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

# include "asa239.h"

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

double alnorm ( double x, int upper )

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

    alnorm() computes the cumulative density of the standard normal distribution.

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 November 2010

  Author:

    Original FORTRAN77 version by David Hill.
    C version by John Burkardt.

  Reference:

    David Hill,
    Algorithm AS 66:
    The Normal Integral,
    Applied Statistics,
    Volume 22, Number 3, 1973, pages 424-427.

  Parameters:

    Input, double X, is one endpoint of the semi-infinite interval
    over which the integration takes place.

    Input, int UPPER, determines whether the upper or lower
    interval is to be integrated:
    1  => integrate from X to + Infinity;
    0 => integrate from - Infinity to X.

    Output, double ALNORM, the integral of the standard normal
    distribution over the desired interval.
*/
{
  double a1 = 5.75885480458;
  double a2 = 2.62433121679;
  double a3 = 5.92885724438;
  double b1 = -29.8213557807;
  double b2 = 48.6959930692;
  double c1 = -0.000000038052;
  double c2 = 0.000398064794;
  double c3 = -0.151679116635;
  double c4 = 4.8385912808;
  double c5 = 0.742380924027;
  double c6 = 3.99019417011;
  double con = 1.28;
  double d1 = 1.00000615302;
  double d2 = 1.98615381364;
  double d3 = 5.29330324926;
  double d4 = -15.1508972451;
  double d5 = 30.789933034;
  double ltone = 7.0;
  double p = 0.398942280444;
  double q = 0.39990348504;
  double r = 0.398942280385;
  int up;
  double utzero = 18.66;
  double value;
  double y;
  double z;

  up = upper;
  z = x;

  if ( z < 0.0 )
  {
    up = !up;
    z = - z;
  }

  if ( ltone < z && ( ( !up ) || utzero < z ) )
  {
    if ( up )
    {
      value = 0.0;
    }
    else
    {
      value = 1.0;
    }
    return value;
  }

  y = 0.5 * z * z;

  if ( z <= con )
  {
    value = 0.5 - z * ( p - q * y
      / ( y + a1 + b1
      / ( y + a2 + b2
      / ( y + a3 ))));
  }
  else
  {
    value = r * exp ( - y )
      / ( z + c1 + d1
      / ( z + c2 + d2
      / ( z + c3 + d3
      / ( z + c4 + d4
      / ( z + c5 + d5
      / ( z + c6 ))))));
  }

  if ( !up )
  {
    value = 1.0 - value;
  }

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

void gamma_inc_values ( int *n_data, double *a, double *x, double *fx )

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

    gamma_inc_values() returns some values of the incomplete Gamma function.

  Discussion:

    The (normalized) incomplete Gamma function P(A,X) is defined as:

      PN(A,X) = 1/Gamma(A) * Integral ( 0 <= T <= X ) T**(A-1) * exp(-T) dT.

    With this definition, for all A and X,

      0 <= PN(A,X) <= 1

    and

      PN(A,INFINITY) = 1.0

    In Mathematica, the function can be evaluated by:

      1 - GammaRegularized[A,X]

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    20 November 2004

  Author:

    John Burkardt

  Reference:

    Milton Abramowitz, Irene Stegun,
    Handbook of Mathematical Functions,
    National Bureau of Standards, 1964,
    ISBN: 0-486-61272-4,
    LC: QA47.A34.

    Stephen Wolfram,
    The Mathematica Book,
    Fourth Edition,
    Cambridge University Press, 1999,
    ISBN: 0-521-64314-7,
    LC: QA76.95.W65.

  Parameters:

    Input/output, int *N_DATA.  The user sets N_DATA to 0 before the
    first call.  On each call, the routine increments N_DATA by 1, and
    returns the corresponding data; when there is no more data, the
    output value of N_DATA will be 0 again.

    Output, double *A, the parameter of the function.

    Output, double *X, the argument of the function.

    Output, double *FX, the value of the function.
*/
{
# define N_MAX 20

  double a_vec[N_MAX] = {
     0.10E+00,
     0.10E+00,
     0.10E+00,
     0.50E+00,
     0.50E+00,
     0.50E+00,
     0.10E+01,
     0.10E+01,
     0.10E+01,
     0.11E+01,
     0.11E+01,
     0.11E+01,
     0.20E+01,
     0.20E+01,
     0.20E+01,
     0.60E+01,
     0.60E+01,
     0.11E+02,
     0.26E+02,
     0.41E+02  };

  double fx_vec[N_MAX] = {
     0.7382350532339351E+00,
     0.9083579897300343E+00,
     0.9886559833621947E+00,
     0.3014646416966613E+00,
     0.7793286380801532E+00,
     0.9918490284064973E+00,
     0.9516258196404043E-01,
     0.6321205588285577E+00,
     0.9932620530009145E+00,
     0.7205974576054322E-01,
     0.5891809618706485E+00,
     0.9915368159845525E+00,
     0.1018582711118352E-01,
     0.4421745996289254E+00,
     0.9927049442755639E+00,
     0.4202103819530612E-01,
     0.9796589705830716E+00,
     0.9226039842296429E+00,
     0.4470785799755852E+00,
     0.7444549220718699E+00 };

