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

using namespace std;

# include "square_monte_carlo.hpp"

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

double *monomial_value ( int m, int n, int e[], double x[] )

//****************************************************************************80
//
//  Purpose:
//
//    MONOMIAL_VALUE evaluates a monomial.
//
//  Discussion:
//
//    This routine evaluates a monomial of the form
//
//      product ( 1 <= i <= m ) x(i)^e(i)
//
//    where the exponents are nonnegative integers.  Note that
//    if the combination 0^0 is encountered, it should be treated
//    as 1.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    05 May 2007
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the spatial dimension.
//
//    Input, int POINT_NUM, the number of points at which the
//    monomial is to be evaluated.
//
//    Input, int E[M], the exponents.
//
//    Input, double X[M*N], the point coordinates.
//
//    Output, double MONOMIAL_VALUE[N], the value of the monomial.
//
{
  int i;
  int j;
  double *v;

  v = new double[n];

  for ( j = 0; j < n; j++ )
  {
    v[j] = 1.0;
  }

  for ( i = 0; i < m; i++ )
  {
    if ( 0 != e[i] )
    {
      for ( j = 0; j < n; j++ )
      {
        v[j] = v[j] * pow ( x[i+j*m], e[i] );
      }
    }
  }

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

double *r8mat_uniform_01_new ( int m, int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8MAT_UNIFORM_01_NEW returns a unit pseudorandom R8MAT.
//
//  Discussion:
//
//    An R8MAT is a doubly dimensioned array of R8's,  stored as a vector
//    in column-major order.
//
//    This routine implements the recursion
//
//      seed = 16807 * seed mod ( 2^31 - 1 )
//      unif = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license.
//
//  Modified:
//
//    03 October 2005
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Springer Verlag, pages 201-202, 1983.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, pages 362-376, 1986.
//
//    Philip Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, pages 136-143, 1969.
//
//  Parameters:
//
//    Input, int M, N, the number of rows and columns.
//
//    Input/output, int &SEED, the "seed" value.  Normally, this
//    value should not be 0, otherwise the output value of SEED
//    will still be 0, and R8_UNIFORM will be 0.  On output, SEED has
//    been updated.
//
//    Output, double R8MAT_UNIFORM_01_NEW[M*N], a matrix of pseudorandom values.
//
{
  int i;
  int j;
  int k;
  double *r;

  r = new double[m*n];

  for ( j = 0; j < n; j++ )
  {
    for ( i = 0; i < m; i++ )
    {
      k = seed / 127773;

      seed = 16807 * ( seed - k * 127773 ) - k * 2836;

      if ( seed < 0 )
      {
        seed = seed + 2147483647;
      }
      r[i+j*m] = ( double ) ( seed ) * 4.656612875E-10;
    }
  }

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

double r8vec_sum ( int n, double a[] )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_SUM returns the sum of an R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    15 October 2004
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of entries in the vector.
//
//    Input, double A[N], the vector.
//
//    Output, double R8VEC_SUM, the sum of the vector.
//
{
  int i;
  double value;

  value = 0.0;
  for ( i = 0; i < n; i++ )
  {
    value = value + a[i];
  }
  return value;
}
//****************************************************************************80

double square01_area ( )

//****************************************************************************80
//
//  Purpose:
//
//    SQUARE01_AREA: area of the unit square in 2D.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 January 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double SQUARE01_AREA, the area
//
{
  double area;

  area = 1.0;

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

double square01_monomial_integral ( int e[] )

//****************************************************************************80
//
//  Purpose:
//
//    SQUARE01_MONOMIAL_INTEGRAL: monomial integrals on the unit square in 2D.
//
//  Discussion:
//
//    The integration region is 
//
//      0 <= X <= 1,
//      0 <= Y <= 1.
//
//    The monomial is F(X,Y) = X^E(1) * Y^E(2).
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 January 2014
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Philip Davis, Philip Rabinowitz,
//    Methods of Numerical Integration,
//    Second Edition,
//    Academic Press, 1984, page 263.
//
//  Parameters:
//
//    Input, int E[2], the exponents.  
//    Each exponent must be nonnegative.
//
//    Output, double SQUARE01_MONOMIAL_INTEGRAL, the integral.
//
{
  double arg;
  int i;
  double integral;
  const int m = 2;

  for ( i = 0; i < m; i++ )
  {
    if ( e[i] < 0 )
    {
      cout << "\n";
      cout << "SQUARE01_MONOMIAL_INTEGRAL - Fatal error!\n";
      cout << "  All exponents must be nonnegative.\n";
      cout << "  E[" << i << "] = " << e[i] << "\n";
      exit ( 1 );
    }
  }

  integral = 1.0;
  for ( i = 0; i < m; i++ )
  {
    integral = integral / ( double ) ( e[i] + 1 );
  }

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

double *square01_sample ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    SQUARE01_SAMPLE samples the unit square in 2D.
//
//  Licensing:
//
//    This code is distributed under the GNU LGPL license. 
//
//  Modified:
//
//    19 January 2014
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Russell Cheng,
//    Random Variate Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998, pages 168.
//
//    Reuven Rubinstein,
//    Monte Carlo Optimization, Simulation, and Sensitivity 
//    of Queueing Networks,
//    Krieger, 1992,
//    ISBN: 0894647644,
//    LC: QA298.R79.
//
//  Parameters:
//
//    Input, int N, the number of points.
//
//    Input/output, int &SEED, a seed for the random 
//    number generator.
//
//    Output, double X[2*N], the points.
//
{
  const int m = 2;
  double *x;

  x = r8mat_uniform_01_new ( m, n, seed );

  return x;
}
//****************************************************************************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 GNU LGPL 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;
  size_t len;
  std::time_t now;

  now = std::time ( NULL );
  tm_ptr = std::localtime ( &now );

  len = std::strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm_ptr );

  std::cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}