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

using namespace std;

# include "cube_integrals.hpp"

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

double cube01_monomial_integral ( int e[] )

//****************************************************************************80
//
//  Purpose:
//
//    CUBE01_MONOMIAL_INTEGRAL: monomial integrals on the unit cube in 3D.
//
//  Discussion:
//
//    The integration region is 
//
//      0 <= X <= 1,
//      0 <= Y <= 1,
//      0 <= Z <= 1.
//
//    The monomial is F(X,Y,Z) = X^E(1) * Y^E(2) * Z^E(3).
//
//  Licensing:
//
//    This code is distributed under the MIT 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[3], the exponents.  
//    Each exponent must be nonnegative.
//
//    Output, double CUBE01_MONOMIAL_INTEGRAL, the integral.
//
{
  int i;
  double integral;
  const int m = 3;

  for ( i = 0; i < m; i++ )
  {
    if ( e[i] < 0 )
    {
      cout << "\n";
      cout << "CUBE01_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 *cube01_sample ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    CUBE01_SAMPLE samples the unit cube in 3D.
//
//  Licensing:
//
//    This code is distributed under the MIT 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[3*N], the points.
//
{
  const int m = 3;
  double *x;

  x = r8mat_uniform_01_new ( m, n, seed );

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

double cube01_volume ( )

//****************************************************************************80
//
//  Purpose:
//
//    CUBE01_VOLUME: volume of the unit cube in 3D.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    19 January 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Output, double CUBE01_VOLUME, the volume.
//
{
  double volume;

  volume = 1.0;

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

int *i4vec_uniform_ab_new ( int n, int a, int b, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    I4VEC_UNIFORM_AB_NEW returns a scaled pseudorandom I4VEC.
//
//  Discussion:
//
//    An I4VEC is a vector of I4's.
//
//    The pseudorandom numbers should be uniformly distributed
//    between A and B.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    24 May 2012
//
//  Author:
//
//    John Burkardt
//
//  Reference:
//
//    Paul Bratley, Bennett Fox, Linus Schrage,
//    A Guide to Simulation,
//    Second Edition,
//    Springer, 1987,
//    ISBN: 0387964673,
//    LC: QA76.9.C65.B73.
//
//    Bennett Fox,
//    Algorithm 647:
//    Implementation and Relative Efficiency of Quasirandom
//    Sequence Generators,
//    ACM Transactions on Mathematical Software,
//    Volume 12, Number 4, December 1986, pages 362-376.
//
//    Pierre L'Ecuyer,
//    Random Number Generation,
//    in Handbook of Simulation,
//    edited by Jerry Banks,
//    Wiley, 1998,
//    ISBN: 0471134031,
//    LC: T57.62.H37.
//
//    Peter Lewis, Allen Goodman, James Miller,
//    A Pseudo-Random Number Generator for the System/360,
//    IBM Systems Journal,
//    Volume 8, Number 2, 1969, pages 136-143.
//
//  Parameters:
//
//    Input, int N, the dimension of the vector.
//
//    Input, int A, B, the limits of the interval.
//
//    Input/output, int &SEED, the "seed" value, which should NOT be 0.
//    On output, SEED has been updated.
//
//    Output, int IVEC_UNIFORM_AB_NEW[N], a vector of random values 
//    between A and B.
//
{
  int c;
  int i;
  const int i4_huge = 2147483647;
  int k;
  float r;
  int value;
  int *x;
  
  if ( seed == 0 )
  {
    cerr << "\n";
    cerr << "I4VEC_UNIFORM_AB_NEW - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }
//
//  Guarantee A <= B.
//
  if ( b < a )
  {
    c = a;
    a = b;
    b = c;
  }

  x = new int[n];

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

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

    if ( seed < 0 )
    {
      seed = seed + i4_huge;
    }

    r = ( float ) ( seed ) * 4.656612875E-10;
//
//  Scale R to lie between A-0.5 and B+0.5.
//
    r = ( 1.0 - r ) * ( ( float ) a - 0.5 ) 
      +         r   * ( ( float ) b + 0.5 );
//
//  Use rounding to convert R to an integer between A and B.
//
    value = round ( r );
//
//  Guarantee A <= VALUE <= B.
//
    if ( value < a )
    {
      value = a;
    }
    if ( b < value )
    {
      value = b;
    }

    x[i] = value;
  }

  return x;
}
//****************************************************************************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 MIT license. 
//
//  Modified:
//
//    08 May 2014
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int M, the spatial dimension.
//
//    Input, int N, 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 MIT 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 MIT 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

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
}