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

# include "wedge_integrals.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)

    The combination 0.0^0 is encountered is treated as 1.0.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 August 2014

  Author:

    John Burkardt

  Parameters:

    Input, int M, the spatial dimension.

    Input, int N, the number of evaluation points.

    Input, int E[M], the exponents.

    Input, double X[M*N], the point coordinates.

    Output, double MONOMIAL_VALUE[N], the monomial values.
*/
{
  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;
}
/******************************************************************************/

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

double *r8vec_uniform_01_new ( int n, int *seed )

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

    R8VEC_UNIFORM_01_NEW returns a unit pseudorandom R8VEC.

  Discussion:

    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:

    19 August 2004

  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 number of entries in the vector.

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

    Output, double R8VEC_UNIFORM_01_NEW[N], the vector of pseudorandom values.
*/
{
  int i;
  const int i4_huge = 2147483647;
  int k;
  double *r;

  if ( *seed == 0 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "R8VEC_UNIFORM_01_NEW - Fatal error!\n" );
    fprintf ( stderr, "  Input value of SEED = 0.\n" );
    exit ( 1 );
  }

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

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

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

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

    r[i] = ( double ) ( *seed ) * 4.656612875E-10;
  }

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

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
}
/******************************************************************************/

double wedge01_integral ( int e[] )

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

    WEDGE01_INTEGRAL returns the integral of a monomial in the unit wedge in 3D.

  Discussion:

    This routine returns the integral of

      product ( 1 <= I <= 3 ) X(I)^E(I)

    over the unit wedge.

    The integration region is:

      0 <= X
      0 <= Y
      X + Y <= 1
      -1 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    17 August 2014

  Author:

    John Burkardt

  Reference:

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

  Parameters:

    Input, int E[3], the exponents.

    Output, double WEDGE01_INTEGRAL, the integral of the monomial.
*/
{
  int i;
  int k;
  double value;

  value = 1.0;

  k = e[0];

  for ( i = 1; i <= e[1]; i++ )
  {
    k = k + 1;
    value = value * ( double ) ( i ) / ( double ) ( k );
  }

  k = k + 1;
  value = value / ( double ) ( k );

  k = k + 1;
  value = value / ( double ) ( k );
/*
  Now account for integration in Z.
*/
  if ( e[2] == - 1 )
  {
    fprintf ( stderr, "\n" );
    fprintf ( stderr, "WEDGE01_INTEGRAL - Fatal error!\n" );
    fprintf ( stderr, "  E(3) = -1 is not a legal input.\n" );
    exit ( 1 );
  }
  else if ( ( e[2] % 2 ) == 1 )
  {
    value = 0.0;
  }
  else
  {
    value = value * 2.0 / ( double ) ( e[2] + 1 );
  }

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

double *wedge01_sample ( int n, int *seed )

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

   WEDGE01_SAMPLE samples points uniformly from the unit wedge in 3D.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 August 2014

  Author:

    John Burkardt

  Reference:

    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 WEDGE01_SAMPLE[3*N], the points.
*/
{
  double *e;
  double e_sum;
  int i;
  int j;
  double *x;

  x = ( double * ) malloc ( 3 * n * sizeof ( double ) );

  for ( j = 0; j < n; j++ )
  {
    e = r8vec_uniform_01_new ( 4, seed );

    for ( i = 0; i < 3; i++ )
    {
      e[i] = - log ( e[i] );
    }

    e_sum = 0.0;
    for ( i = 0; i < 3; i++ )
    {
      e_sum = e_sum + e[i];
    }

    x[0+j*3] = e[0] / e_sum;
    x[1+j*3] = e[1] / e_sum;
    x[2+j*3] = 2.0 * e[3] - 1.0;

    free ( e );
  }

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

double wedge01_volume ( )

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

    WEDGE01_VOLUME returns the volume of the unit wedge in 3D.

  Discussion:

    The unit wedge is:

      0 <= X
      0 <= Y
      X + Y <= 1
      -1 <= Z <= 1.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    17 August 2014

  Author:

    John Burkardt

  Parameters:

    Output, double WEDGE01_VOLUME, the volume of the unit wedge.
*/
{
  static double value = 1.0;

  return value;
}