# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iostream>
# include <iomanip>
using namespace std;
# include "chebyshev.hpp"
int main ( );
void test01 ( );
double f1 ( double x );
double f2 ( double x );
double f3 ( double x );
void timestamp ( );
//****************************************************************************80
int main ( )
//****************************************************************************80
//
// Purpose:
//
// chebyshev_test() tests chebyshev().
//
// Licensing:
//
// This code is distributed under the MIT license. 
//
// Modified:
//
// 14 September 2011
//
// Author:
//
// John Burkardt
//
{
 timestamp ( );
 cout << "\n";
 cout << "CHEBYSHEV_TEST():\n";
 cout << " C++ version\n";
 cout << " Test CHEBYSHEV().\n";
 
 test01 ( );
//
// Terminate.
//
 cout << "\n";
 cout << "CHEBYSHEV_TEST():\n";
 cout << " Normal end of execution.\n";
 cout << "\n";
 timestamp ( );
 return 0;
}
//****************************************************************************80
void test01 ( )
//****************************************************************************80
//
// Purpose:
//
// TEST01 tests CHEBYSHEV_COEFFICIENTS and CHEBYSHEV_INTERPOLANT.
//
// Licensing:
//
// This code is distributed under the MIT license.
//
// Modified:
//
// 14 September 2011
//
// Author:
//
// John Burkardt
//
{
 double a;
 double b;
 double *c;
 double *fc;
 int i;
 int m;
 int n;
 double *x;
 
 cout << "\n";
 cout << "CHEBYSHEV_TEST01\n";
 cout << " CHEBYSHEV_COEFFICIENTS computes the coefficients of the\n";
 cout << " Chebyshev interpolant.\n";
 cout << " CHEBYSHEV_INTERPOLANT evaluates the interpolant.\n";
 n = 5;
 a = -1.0;
 b = +1.0;
 c = chebyshev_coefficients ( a, b, n, f1 );
 x = chebyshev_zeros ( n );
 for ( i = 0; i < n; i++ )
 {
 x[i] = 0.5 * ( a + b ) + x[i] * 0.5 * ( b - a );
 }
 m = n;
 fc = chebyshev_interpolant ( a, b, n, c, m, x );
 cout << "\n";
 cout << " F(X) is a trig function:\n";
 cout << "\n";
 cout << " X C(I) F(X) C(F)(X)\n";
 cout << "\n";
 for ( i = 0; i < n; i++ )
 {
 cout << " " << setw(14) << x[i]
 << " " << setw(14) << c[i]
 << " " << setw(14) << f1 ( x[i] )
 << " " << setw(14) << fc[i] << "\n";
 }
 delete [] c;
 delete [] fc;
 delete [] x;
//
// Try a variant interval.
//
 n = 5;
 a = 0.0;
 b = +3.0;
 c = chebyshev_coefficients ( a, b, n, f1 );
 x = chebyshev_zeros ( n );
 for ( i = 0; i < n; i++ )
 {
 x[i] = 0.5 * ( a + b ) + x[i] * 0.5 * ( b - a );
 }
 m = n;
 fc = chebyshev_interpolant ( a, b, n, c, m, x );
 cout << "\n";
 cout << " Consider the same F(X), but now over [0,3]:\n";
 cout << "\n";
 cout << " X C(I) F(X) C(F)(X)\n";
 cout << "\n";
 for ( i = 0; i < n; i++ )
 {
 cout << " " << setw(14) << x[i]
 << " " << setw(14) << c[i]
 << " " << setw(14) << f1 ( x[i] )
 << " " << setw(14) << fc[i] << "\n";
 }
 delete [] c;
 delete [] fc;
 delete [] x;
//
// Try a higher order.
//
 n = 10;
 a = -1.0;
 b = +1.0;
 c = chebyshev_coefficients ( a, b, n, f1 );
 x = chebyshev_zeros ( n );
 for ( i = 0; i < n; i++ )
 {
 x[i] = 0.5 * ( a + b ) + x[i] * 0.5 * ( b - a );
 }
 m = n;
 fc = chebyshev_interpolant ( a, b, n, c, m, x );
 cout << "\n";
 cout << " Consider the same F(X), but now with higher order:\n";
 cout << "\n";
 cout << " X C(I) F(X) C(F)(X)\n";
 cout << "\n";
 for ( i = 0; i < n; i++ )
 {
 cout << " " << setw(14) << x[i]
 << " " << setw(14) << c[i]
 << " " << setw(14) << f1 ( x[i] )
 << " " << setw(14) << fc[i] << "\n";
 }
 delete [] c;
 delete [] fc;
 delete [] x;
//
// Try a polynomial.
