# include <cstdlib>
# include <iostream>
# include <fstream>
# include <iomanip>
# include <cmath>
# include <ctime>
# include <cstring>

using namespace std;

# include "square_arbq_rule.hpp"

int main ( );
void test01 ( int degree, int n );
void test02 ( int degree, int n, string header );
void test03 ( int degree, int n, string header );
void test04 ( int degree, int n );

//****************************************************************************80

int main ( )

//****************************************************************************80
//
//  Purpose:
//
//    MAIN is the main program for SQUARE_ARBQ_RULE_PRB.
//
//  Discussion:
//
//    SQUARE_ARBQ_RULE_PRB tests the SQUARE_ARBQ_RULE library.
//
//  Licensing:
//
//    This code is distributed under the GNU GPL license.
//
//  Modified:
//
//    08 July 2014
//
//  Author:
//
//    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
//    This C++ version by John Burkardt.
//
//  Reference:
//
//    Hong Xiao, Zydrunas Gimbutas,
//    A numerical algorithm for the construction of efficient quadrature
//    rules in two and higher dimensions,
//    Computers and Mathematics with Applications,
//    Volume 59, 2010, pages 663-676.
//
{
  int degree;
  string header;
  int n;

  timestamp ( );
  cout << "\n";
  cout << "SQUARE_ARBQ_RULE_PRB\n";
  cout << "  C++ version\n";
  cout << "  Test the SQUARE_ARBQ_RULE library.\n";

  degree = 8;
  n = square_arbq_size ( degree );
  header = "square08";

  test01 ( degree, n );

  test02 ( degree, n, header );

  test03 ( degree, n, header );

  test04 ( degree, n );
//
//  Terminate.
//
  cout << "\n";
  cout << "SQUARE_ARBQ_RULE_PRB\n";
  cout << "  Normal end of execution.\n";
  cout << "\n";
  timestamp ( );

  return 0;
}
//****************************************************************************80

void test01 ( int degree, int n )

//****************************************************************************80
//
//  Purpose:
//
//    TEST01 calls SQUAREARBQ for a quadrature rule of given order.
//
//  Licensing:
//
//    This code is distributed under the GNU GPL license.
//
//  Modified:
//
//    02 July 2014
//
//  Author:
//
//    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
//    This C++ version by John Burkardt.
//
//  Reference:
//
//    Hong Xiao, Zydrunas Gimbutas,
//    A numerical algorithm for the construction of efficient quadrature
//    rules in two and higher dimensions,
//    Computers and Mathematics with Applications,
//    Volume 59, 2010, pages 663-676.
//
//  Parameters:
//
//    Input, int DEGREE, the desired total polynomial degree exactness
//    of the quadrature rule.
//
//    Input, int N, the number of nodes.
//
{
  double area;
  double d;
  int j;
  double *w;
  double *x;

  cout << "\n";
  cout << "TEST01\n";
  cout << "  Symmetric quadrature rule for a square.\n";
  cout << "  Polynomial exactness degree DEGREE = " << degree << "\n";

  area = 4.0;
//
//  Retrieve and print a symmetric quadrature rule.
//
  x = new double[2*n];
  w = new double[n];

  square_arbq ( degree, n, x, w );

  cout << "\n";
  cout << "  Number of nodes N = " << n << "\n";

  cout << "\n";
  cout << "     J  W       X       Y\n";
  cout << "\n";
  for ( j = 0; j < n; j++ )
  {
    cout << setw(4) << j << "  "
         << setw(14) << w[j] << "  "
         << setw(14) << x[0+j*2] << "  "
         << setw(14) << x[1+j*2] << "\n";
  }

  d = r8vec_sum ( n, w );

  cout << "   Sum  " << d << "\n";
  cout << "  Area  " << area << "\n";

  return;
}
//****************************************************************************80

void test02 ( int degree, int n, string header )

//****************************************************************************80
//
//  Purpose:
//
//    TEST02 gets a rule and writes it to a file.
//
//  Licensing:
//
//    This code is distributed under the GNU GPL license.
//
//  Modified:
//
//    02 July 2014
//
//  Author:
//
//    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
//    This C++ version by John Burkardt.
//
//  Reference:
//
//    Hong Xiao, Zydrunas Gimbutas,
//    A numerical algorithm for the construction of efficient quadrature
//    rules in two and higher dimensions,
//    Computers and Mathematics with Applications,
//    Volume 59, 2010, pages 663-676.
//
//  Parameters:
//
//    Input, int DEGREE, the desired total polynomial degree exactness
//    of the quadrature rule.  0 <= DEGREE <= 50.
//
//    Input, int N, the number of nodes to be used by the rule.
//
//    Input, string HEADER, an identifier for the filenames.
//
{
  int i;
  ofstream rule_unit;
  string rule_filename;
  double *w;
  double *x;

