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test_approx_prb.cpp
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# include <cstdlib>
# include <iostream>
# include <iomanip>
using namespace std;
# include "test_approx.hpp"
# include "spline.hpp"
int main ( );
void test01 ( );
void test02 ( );
void test03 ( );
void test04 ( );
void test05 ( );
void test06 ( );
void test07 ( );
void test08 ( );
void test09 ( );
void test10 ( );
void test11 ( );
void test12 ( );
void test13 ( );
//****************************************************************************80
int main ( )
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TEST_APPROX_PRB.
//
// Discussion:
//
// TEST_APPROX_PRB tests the TEST_APPROX library.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
timestamp ( );
cout << "\n";
cout << "TEST_APPROX_PRB\n";
cout << " C++ version\n";
cout << " Test the TEST_APPROX library.\n";
test01 ( );
test02 ( );
test03 ( );
test04 ( );
test05 ( );
test06 ( );
test07 ( );
test08 ( );
test09 ( );
test10 ( );
test11 ( );
test12 ( );
test13 ( );
//
// Terminate.
//
cout << "\n";
cout << "TEST_APPROX_PRB\n";
cout << " Normal end of execution.\n";
cout << "\n";
timestamp ( );
return 0;
}
//****************************************************************************80
void test01 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST01 shows how P00_TITLE can be called.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
int prob;
int prob_num;
string title;
cout << "\n";
cout << "TEST01\n";
cout << " Demonstrate some of the bookkeeping routines.\n";
cout << " P00_PROB_NUM returns the number of problems.\n";
cout << " P00_TITLE returns the problem title.\n";
cout << " P00_LIMIT returns the problem limits.\n";
prob_num = p00_prob_num ( );
cout << "\n";
cout << " Number of problems = " << prob_num << "\n";
cout << "\n";
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
cout << " " << setw(2) << prob
<< " \"" << title << "\"\n";
}
return;
}
//****************************************************************************80
void test02 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST02 shows how P00_STORY can be called.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
int prob;
int prob_num;
cout << "\n";
cout << "TEST02\n";
cout << " P00_STORY prints the problem \"story\".\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
cout << "\n";
cout << " Problem " << prob << "\n";
p00_story ( prob );
}
return;
}
//****************************************************************************80
void test03 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST03 uses polynomial interpolation on data vector problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
double *diftab;
int i;
int j;
int jhi;
char mark;
int max_tab = 12;
int ntab;
int data_num;
int prob;
int prob_num;
string title;
double x;
double *xdata;
double yapprox;
double *ydata;
cout << "\n";
cout << "TEST03\n";
cout << " Polynomial interpolation to a vector of data.\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
cout << "\n";
cout << " Problem " << prob << "\n";
cout << " " << title << "\n";
data_num = p00_data_num ( prob );
cout << " DATA_NUM = " << data_num << "\n";
if ( max_tab < data_num )
{
cout << "\n";
cout << " Skipped problem " << prob << "\n";
cout << " Too big.\n";
}
else
{
xdata = new double[data_num];
ydata = new double[data_num];
diftab = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
ntab = data_num;
cout << "\n";
cout << " Interpolating polynomial order = " << ntab << "\n";
cout << "\n";
//
// Construct the interpolating polynomial via finite differences.
//
data_to_dif ( ntab, xdata, ydata, diftab );
//
// Print out the approximation, including midpoints of the intervals.
//
for ( i = 1; i <= ntab; i++ )
{
if ( i < ntab )
{
jhi = 2;
}
else
{
jhi = 1;
}
for ( j = 1; j <= jhi; j++ )
{
if ( i < ntab )
{
x = ( ( double ) ( jhi - j + 1 ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jhi );
}
else
{
x = xdata[ntab-1];
}
if ( j == 1 )
{
mark = '*';
}
else
{
mark = ' ';
}
yapprox = dif_val ( ntab, xdata, diftab, x );
cout << " " << mark
<< " " << setw(14) << x
<< " " << setw(14) << yapprox << "\n";
}
}
delete [] diftab;
delete [] xdata;
delete [] ydata;
}
}
return;
}
//****************************************************************************80
void test04 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST04 uses linear spline interpolation on all problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
double a;
double b;
int i;
int imax;
char mark;
int data_num;
int prob;
int prob_num;
string title;
double *xdata;
double xval;
double *ydata;
double ypval;
double yval;
cout << "\n";
cout << "TEST04\n";
cout << " Linear spline interpolation.\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
a = xdata[0];
b = xdata[data_num-1];
cout << "\n";
cout << " Problem " << prob << "\n";
cout << " " << title << "\n";
cout << "\n";
cout << " X Y Y'\n";
cout << "\n";
//
// Evaluate the interpolation function.
