# include <stdlib.h>
# include <stdio.h>
# include <math.h>
# include <time.h>
# include <string.h>

# include "pyramid_monte_carlo.h"

/******************************************************************************/

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

/******************************************************************************/
/*
  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 = ( double * ) malloc ( n * sizeof ( double ) );

  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;
}
/******************************************************************************/

double pyramid01_integral ( int expon[3] )

/******************************************************************************/
/*
  Purpose:

    PYRAMID01_INTEGRAL: monomial integral in a unit pyramid.

  Discussion:

    This function returns the value of the integral of X^ALPHA Y^BETA Z^GAMMA
    over the unit pyramid.

    The integration region is:

    - ( 1 - Z ) <= X <= 1 - Z
    - ( 1 - Z ) <= Y <= 1 - Z
              0 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    24 March 2008

  Author:

    John Burkardt

  Reference:

    Arthur Stroud,
    Approximate Calculation of Multiple Integrals,
    Prentice Hall, 1971,
    ISBN: 0130438936,
    LC: QA311.S85.

  Parameters:

    Input, int EXPON[3], the exponents.

    Output, double PYRAMID01_INTEGRAL, the integral of the monomial
    over the pyramid.
*/
{
  int i;
  int i_hi;
  double value;

  value = 0.0;

  if ( ( expon[0] % 2 ) == 0 && ( expon[1] % 2 ) == 0 )
  {
    i_hi = 2 + expon[0] + expon[1];

    for ( i = 0; i <= i_hi; i++ )
    {
      value = value + r8_mop ( i ) * r8_choose ( i_hi, i ) 
      / ( double ) ( i + expon[2] + 1 );
    }

    value = value 
          * 2.0 / ( double ) ( expon[0] + 1 )
          * 2.0 / ( double ) ( expon[1] + 1 );
  }

  return value;
}
/******************************************************************************/

double *pyramid01_sample ( int n, int *seed )

/******************************************************************************/
/*
  Purpose:

    PYRAMID01_SAMPLE: sample the unit pyramid.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    14 April 2014

  Author:

    John Burkardt

  Parameters:

    Input, int N, the number of samples desired.

    Input/output, int *SEED, a seed for the random
    number generator.

    Output, double PYRAMID01_SAMPLE[3*N], the sample values.
*/
{
  int j;
  static int m = 3;
  static double one_third = 1.0 / 3.0;
  double *x;

  x = r8mat_uniform_01_new ( m, n, seed );

  for ( j = 0; j < n; j++ )
  {
    x[2+j*3] = 1.0 - pow ( x[2+j*3], one_third );
    x[1+j*3] = ( 1.0 - x[2+j*3] ) * ( 2.0 * x[1+j*3] - 1.0 );
    x[0+j*3] = ( 1.0 - x[2+j*3] ) * ( 2.0 * x[0+j*3] - 1.0 );
  }

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

double pyramid01_volume ( )

/******************************************************************************/
/*
  Purpose:

    PYRAMID01_VOLUME: volume of a unit pyramid with square base.

  Discussion:

    The volume of this unit pyramid is 4/3.

    The integration region is:

      - ( 1 - Z ) <= X <= 1 - Z
      - ( 1 - Z ) <= Y <= 1 - Z
                0 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    14 April 2014

  Author:

    John Burkardt

  Parameters:

    Output, double PYRAMID01_VOLUME, the volume of the pyramid.
*/
{
  double volume;

  volume = 4.0 / 3.0;

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

double r8_choose ( int n, int k )

/******************************************************************************/
/*
  Purpose:

    R8_CHOOSE computes the binomial coefficient C(N,K) as an R8.

  Discussion:

    The value is calculated in such a way as to avoid overflow and
    roundoff.  The calculation is done in R8 arithmetic.

    The formula used is:

      C(N,K) = N! / ( K! * (N-K)! )

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 July 2008

  Author:

    John Burkardt

  Reference:

    ML Wolfson, HV Wright,
    Algorithm 160:
    Combinatorial of M Things Taken N at a Time,
    Communications of the ACM,
    Volume 6, Number 4, April 1963, page 161.

  Parameters:

    Input, int N, K, the values of N and K.

    Output, double R8_CHOOSE, the number of combinations of N
    things taken K at a time.
*/
{
  int i;
  int mn;
  int mx;
  double value;

  if ( k < n - k )
  {
    mn = k;
    mx = n - k;
  }
  else
  {
    mn = n - k;
    mx = k;
  }

  if ( mn < 0 )
  {
    value = 0.0;
  }
  else if ( mn == 0 )
  {
    value = 1.0;
  }
  else
  {
    value = ( double ) ( mx + 1 );

    for ( i = 2; i <= mn; i++ )
    {
      value = ( value * ( double ) ( mx + i ) ) / ( double ) i;
    }
  }

  return value;
}
/******************************************************************************/

double r8_mop ( int i )

/******************************************************************************/
/*
  Purpose:

    R8_MOP returns the I-th power of -1 as an R8 value.

