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

using namespace std;

# include "annulus_monte_carlo.hpp"

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

double annulus_area ( double center[2], double r1, double r2 )

//****************************************************************************80
//
//  Purpose:
//
//    ANNULUS_AREA returns the area of an annulus in 2D.
//
//  Discussion:
//
//    A circular annulus with center (XC,YC), inner radius R1 and
//    outer radius R2, is the set of points (X,Y) so that
//
//      R1^2 <= (X-XC)^2 + (Y-YC)^2 <= R2^2
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    06 July 2018
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double CENTER[2], coordinates of the center.
//    This information is not actually needed to compute the area.
//
//    Input, double R1, R2, the inner and outer radius of the disk.
//    0.0 <= R1 <= R2.
//
//    Output, double ANNULUS_AREA, the area of the annulus.
//
{
  double area;
  const double r8_pi = 3.141592653589793;

  if ( r1 < 0.0 )
  {
    cout << "\n";
    cout << "ANNULUS_AREA - Fatal error!\n";
    cout << "  Inner radius R1 < 0.0.\n";
    exit ( 1 );
  }

  if ( r2 < r1 )
  {
    cout << "\n";
    cout << "ANNULUS_AREA - Fatal error!\n";
    cout << "  Outer radius R2 < R1 = inner radius.\n";
    exit ( 1 );
  }

  area = r8_pi * ( r2 + r1 ) * ( r2 - r1 );

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

double *annulus_sample ( double center[2], double r1, double r2, int n, 
  int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    ANNULUS_SAMPLE uniformly samples a general annulus in 2D.
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    06 July 2018
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, double CENTER[2], coordinates of the center.
//
//    Input, double R1, R2, the inner and outer radius.
//
//    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.
//
{
  int i;
  int j;
  double *p;
  double *r;
  const double r8_pi = 3.141592653589793;
  double *theta;

  if ( r1 < 0.0 )
  {
    cout << "\n";
    cout << "ANNULUS_SAMPLE - Fatal error!\n";
    cout << "  Inner radius R1 < 0.0.\n";
    exit ( 1 );
  }

  if ( r2 < r1 )
  {
    cout << "\n";
    cout << "ANNULUS_SAMPLE - Fatal error!\n";
    cout << "  Outer radius R2 < R1 = inner radius.\n";
    exit ( 1 );
  }

  theta = r8vec_uniform_01_new ( n, seed );

  for ( i = 0; i < n; i++ )
  {
    theta[i] = theta[i] * 2.0 * r8_pi;
  }

  r = r8vec_uniform_01_new ( n, seed );

  for ( i = 0; i < n; i++ )
  {
    r[i] = sqrt ( ( 1.0 - r[i] ) * r1 * r1 
         +                r[i]   * r2 * r2 );
  }

  p = new double[2*n];

  for ( j = 0; j < n; j++ )
  {
    p[0+j*2] = center[0] + r[j] * cos ( theta[j] );
    p[1+j*2] = center[1] + r[j] * sin ( theta[j] );
  }

  delete [] r;
  delete [] theta;

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

double disk01_monomial_integral ( int e[2] )

//****************************************************************************80
//
//  Purpose:
//
//    DISK01_MONOMIAL_INTEGRAL returns monomial integrals in the unit disk in 2D.
//
//  Discussion:
//
//    The integration region is 
//
//      X^2 + Y^2 <= 1.
//
//    The monomial is F(X,Y) = X^E(1) * Y^E(2).
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    03 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 of X and Y in the 
//    monomial.  Each exponent must be nonnegative.
//
//    Output, double DISK01_MONOMIAL_INTEGRAL, the integral.
//
{
  double arg;
  int i;
  double integral;
  const double r = 1.0;
  double s;

  if ( e[0] < 0 || e[1] < 0 )
  {
    cerr << "\n";
    cerr << "DISK01_MONOMIAL_INTEGRAL - Fatal error!\n";
    cerr << "  All exponents must be nonnegative.\n";
    cerr << "  E[0] = " << e[0] << "\n";
    cerr << "  E[1] = " << e[1] << "\n";
    exit ( 1 );
  }

  if ( ( e[0] % 2 ) == 1 || ( e[1] % 2 ) == 1 )
  {
    integral = 0.0;
  }
  else
  {
    integral = 2.0;

    for ( i = 0; i < 2; i++ )
    {
      arg = 0.5 * ( double ) ( e[i] + 1 );
      integral = integral * tgamma ( arg );
    }
    arg = 0.5 * ( double ) ( e[0] + e[1] + 2 );
    integral = integral / tgamma ( arg );
  }
//
//  Adjust the surface integral to get the volume integral.
//
  s = e[0] + e[1] + 2;
  integral = integral * pow ( r, s ) / ( double ) ( s );

