# include <cstdlib>
# include <iostream>
# include <cmath>
# include <ctime>

using namespace std;

# include "line_nco_rule.hpp"

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

void line_nco_rule ( int n, double a, double b, double x[], double w[] )

//****************************************************************************80
//
//  Purpose:
//
//    LINE_NCO_RULE computes a Newton-Cotes Open (NCO) quadrature rule.
//
//  Discussion:
//
//    The integral:
//
//      Integral ( A <= X <= B ) F(X) dx
//
//    The quadrature rule:
//
//      Sum ( 1 <= I <= N ) W(I) * F ( X(I) ).
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    28 July 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the order.
//
//    Input, double A, B, the endpoints of the interval.
//
//    Input, double X[N], the abscissas.
//
//    Output, double W[N], the weights.
//
{
  double *d;
  int i;
  int j;
  int k;
  double y_a;
  double y_b;
//
//  Define the points X.
//
  r8vec_linspace2 ( n, a, b, x );

  d = new double[n];

  for ( i = 0; i < n; i++ )
  {
//
//  Compute the Lagrange basis polynomial which is 1 at XTAB(I),
//  and zero at the other nodes.
//
    for ( j = 0; j < n; j++ )
    {
      d[j] = 0.0;
    }
    d[i] = 1.0;

    for ( j = 2; j <= n; j++ )
    {
      for ( k = j; k <= n; k++ )
      {
        d[n+j-k-1] = ( d[n+j-k-2] - d[n+j-k-1] ) / ( x[n-k] - x[n+j-k-1] );
      }
    }
    for ( j = 1; j <= n - 1; j++ )
    {
      for ( k = 1; k <= n - j; k++ )
      {
        d[n-k-1] = d[n-k-1] - x[n-k-j] * d[n-k];
      }
    }
//
//  Evaluate the antiderivative of the polynomial at the endpoints.
//
    y_a = d[n-1] / ( double ) ( n );
    for ( j = n - 2; 0 <= j; j-- )
    {
      y_a = y_a * a + d[j] / ( double ) ( j + 1 );
    }
    y_a = y_a * a;

    y_b = d[n-1] / ( double ) ( n );
    for ( j = n - 2; 0 <= j; j-- )
    {
      y_b = y_b * b + d[j] / ( double ) ( j + 1 );
    }
    y_b = y_b * b;

    w[i] = y_b - y_a;
  }

  delete [] d;

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

void r8vec_linspace2 ( int n, double a_first, double a_last, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_LINSPACE creates a vector of linearly spaced values.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    4 points evenly spaced between 0 and 12 will yield 2, 4, 6, 8, 10.
//
//    In other words, the interval is divided into N+1 even subintervals,
//    and the endpoints of internal intervals are used as the points.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    18 September 2012
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double A_FIRST, A_LAST, the first and last entries.
//
//    Output, double A[N], a vector of linearly spaced data.
//
{
  int i;

  if ( n == 1 )
  {
    a[0] = ( a_first + a_last ) / 2.0;
  }
  else
  {
    for ( i = 0; i < n; i++ )
    {
      a[i] = ( ( double ) ( n - i     ) * a_first 
             + ( double ) (     i + 1 ) * a_last ) 
             / ( double ) ( n     + 1 );
    }
  }
  return;
}
//****************************************************************************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:
//
//    08 July 2009
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# 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
}