//
 n = 10;
 a = -1.0;
 b = +1.0;
 c = chebyshev_coefficients ( a, b, n, f3 );
 x = chebyshev_zeros ( n );
 for ( i = 0; i < n; i++ )
 {
 x[i] = 0.5 * ( a + b ) + x[i] * 0.5 * ( b - a );
 }
 m = n;
 fc = chebyshev_interpolant ( a, b, n, c, m, x );
 cout << "\n";
 cout << " F(X) is a degree 4 polynomial:\n";
 cout << "\n";
 cout << " X C(I) F(X) C(F)(X)\n";
 cout << "\n";
 for ( i = 0; i < n; i++ )
 {
 cout << " " << setw(14) << x[i]
 << " " << setw(14) << c[i]
 << " " << setw(14) << f3 ( x[i] )
 << " " << setw(14) << fc[i] << "\n";
 }
 delete [] c;
 delete [] fc;
 delete [] x;
//
// Try a function with decaying behavior.
//
 n = 10;
 a = -1.0;
 b = +1.0;
 c = chebyshev_coefficients ( a, b, n, f2 );
 x = chebyshev_zeros ( n );
 for ( i = 0; i < n; i++ )
 {
 x[i] = 0.5 * ( a + b ) + x[i] * 0.5 * ( b - a );
 }
 m = n;
 fc = chebyshev_interpolant ( a, b, n, c, m, x );
 cout << "\n";
 cout << " The polynomial approximation to F(X) decays:\n";
 cout << "\n";
 cout << " X C(I) F(X) C(F)(X)\n";
 cout << "\n";
 for ( i = 0; i < n; i++ )
 {
 cout << " " << setw(14) << x[i]
 << " " << setw(14) << c[i]
 << " " << setw(14) << f2 ( x[i] )
 << " " << setw(14) << fc[i] << "\n";
 }
 delete [] c;
 delete [] fc;
 delete [] x;
 return;
}
//****************************************************************************80
double f1 ( double x )
//****************************************************************************80
//
// Purpose:
//
// F1 evaluates a function that can be used for Chebyshev interpolation.
//
// Licensing:
//
// This code is distributed under the MIT license.
//
// Modified:
//
// 14 September 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, a point where the function is to be evaluated.
//
// Output, double F1, the function value.
//
{
 double pi = 3.141592653589793;
 double value;
 value = cos ( 2.0 * pi * x ) * sin ( 3.0 * pi * x );
 return value;
}
//****************************************************************************80
double f2 ( double x )
//****************************************************************************80
//
// Purpose:
//
// F2 evaluates a function that can be used for Chebyshev interpolation.
//
// Licensing:
//
// This code is distributed under the MIT license.
//
// Modified:
//
// 14 September 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, a point where the function is to be evaluated.
//
// Output, double F2, the function value.
//
{
 double value;
 value = exp ( x );
 return value;
}
//****************************************************************************80
double f3 ( double x )
//****************************************************************************80
//
// Purpose:
//
// F3 evaluates a function that can be used for Chebyshev interpolation.
//
// Licensing:
//
// This code is distributed under the MIT license.
//
// Modified:
//
// 14 September 2011
//
// Author:
//
// John Burkardt
//
// Parameters:
//
// Input, double X, a point where the function is to be evaluated.
//
// Output, double F3, the function values.
//
{
 double value;
 value = ( x - 3.0 ) * ( x - 1.0 ) * ( x - 1.0 ) * ( x + 2.0 );
 return value;
}
//****************************************************************************80
void timestamp ( )
//****************************************************************************80
//
// Purpose:
//
// TIMESTAMP prints the current YMDHMS date as a time stamp.
//
// Example:
//
// 31 May 2001 09:45:54 AM
//
// Licensing:
//
// This code is distributed under the MIT license. 
//
// Modified:
//
// 19 March 2018
//
// Author:
//
// John Burkardt
//
{
# define TIME_SIZE 40
 static char time_buffer[TIME_SIZE];
 const struct std::tm *tm_ptr;
 std::time_t now;
 now = std::time ( NULL );
 tm_ptr = std::localtime ( &now );
 std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );
 std::cout << time_buffer << "\n";
 return;
# undef TIME_SIZE
}
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