ( "\n" );
printf ( " P00_PROBLEM_NUM: number of problems is %d\n", problem_num );
printf ( "\n" );
printf ( " Problem Title\n" );
printf ( "\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
title = p00_title ( problem );
printf ( " %8d \"%s\".\n", problem, title );
free ( title );
}
return;
}
void test01 ( void )
/******************************************************************************/
/*
Purpose:
TEST01 simply prints the title of each problem.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
17 February 2012
Author:
John Burkardt
*/
{
int problem_num;
int problem;
char title[100];
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " For each problem, print the title.\n" );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
printf ( "\n" );
printf ( " Problem Title\n" );
printf ( "\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
p00_title ( problem, title );
printf ( " %6d %s\n", problem, title );
}
return;
}
void test01 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST01 simply prints the title of each function.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 28 August 2012
//
// Author:
//
// John Burkardt
//
{
int prob;
int prob_num;
char *title;
printf ( "\n" );
printf ( "TEST01\n" );
printf ( " Print the title of each function.\n" );
prob_num = p00_prob_num ( );
printf ( "\n" );
printf ( " There are %d functions available:\n", prob_num );
printf ( " Index Title\n" );
printf ( "\n" );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
printf ( " %2d %s\n", prob, title );
free ( title );
}
return;
}
void test02 ( void )
/******************************************************************************/
/*
Purpose:
TEST02 evaluates the objective function at each starting point.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
17 February 2012
Author:
John Burkardt
*/
{
double *a;
double *b;
double *f;
double *fs;
int i;
int know;
int m;
int n = 100000;
int problem;
int problem_num;
int seed;
char title[100];
double *x;
double *xs;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " For each problem, evaluate the function at many points.\n" );
printf ( " Number of sample points = %d\n", n );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
for ( problem = 1; problem <= problem_num; problem++ )
{
printf ( "\n" );
printf ( " Problem %d\n", problem );
p00_title ( problem, title );
printf ( " %s\n", title );
m = p00_m ( problem );
printf ( " M = %d\n", m );
a = ( double * ) malloc ( m * sizeof ( double ) );
b = ( double * ) malloc ( m * sizeof ( double ) );
p00_ab ( problem, m, a, b );
printf ( "\n" );
printf ( " I A(i) B(i)\n" );
printf ( "\n" );
for ( i = 0; i < m; i++ )
{
printf ( " %4d %10g %10g\n", i, a[i], b[i] );
}
seed = 123456789;
x = r8col_uniform_new ( m, n, a, b, &seed );
f = p00_f ( problem, m, n, x );
printf ( "\n" );
printf ( " Max(F) = %g\n", r8vec_max ( n, f ) );
printf ( " Min(F) = %g\n", r8vec_min ( n, f ) );
know = 0;
xs = p00_sol ( problem, m, &know );
if ( know != 0 )
{
fs = p00_f ( problem, m, 1, xs );
printf ( " F(X*) = %g\n", fs[0] );
free ( fs );
free ( xs );
}
else
{
printf ( " X* is not given.\n" );
}
free ( a );
free ( b );
free ( f );
free ( x );
}
return;
}
void test06 ( void )
/******************************************************************************/
/*
Purpose:
TEST06 carries out a version of Brent's derivative-free minimizer.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
03 February 2012
Author:
John Burkardt
*/
{
double a;
double b;
double fa;
double fb;
double fx;
int problem_num;
int problem;
char title[50];
double tol = 0.000001;
double x;
printf ( "\n" );
printf ( "TEST06\n" );
printf ( " For each problem, use Brent's method.\n" );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
for ( problem = 1; problem <= problem_num; problem++ )
{
p00_title ( problem, title );
printf ( "\n" );
printf ( " Problem %d\n", problem );
printf ( " %s\n", title );
p00_interval ( problem, &a, &b );
fa = p00_f ( problem, a );
fb = p00_f ( problem, b );
