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 test02 ( )
/******************************************************************************/
/*
Purpose:
TEST02 tests P00_EXACT.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
*/
{
double exact;
int m;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " P00_EXACT returns the \"exact\" integral.\n" );
problem_num = p00_problem_num ( );
m = 4;
p06_param ( 'S', 'M', &m );
printf ( "\n" );
printf ( " Problem EXACT\n" );
printf ( "\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
printf ( " %8d %24.16g\n", problem, exact );
}
return;
}
void test02 ( )
/******************************************************************************/
/*
Purpose:
TEST02 tests P00_ALPHA and P00_EXACT.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
14 September 2012
Author:
John Burkardt
*/
{
double alpha;
double exact;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST02\n" );
printf ( " P00_ALPHA returns the lower limit of integration.\n" );
printf ( " P00_EXACT returns the \"exact\" integral.\n" );
problem_num = p00_problem_num ( );
printf ( "\n" );
printf ( " Problem ALPHA EXACT\n" );
printf ( "\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
alpha = p00_alpha ( problem );
exact = p00_exact ( problem );
printf ( " %8d %14g %24.16g\n", problem, alpha, exact );
}
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 test06 ( )
/******************************************************************************/
/*
Purpose:
TEST06 tests P00_MONTE_CARLO.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
*/
{
double error;
double estimate;
double exact;
int m;
int order;
int order_log;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST06\n" );
printf ( " P00_MONTE_CARLO uses a weighted form of the Monte Carlo method\n" );
printf ( " to estimate a Hermite integral on (-oo,+oo).\n" );
problem_num = p00_problem_num ( );
m = 4;
p06_param ( 'S', 'M', &m );
printf ( "\n" );
printf (
" Problem Order Estimate Exact Error\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
order = 128;
printf ( "\n" );
for ( order_log = 0; order_log <= 6; order_log++ )
{
estimate = p00_monte_carlo ( problem, order );
error = r8_abs ( exact - estimate );
printf ( " %8d %8d %14.6g %14.6g %14.6g\n",
problem, order, estimate, exact, error );
order = order * 4;
}
}
return;
}
void test04 ( )
/******************************************************************************/
/*
Purpose:
TEST04 tests P00_TURING.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
*/
{
double error;
double estimate;
double exact;
double h;
int m;
int n;
int order_log;
int problem;
int problem_num;
int test;
double tol;
printf ( "\n" );
printf ( "TEST04\n" );
printf ( " P00_TURING applies a Turing procedure\n" );
printf ( " to estimate an integral on (-oo,+oo).\n" );
problem_num = p00_problem_num ( );
m = 4;
p06_param ( 'S', 'M', &m );
for ( test = 1; test <= 2; test++ )
{
if ( test == 1 )
{
tol = 1.0E-4;
}
else if ( test == 2 )
{
tol = 1.0E-07;
}
printf ( "\n" );
printf ( " Using a tolerance of TOL = %g\n", tol );
printf ( "\n" );
printf (
" Problem Order Estimate Exact Error\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
h = 1.0;
printf ( "\n" );
for ( order_log = 0; order_log <= 6; order_log++ )
{
estimate = p00_turing ( problem, h, tol, &n );
error = r8_abs ( exact - estimate );
printf ( " %8d %10g %8d %14.6g %14.6g %14.6g\n",
problem, h, n, estimate, exact, error );
h = h / 2.0;
}
}
}
return;
}
void test03 ( )
/******************************************************************************/
/*
Purpose:
TEST03 tests P00_GAUSS_HERMITE.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
11 September 2012
Author:
John Burkardt
*/
{
double error;
double estimate;
double exact;
int m;
int order;
int order_log;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST03\n" );
printf ( " P00_GAUSS_HERMITE applies a Gauss-Hermite rule\n" );
printf ( " to estimate an integral on (-oo,+oo).\n" );
problem_num = p00_problem_num ( );
m = 4;
p06_param ( 'S', 'M', &m );
printf ( "\n" );
printf ( " Problem Order Estimate Exact Error\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
order = 1;
printf ( "\n" );
for ( order_log = 0; order_log <= 6; order_log++ )
{
estimate = p00_gauss_hermite ( problem, order );
error = r8_abs ( exact - estimate );
printf ( " %8d %8d %14.6g %14.6g %14.6g\n",
problem, order, estimate, exact, error );
order = order * 2;
}
}
return;
}
void test05 ( )
/******************************************************************************/
/*
Purpose:
TEST05 tests P00_RAT_TRANSFORM.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
14 September 2012
Author:
John Burkardt
*/
{
double error;
double estimate;
double exact;
int order;
int order_log;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST05\n" );
printf ( " P00_RAT_TRANSFORM applies a rational transform\n" );
printf ( " to estimate an integral on [ALPHA,+oo)\n" );
printf ( " as a transformed integral on (0,1/(1+ALPHA)],\n" );
printf ( " and applying a Gauss-Legendre rule.\n" );
problem_num = p00_problem_num ( );
printf ( "\n" );
printf ( " Exact\n" );
printf ( " Problem Order Estimate Error\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
order = 1;
printf ( "\n" );
printf ( " %8d %14.6g\n", problem, exact );
for ( order_log = 0; order_log <= 6; order_log++ )
{
estimate = p00_rat_transform ( problem, order );
error = r8_abs ( exact - estimate );
printf ( " %8d %14.6g %14.6g\n", order, estimate, error );
order = order * 2;
}
}
return;
}
void test03 ( )
/******************************************************************************/
/*
Purpose:
TEST03 tests P00_GAUSS_LAGUERRE.
Licensing:
This code is distributed under the GNU LGPL license.
Modified:
14 September 2012
Author:
John Burkardt
*/
{
double error;
double estimate;
double exact;
int order;
int order_log;
int problem;
int problem_num;
printf ( "\n" );
printf ( "TEST03\n" );
printf ( " P00_GAUSS_LAGUERRE applies a Gauss-Laguerre rule\n" );
printf ( " to estimate an integral on [ALPHA,+oo).\n" );
problem_num = p00_problem_num ( );
printf ( "\n" );
printf ( " Exact\n" );
printf ( " Problem Order Estimate Error\n" );
for ( problem = 1; problem <= problem_num; problem++ )
{
exact = p00_exact ( problem );
order = 1;
printf ( "\n" );
printf ( " %8d %14.6g\n", problem, exact );
for ( order_log = 0; order_log <= 6; order_log++ )
{
estimate = p00_gauss_laguerre ( problem, order );
error = r8_abs ( exact - estimate );
printf ( " %8d %14.6g %14.6g\n", order, estimate, error );
order = order * 2;
}
}
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;
}