  return integral;
}
//****************************************************************************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 r8_uniform_01 ( int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8_UNIFORM_01 returns a unit pseudorandom R8.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = seed / ( 2^31 - 1 )
//
//    The integer arithmetic never requires more than 32 bits,
//    including a sign bit.
//
//    If the initial seed is 12345, then the first three computations are
//
//      Input     Output      R8_UNIFORM_01
//      SEED      SEED
//
//         12345   207482415  0.096616
//     207482415  1790989824  0.833995
//    1790989824  2035175616  0.947702
//
//  Licensing:
//
//    This code is distributed under the MIT license. 
//
//  Modified:
//
//    09 April 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/output, int &SEED, the "seed" value.  Normally, this
//    value should not be 0.  On output, SEED has been updated.
//
//    Output, double R8_UNIFORM_01, a new pseudorandom variate, 
//    strictly between 0 and 1.
//
{
  int i4_huge = 2147483647;
  int k;
  double r;

  if ( seed == 0 )
  {
    cerr << "\n";
    cerr << "R8_UNIFORM_01 - Fatal error!\n";
    cerr << "  Input value of SEED = 0.\n";
    exit ( 1 );
  }

  k = seed / 127773;

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

  if ( seed < 0 )
  {
    seed = seed + i4_huge;
  }
  r = ( double ) ( seed ) * 4.656612875E-10;

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

double *r8vec_normal_01_new ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_NORMAL_01_NEW returns a unit pseudonormal R8VEC.
//
//  Discussion:
//
//    An R8VEC is a vector of R8's.
//
//    The standard normal probability distribution function (PDF) has
//    mean 0 and standard deviation 1.
//
//  Licensing:
//
//    This code is distributed under the MIT license.
//
//  Modified:
//
//    06 August 2013
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    Input, int N, the number of values desired.
//
//    Input/output, int &SEED, a seed for the random number generator.
//
//    Output, double R8VEC_NORMAL_01_NEW[N], a sample of the standard normal PDF.
//
//  Local parameters:
//
//    Local, double R[N+1], is used to store some uniform random values.
//    Its dimension is N+1, but really it is only needed to be the
//    smallest even number greater than or equal to N.
//
//    Local, int X_LO, X_HI, records the range of entries of
//    X that we need to compute.
//
{
  int i;
  int m;
  const double pi = 3.141592653589793;
  double *r;
  double *x;
  int x_hi;
  int x_lo;

  x = new double[n];
//
//  Record the range of X we need to fill in.
//
  x_lo = 1;
  x_hi = n;
//
//  If we need just one new value, do that here to avoid null arrays.
//
  if ( x_hi - x_lo + 1 == 1 )
  {
    r = r8vec_uniform_01_new ( 2, seed );

    x[x_hi-1] = sqrt ( -2.0 * log ( r[0] ) ) * cos ( 2.0 * pi * r[1] );

    delete [] r;
  }
//
//  If we require an even number of values, that's easy.
//
  else if ( ( x_hi - x_lo + 1 ) % 2 == 0 )
  {
    m = ( x_hi - x_lo + 1 ) / 2;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2*m-2; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( -2.0 * log ( r[i] ) ) * cos ( 2.0 * pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( -2.0 * log ( r[i] ) ) * sin ( 2.0 * pi * r[i+1] );
    }

    delete [] r;
  }
//
//  If we require an odd number of values, we generate an even number,
//  and handle the last pair specially, storing one in X(N), and
//  saving the other for later.
//
  else
  {
    x_hi = x_hi - 1;

    m = ( x_hi - x_lo + 1 ) / 2 + 1;

    r = r8vec_uniform_01_new ( 2*m, seed );

    for ( i = 0; i <= 2*m-4; i = i + 2 )
    {
      x[x_lo+i-1] = sqrt ( -2.0 * log ( r[i] ) ) * cos ( 2.0 * pi * r[i+1] );
      x[x_lo+i  ] = sqrt ( -2.0 * log ( r[i] ) ) * sin ( 2.0 * pi * r[i+1] );
    }

    i = 2*m - 2;

    x[x_lo+i-1] = sqrt ( -2.0 * log ( r[i] ) ) * cos ( 2.0 * pi * r[i+1] );

    delete [] r;
  }

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

double *r8vec_uniform_01_new ( int n, int &seed )

//****************************************************************************80
//
//  Purpose:
//
//    R8VEC_UNIFORM_01_NEW returns a new unit pseudorandom R8VEC.
//
//  Discussion:
//
//    This routine implements the recursion
//
//      seed = ( 16807 * seed ) mod ( 2^31 - 1 )
//      u = 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;
  int i4_huge = 2147483647;
  int k;
  double *r;

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

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

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