printf ( "\n" );
printf ( " Initial interval [A,B]:\n" );
printf ( "\n" );
printf ( " A, B: %16g %16g\n", a, b );
printf ( " FA, FB: %16g %16g\n", fa, fb );
x = p00_fmin ( &a, &b, problem, tol );
fa = p00_f ( problem, a );
fb = p00_f ( problem, b );
fx = p00_f ( problem, x );
printf ( "\n" );
printf ( " Final interval [A,X*,B]:\n" );
printf ( "\n" );
printf ( " A, X*, B: %16g %16g %16g\n", a, x, b );
printf ( " FA, FX*, FB: %16g %16g %16g\n", fa, fx, fb );
}
return;
}
void test05 ( void )
/******************************************************************************/
/*
Purpose:
TEST05 carries out a simple bisection method.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
03 February 2012
Author:
John Burkardt
*/
{
double a;
double b;
double c;
double d;
double e;
double fa;
double fb;
double fc;
double fd;
double fe;
int i;
int max_step = 10;
int problem_num;
int problem;
char title[50];
printf ( "\n" );
printf ( "TEST05\n" );
printf ( " For each problem, take a few steps of \n" );
printf ( " the bisection method.\n" );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
for ( problem = 1; problem <= problem_num; problem++ )
{
p00_title ( problem, title );
printf ( "\n" );
printf ( " Problem %d\n", problem );
printf ( " %s\n", title );
p00_interval ( problem, &a, &c );
b = 0.5 * ( a + c );
fa = p00_f ( problem, a );
fc = p00_f ( problem, c );
fb = p00_f ( problem, b );
i = 0;
printf ( "\n" );
printf ( " %d\n", i );
printf ( " X: %10g %10g %10g\n", a, b, c );
printf ( " F: %10g %10g %10g\n", fa, fb, fc );
for ( i = 1; i <= max_step; i++ )
{
d = 0.5 * ( a + b );
fd = p00_f ( problem, d );
e = 0.5 * ( b + c );
fe = p00_f ( problem, e );
if ( fd <= fb )
{
c = b;
fc = fb;
b = d;
fb = fd;
}
else if ( fe <= fb )
{
a = b;
fa = fb;
b = e;
fb = fe;
}
else
{
a = d;
fa = fd;
c = e;
fc = fe;
}
printf ( " %d\n", i );
printf ( " X: %10g %10g %10g\n", a, b, c );
printf ( " F: %10g %10g %10g\n", fa, fb, fc );
}
}
return;
}
void test04 ( void )
/******************************************************************************/
/*
Purpose:
TEST04 compares the exact and approximate second derivatives.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
03 February 2012
Author:
John Burkardt
*/
{
double f2;
double f2_dif;
int problem_num;
int problem;
char title[50];
double x;
printf ( "\n" );
printf ( "TEST04\n" );
printf ( " For each problem, compare the exact and\n" );
printf ( " approximate second derivatives at the starting point.\n" );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
for ( problem = 1; problem <= problem_num; problem++ )
{
p00_title ( problem, title );
printf ( "\n" );
printf ( " Problem %d\n", problem );
printf ( " %s\n", title );
x = p00_start ( problem );
printf ( "\n" );
printf ( " X:\n" );
printf ( " %g\n", x );
f2 = p00_f2 ( problem, x );
printf ( " F\"(X) (exact):\n" );
printf ( " %g\n", f2 );
f2_dif = p00_f2_dif ( problem, x );
printf ( " F\"(X) (difference):\n" );
printf ( " %g\n", f2_dif );
}
return;
}
void test02 ( void )
/******************************************************************************/
/*
Purpose:
TEST02 evaluates the objective function at each starting point.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
03 February 2012
Author:
John Burkardt
*/
{
double f_sol;
double f_start;
int know;
int problem_num;
int problem;
char title[50];
double x;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " For each problem, evaluate the function\n" );
printf ( " at the starting point and the solution.\n" );
/*
Get the number of problems.
*/
problem_num = p00_problem_num ( );
for ( problem = 1; problem <= problem_num; problem++ )
{
p00_title ( problem, title );
printf ( "\n" );
printf ( " Problem %d\n", problem );
printf ( " %s\n", title );
printf ( "\n" );
x = p00_start ( problem );
f_start = p00_f ( problem, x );
printf ( " F(X_START) = %g\n", f_start );
p00_sol ( problem, &know, &x );
if ( 0 < know )
{
f_sol = p00_f ( problem, x );
printf ( " F(X_SOL) = %g\n", f_sol );
}
}
return;
}