  Discussion:

    An R8 is an double value.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    01 July 2008

  Author:

    John Burkardt

  Parameters:

    Input, int I, the power of -1.

    Output, double R8_MOP, the I-th power of -1.
*/
{
  double value;

  if ( ( i % 2 ) == 0 )
  {
    value = + 1.0;
  }
  else
  {
    value = - 1.0;
  }

  return value;
}
/******************************************************************************/

void r8mat_transpose_print ( int m, int n, double a[], char *title )

/******************************************************************************/
/*
  Purpose:

    R8MAT_TRANSPOSE_PRINT prints an R8MAT, transposed.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    28 May 2008

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A[M*N], an M by N matrix to be printed.

    Input, char *TITLE, a title.
*/
{
  r8mat_transpose_print_some ( m, n, a, 1, 1, m, n, title );

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

void r8mat_transpose_print_some ( int m, int n, double a[], int ilo, int jlo,
  int ihi, int jhi, char *title )

/******************************************************************************/
/*
  Purpose:

    R8MAT_TRANSPOSE_PRINT_SOME prints some of an R8MAT, transposed.

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, stored as a vector
    in column-major order.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    10 September 2013

  Author:

    John Burkardt

  Parameters:

    Input, int M, N, the number of rows and columns.

    Input, double A[M*N], an M by N matrix to be printed.

    Input, int ILO, JLO, the first row and column to print.

    Input, int IHI, JHI, the last row and column to print.

    Input, char *TITLE, a title.
*/
{
# define INCX 5

  int i;
  int i2;
  int i2hi;
  int i2lo;
  int i2lo_hi;
  int i2lo_lo;
  int inc;
  int j;
  int j2hi;
  int j2lo;

  fprintf ( stdout, "\n" );
  fprintf ( stdout, "%s\n", title );

  if ( m <= 0 || n <= 0 )
  {
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  (None)\n" );
    return;
  }

  if ( ilo < 1 )
  {
    i2lo_lo = 1;
  }
  else
  {
    i2lo_lo = ilo;
  }

  if ( ihi < m )
  {
    i2lo_hi = m;
  }
  else
  {
    i2lo_hi = ihi;
  }

  for ( i2lo = i2lo_lo; i2lo <= i2lo_hi; i2lo = i2lo + INCX )
  {
    i2hi = i2lo + INCX - 1;

    if ( m < i2hi )
    {
      i2hi = m;
    }
    if ( ihi < i2hi )
    {
      i2hi = ihi;
    }

    inc = i2hi + 1 - i2lo;

    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Row:" );
    for ( i = i2lo; i <= i2hi; i++ )
    {
      fprintf ( stdout, "  %7d     ", i - 1 );
    }
    fprintf ( stdout, "\n" );
    fprintf ( stdout, "  Col\n" );
    fprintf ( stdout, "\n" );

    if ( jlo < 1 )
    {
      j2lo = 1;
    }
    else
    {
      j2lo = jlo;
    }
    if ( n < jhi )
    {
      j2hi = n;
    }
    else
    {
      j2hi = jhi;
    }
    for ( j = j2lo; j <= j2hi; j++ )
    {
      fprintf ( stdout, "%5d:", j - 1 );
      for ( i2 = 1; i2 <= inc; i2++ )
      {
        i = i2lo - 1 + i2;
        fprintf ( stdout, "  %14g", a[(i-1)+(j-1)*m] );
      }
      fprintf ( stdout, "\n" );
    }
  }

  return;
# undef INCX
}
/******************************************************************************/

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

/******************************************************************************/
/*
  Purpose:

    R8MAT_UNIFORM_01_NEW fills an R8MAT with pseudorandom values scaled to [0,1].

  Discussion:

    An R8MAT is a doubly dimensioned array of R8 values, 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:

    30 June 2009

  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 = ( double * ) malloc ( m * n * sizeof ( double ) );

  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;
}
/******************************************************************************/

double r8vec_sum ( int n, double a[] )

/******************************************************************************/
/*
  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:

    26 August 2008

  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;
}
/******************************************************************************/

void timestamp ( )

/******************************************************************************/
/*
  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:

    24 September 2003

  Author:

    John Burkardt

  Parameters:

    None
*/
{
# define TIME_SIZE 40

  static char time_buffer[TIME_SIZE];
  const struct tm *tm;
  time_t now;

  now = time ( NULL );
  tm = localtime ( &now );

  strftime ( time_buffer, TIME_SIZE, "%d %B %Y %I:%M:%S %p", tm );

  fprintf ( stdout, "%s\n", time_buffer );

  return;
# undef TIME_SIZE
}