  cout << "\n";
  cout << "TEST02\n";
  cout << "  Get a quadrature rule for the symmetric square.\n";
  cout << "  Then write it to a file.\n";
  cout << "  Polynomial exactness degree DEGREE = " << degree << "\n";
//
//  Retrieve a symmetric quadrature rule.
//
  x = new double[2*n];
  w = new double[n];

  square_arbq ( degree, n, x, w );
//
//  Write the points and weights to a file.
//
  rule_filename = header + ".txt";

  rule_unit.open ( rule_filename.c_str ( ) );
  for ( i = 0; i < n; i++ )
  {
    rule_unit << x[0+i*2] << "  "
              << x[1+i*2] << "  "
              << w[i] << "\n";
  }
  rule_unit.close ( );
  cout << "\n";
  cout << "  Quadrature rule written to file '" << rule_filename << "'\n";

  delete [] w;
  delete [] x;

  return;
}
//****************************************************************************80

void test03 ( int degree, int n, string header )

//****************************************************************************80
//
//  Purpose:
//
//    TEST03 gets a rule and creates GNUPLOT input files.
//
//  Licensing:
//
//    This code is distributed under the GNU GPL license.
//
//  Modified:
//
//    02 July 2014
//
//  Author:
//
//    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
//    This C++ version by John Burkardt.
//
//  Reference:
//
//    Hong Xiao, Zydrunas Gimbutas,
//    A numerical algorithm for the construction of efficient quadrature
//    rules in two and higher dimensions,
//    Computers and Mathematics with Applications,
//    Volume 59, 2010, pages 663-676.
//
//  Parameters:
//
//    Input, int DEGREE, the desired total polynomial degree exactness
//    of the quadrature rule.  0 <= DEGREE <= 50.
//
//    Input, int N, the number of nodes to be used by the rule.
//
//    Input, string HEADER, an identifier for the filenames.
//
{
  int i;
  double *w;
  double *x;

  cout << "\n";
  cout << "TEST03\n";
  cout << "  Get a quadrature rule for the symmetric square.\n";
  cout << "  Set up GNUPLOT graphics input.\n";
  cout << "  Polynomial exactness degree DEGREE = " << degree << "\n";
//
//  Retrieve a symmetric quadrature rule.
//
  x = new double[2*n];
  w = new double[n];

  square_arbq ( degree, n, x, w );
//
//  Create files for input to GNUPLOT.
//
  square_arbq_gnuplot ( n, x, header );

  delete [] w;
  delete [] x;

  return;
}
//****************************************************************************80

void test04 ( int degree, int n )

//****************************************************************************80
//
//  Purpose:
//
//    TEST04 gets a rule and tests its accuracy.
//
//  Licensing:
//
//    This code is distributed under the GNU GPL license.
//
//  Modified:
//
//    02 July 2014
//
//  Author:
//
//    Original FORTRAN77 version by Hong Xiao, Zydrunas Gimbutas.
//    This C++ version by John Burkardt.
//
//  Reference:
//
//    Hong Xiao, Zydrunas Gimbutas,
//    A numerical algorithm for the construction of efficient quadrature
//    rules in two and higher dimensions,
//    Computers and Mathematics with Applications,
//    Volume 59, 2010, pages 663-676.
//
//  Parameters:
//
//    Input, int DEGREE, the desired total polynomial degree exactness
//    of the quadrature rule.  0 <= DEGREE <= 50.
//
//    Input, int N, the number of nodes to be used by the rule.
//
{
  double area;
  double d;
  int i;
  int j;
  int npols;
  double *pols;
  double *rints;
  double *w;
  double *x;
  double z[2];

  cout << "\n";
  cout << "TEST04\n";
  cout << "  Get a quadrature rule for the symmetric square.\n";
  cout << "  Test its accuracy.\n";
  cout << "  Polynomial exactness degree DEGREE = " << degree << "\n";
//
//  Retrieve a symmetric quadrature rule.
//
  x = new double[2*n];
  w = new double[n];

  square_arbq ( degree, n, x, w );

  npols = ( ( degree + 1 ) * ( degree + 2 ) ) / 2;
  rints = new double[npols];

  for ( j = 0; j < npols; j++ )
  {
    rints[j] = 0.0;
  }

  for ( i = 0; i < n; i++ )
  {
    z[0] = x[0+i*2];
    z[1] = x[1+i*2];

    pols = lege2eva ( degree, z );
    for ( j = 0; j < npols; j++ )
    {
      rints[j] = rints[j] + w[i] * pols[j];
     }
    delete [] pols;
  }

  area = 4.0;

  d = 0.0;
  d = pow ( rints[0] - sqrt ( area ), 2 );
  for ( i = 1; i < npols; i++ )
  {
    d = d + pow ( rints[i], 2 );
  }
  d = sqrt ( d ) / ( double ) ( npols );

  cout << "\n";
  cout << "  RMS error = " << d << "\n";

  delete [] rints;
  delete [] w;
  delete [] x;

  return;
}