//
imax = 2 * data_num - 1;
for ( i = 1; i <= imax; i++ )
{
xval = ( ( double ) ( imax - i ) * a
+ ( double ) ( i - 1 ) * b )
/ ( double ) ( imax - 1 );
spline_linear_val ( data_num, xdata, ydata, xval, &yval, &ypval );
if ( ( i % 2 ) == 1 )
{
mark = '*';
}
else
{
mark = ' ';
}
cout << " " << mark
<< " " << setw(14) << xval
<< " " << setw(14) << yval
<< " " << setw(14) << ypval << "\n";
}
delete [] xdata;
delete [] ydata;
}
return;
}
//****************************************************************************80
void test05 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST05 uses Overhauser spline interpolation on all problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
double a;
double b;
int i;
int j;
int jhi;
int jmax;
char mark;
int data_num;
int num_dim = 1;
int prob;
int prob_num;
string title;
double *xdata;
double xval;
double *ydata;
double yval;
cout << "\n";
cout << "TEST05\n";
cout << " Overhauser spline interpolation.\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
a = xdata[0];
b = xdata[data_num-1];
cout << "\n";
cout << " Problem " << prob << "\n";
cout << " " << title << "\n";
cout << "\n";
cout << " X Y\n";
cout << "\n";
//
// Evaluate the interpolation function.
//
for ( i = 1; i < data_num; i++ )
{
jmax = 3;
if ( i == data_num - 1 )
{
jhi = jmax;
}
else
{
jhi = jmax - 1;
}
for ( j = 1; j <= jhi; j++ )
{
xval = ( ( double ) ( jmax - j ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jmax - 1 );
spline_overhauser_val ( num_dim, data_num, xdata, ydata, xval, &yval );
if ( j == 1 || j == 3 )
{
mark = '*';
}
else
{
mark = ' ';
}
cout << " " << mark
<< " " << setw(14) << xval
<< " " << setw(14) << yval << "\n";
}
}
delete [] xdata;
delete [] ydata;
}
return;
}
//****************************************************************************80
void test06 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST06 uses cubic spline interpolation on all problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
double a;
double b;
int i;
int ibcbeg;
int ibcend;
int j;
int jhi;
int jmax;
char mark;
int data_num;
int prob;
int prob_num;
string title;
double *xdata;
double xval;
double ybcbeg;
double ybcend;
double *ydata;
double *ypp;
double yppval;
double ypval;
double yval;
ibcbeg = 0;
ibcend = 0;
ybcbeg = 0.0;
ybcend = 0.0;
cout << "\n";
cout << "TEST06\n";
cout << " Cubic spline interpolation.\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
ypp = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
a = xdata[0];
b = xdata[data_num-1];
//
// Set up the interpolation function.
//
ypp = spline_cubic_set ( data_num, xdata, ydata, ibcbeg, ybcbeg,
ibcend, ybcend );
cout << "\n";
cout << " Problem " << prob << "\n";
cout << " " << title << "\n";
cout << "\n";
cout << " X Y\n";
cout << "\n";
//
// Evaluate the interpolation function.
//
for ( i = 1; i < data_num; i++ )
{
jmax = 3;
if ( i == data_num - 1 )
{
jhi = jmax;
}
else
{
jhi = jmax - 1;
}
for ( j = 1; j <= jhi; j++ )
{
xval = ( ( double ) ( jmax - j ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jmax - 1 );
yval = spline_cubic_val ( data_num, xdata, ydata, ypp, xval, &ypval, &yppval );
if ( j == 1 || j == 3 )
{
mark = '*';
}
else
{
mark = ' ';
}
cout << " " << mark
<< " " << setw(14) << xval
<< " " << setw(14) << yval << "\n";
}
}
delete [] xdata;
delete [] ydata;
delete [] ypp;
}
return;
}
//****************************************************************************80
void test07 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST07 plots an Overhauser spline interpolant for problem 7.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
string approx_filename = "test07_approx.txt";
string data_filename = "test07_data.txt";
int i;
int j;
int jhi;
int jmax = 7;
int data_num;
int nplot;
int num_dim = 1;
int plot;
int prob;
double *xdata;
double *xplot;
double xval;
double *ydata;
double *yplot;
double yval;
cout << "\n";
cout << "TEST07\n";
cout << " Plot an Overhauser spline interpolant for problem 7.\n";
//
// Get the problem data.
//
prob = 7;
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
r8vec2_write ( data_filename, data_num, xdata, ydata );
cout << "\n";
cout << " Data values stored in \"" << data_filename << "\".\n";
//
// Evaluate the approximating function.