  double x_vec[N_MAX] = {
     0.30E-01,
     0.30E+00,
     0.15E+01,
     0.75E-01,
     0.75E+00,
     0.35E+01,
     0.10E+00,
     0.10E+01,
     0.50E+01,
     0.10E+00,
     0.10E+01,
     0.50E+01,
     0.15E+00,
     0.15E+01,
     0.70E+01,
     0.25E+01,
     0.12E+02,
     0.16E+02,
     0.25E+02,
     0.45E+02 };

  if ( *n_data < 0 )
  {
    *n_data = 0;
  }

  *n_data = *n_data + 1;

  if ( N_MAX < *n_data )
  {
    *n_data = 0;
    *a = 0.0;
    *x = 0.0;
    *fx = 0.0;
  }
  else
  {
    *a = a_vec[*n_data-1];
    *x = x_vec[*n_data-1];
    *fx = fx_vec[*n_data-1];
  }

  return;
# undef N_MAX
}
/******************************************************************************/

double gammad ( double x, double p, int *ifault )

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

    gammad() computes the Incomplete Gamma Integral

  Licensing:

    This code is distributed under the MIT license. 

  Modified:

    13 November 2010

  Author:

    Original FORTRAN77 version by B Shea.
    C version by John Burkardt.

  Reference:

    B Shea,
    Algorithm AS 239:
    Chi-squared and Incomplete Gamma Integral,
    Applied Statistics,
    Volume 37, Number 3, 1988, pages 466-473.

  Parameters:

    Input, double X, P, the parameters of the incomplete
    gamma ratio.  0 <= X, and 0 < P.

    Output, int IFAULT, error flag.
    0, no error.
    1, X < 0 or P <= 0.

    Output, double GAMMAD, the value of the incomplete
    Gamma integral.
*/
{
  double a;
  double an;
  double arg;
  double b;
  double c;
  double elimit = - 88.0;
  double oflo = 1.0E+37;
  double plimit = 1000.0;
  double pn1;
  double pn2;
  double pn3;
  double pn4;
  double pn5;
  double pn6;
  double rn;
  double tol = 1.0E-14;
  int upper;
  double value;
  double xbig = 1.0E+08;

  value = 0.0;
/*
  Check the input.
*/
  if ( x < 0.0 )
  {
    *ifault = 1;
    return value;
  }

  if ( p <= 0.0 )
  {
    *ifault = 1;
    return value;
  }

  *ifault = 0;

  if ( x == 0.0 )
  {
    value = 0.0;
    return value;
  }
/*
  If P is large, use a normal approximation.
*/
  if ( plimit < p )
  {
    pn1 = 3.0 * sqrt ( p ) * ( pow ( x / p, 1.0 / 3.0 )
    + 1.0 / ( 9.0 * p ) - 1.0 );

    upper = 0;
    value = alnorm ( pn1, upper );
    return value;
  }
/*
  If X is large set value = 1.
*/
  if ( xbig < x )
  {
    value = 1.0;
    return value;
  }
/*
  Use Pearson's series expansion.
*/
  if ( x <= 1.0 || x < p )
  {
    arg = p * log ( x ) - x - lgamma ( p + 1.0 );
    c = 1.0;
    value = 1.0;
    a = p;

    for ( ; ; )
    {
      a = a + 1.0;
      c = c * x / a;
      value = value + c;

      if ( c <= tol )
      {
        break;
      }
    }

    arg = arg + log ( value );

    if ( elimit <= arg )
    {
      value = exp ( arg );
    }
    else
    {
      value = 0.0;
    }
  }
/*
  Use a continued fraction expansion.
*/
  else
  {
    arg = p * log ( x ) - x - lgamma ( p );
    a = 1.0 - p;
    b = a + x + 1.0;
    c = 0.0;
    pn1 = 1.0;
    pn2 = x;
    pn3 = x + 1.0;
    pn4 = x * b;
    value = pn3 / pn4;

    for ( ; ; )
    {
      a = a + 1.0;
      b = b + 2.0;
      c = c + 1.0;
      an = a * c;
      pn5 = b * pn3 - an * pn1;
      pn6 = b * pn4 - an * pn2;

      if ( pn6 != 0.0 )
      {
        rn = pn5 / pn6;

        if ( fabs ( value - rn ) <= r8_min ( tol, tol * rn ) )
        {
          break;
        }
        value = rn;
      }

      pn1 = pn3;
      pn2 = pn4;
      pn3 = pn5;
      pn4 = pn6;
/*
  Re-scale terms in continued fraction if terms are large.
*/
      if ( oflo <= abs ( pn5 ) )
      {
        pn1 = pn1 / oflo;
        pn2 = pn2 / oflo;
        pn3 = pn3 / oflo;
        pn4 = pn4 / oflo;
      }
    }

    arg = arg + log ( value );

    if ( elimit <= arg )
    {
      value = 1.0 - exp ( arg );
    }
    else
    {
      value = 1.0;
    }
  }

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

double r8_min ( double x, double y )

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

    r8_min() returns the minimum of two R8's.

  Licensing:

    This code is distributed under the MIT license.

  Modified:

    31 August 2004

  Author:

    John Burkardt

  Parameters:

    Input, double X, Y, the quantities to compare.

    Output, double R8_MIN, the minimum of X and Y.
*/
{
  double value;

  if ( y < x )
  {
    value = y;
  }
  else
  {
    value = x;
  }
  return value;
}