//
nplot = ( jmax - 1 ) * ( data_num - 1 ) + 1;
xplot = new double[nplot];
yplot = new double[nplot];
plot = 0;
for ( i = 1; i < data_num; i++ )
{
if ( i == data_num - 1 )
{
jhi = jmax;
}
else
{
jhi = jmax - 1;
}
for ( j = 1; j <= jhi; j++ )
{
xval = ( ( double ) ( jmax - j ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jmax - 1 );
spline_overhauser_val ( num_dim, data_num, xdata, ydata, xval, &yval );
xplot[plot] = xval;
yplot[plot] = yval;
plot = plot + 1;
}
}
r8vec2_write ( approx_filename, nplot, xplot, yplot );
cout << " Approximant values stored in \"" << approx_filename << "\".\n";
delete [] xdata;
delete [] xplot;
delete [] ydata;
delete [] yplot;
return;
}
//****************************************************************************80
void test08 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST08 plots a cubic spline interpolant for problem 7.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
string approx_filename = "test08_approx.txt";
string data_filename = "test08_data.txt";
int i;
int ibcbeg;
int ibcend;
int j;
int jhi;
int jmax = 7;
int data_num;
int nplot;
int plot;
int prob;
double *xdata;
double *xplot;
double xval;
double ybcbeg;
double ybcend;
double *ydata;
double *yplot;
double *ypp;
double yppval;
double ypval;
double yval;
cout << "\n";
cout << "TEST08\n";
cout << " Plot a cubic spline interpolant for problem 7.\n";
prob = 7;
//
// Get the data.
//
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
ypp = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
r8vec2_write ( data_filename, data_num, xdata, ydata );
cout << "\n";
cout << " Data values stored in \"" << data_filename << "\".\n";
//
// Set up the interpolation function.
//
ibcbeg = 0;
ibcend = 0;
ybcbeg = 0.0;
ybcend = 0.0;
ypp = spline_cubic_set ( data_num, xdata, ydata, ibcbeg, ybcbeg, ibcend, ybcend );
//
// Evaluate the interpolation function.
//
plot = 0;
nplot = ( jmax - 1 ) * ( data_num - 1 ) + 1;
xplot = new double[nplot];
yplot = new double[nplot];
for ( i = 1; i < data_num; i++ )
{
if ( i == data_num - 1 )
{
jhi = jmax;
}
else
{
jhi = jmax - 1;
}
for ( j = 1; j <= jhi; j++ )
{
xval = ( ( double ) ( jmax - j ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jmax - 1 );
yval = spline_cubic_val ( data_num, xdata, ydata, ypp, xval, &ypval,
&yppval );
xplot[plot] = xval;
yplot[plot] = yval;
plot = plot + 1;
}
}
r8vec2_write ( approx_filename, nplot, xplot, yplot );
cout << " Approximant values stored in \"" << approx_filename << "\".\n";
delete [] xdata;
delete [] xplot;
delete [] ydata;
delete [] yplot;
delete [] ypp;
return;
}
//****************************************************************************80
void test09 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST09 uses B spline approximation on all problems.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
double a;
double b;
int i;
int j;
int jhi;
int jmax;
char mark;
int data_num;
int prob;
int prob_num;
string title;
double *xdata;
double xval;
double *ydata;
double yval;
cout << "\n";
cout << "TEST09\n";
cout << " B spline approximation.\n";
prob_num = p00_prob_num ( );
for ( prob = 1; prob <= prob_num; prob++ )
{
title = p00_title ( prob );
data_num = p00_data_num ( prob );
xdata = new double[data_num];
ydata = new double[data_num];
p00_dat ( prob, data_num, xdata, ydata );
a = xdata[0];
b = xdata[data_num-1];
cout << "\n";
cout << " Problem " << prob << "\n";
cout << " " << title << "\n";
cout << "\n";
cout << " X Y\n";
cout << "\n";
//
// Evaluate the interpolation function.
//
for ( i = 1; i < data_num; i++ )
{
jmax = 3;
if ( i == data_num - 1 )
{
jhi = jmax;
}
else
{
jhi = jmax - 1;
}
for ( j = 1; j <= jhi; j++ )
{
xval = ( ( double ) ( jmax - j ) * xdata[i-1]
+ ( double ) ( j - 1 ) * xdata[i] )
/ ( double ) ( jmax - 1 );
yval = spline_b_val ( data_num, xdata, ydata, xval );
if ( j == 1 || j == 3 )
{
mark = '*';
}
else
{
mark = ' ';
}
cout << " " << mark
<< " " << setw(14) << xval
<< " " << setw(14) << yval << "\n";
}
}
delete [] xdata;
delete [] ydata;
}
return;
}
//****************************************************************************80
void test10 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST10 plots a B spline approximant for problem 7.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 26 August 2011
//
// Author:
//
// John Burkardt
//
{
string approx_filename = "test10_approx.txt";
string data_filename = "test10_data.txt";
int i;
int j;
int jhi;
int jmax = 7;