asa121.cpp

//-------------------------------------------------------------------------------------
//
// Modified from:  http://people.sc.fsu.edu/~burkardt/cpp_src/asa121/asa121.C
// Obtained on April 15th, 2010
//
// This file (and the website it comes from) don't contain any information about
// its licensing. It is probably in the public domain.
//
// The author is John Burkardt, closely based on the publication by Schneider.
// He (Burkardt) is working at Virginia Tech. The website has been updated recently,
// but there is no contact information.
//
// Accuracy: According to the paper, should be at least 6 digits.
//
//-------------------------------------------------------------------------------------
# include <cstdlib>
# include <iostream>
# include <iomanip>
# include <ctime>

using namespace std;

# include "asa121.hpp"

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

void timestamp ( void )

//****************************************************************************80
//
//  Purpose:
//
//    TIMESTAMP prints the current YMDHMS date as a time stamp.
//
//  Example:
//
//    31 May 2001 09:45:54 AM
//
//  Modified:
//
//    24 September 2003
//
//  Author:
//
//    John Burkardt
//
//  Parameters:
//
//    None
//
{
# define TIME_SIZE 40

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

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

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

  cout << time_buffer << "\n";

  return;
# undef TIME_SIZE
}
//****************************************************************************80

double trigam ( double x, int *ifault )

//****************************************************************************80
//
//  Purpose:
//
//    TRIGAM calculates trigamma(x) = d**2 log(gamma(x)) / dx**2
//
//  Modified:
//
//    19 January 2008
//
//  Author:
//
//    BE Schneider
//    Modifications by John Burkardt
//
//  Reference:
//
//    BE Schneider,
//    Algorithm AS 121:
//    Trigamma Function,
//    Applied Statistics, 
//    Volume 27, Number 1, pages 97-99, 1978.
//
//  Parameters:
//
//    Input, double X, the argument of the trigamma function.
//    0 < X.
//
//    Output, int *IFAULT, error flag.
//    0, no error.
//    1, X <= 0.
//
//    Output, double TRIGAM, the value of the trigamma function at X.
//
{
  double a = 0.0001;
  double b = 5.0;
  double b2 =  0.1666666667;
  double b4 = -0.03333333333;
  double b6 =  0.02380952381;
  double b8 = -0.03333333333;
  double value;
  double y;
  double z;
//
//  Check the input.
//
  if ( x <= 0.0 )
  {
    *ifault = 1;
    value = 0.0;
    return value;
  }

  *ifault = 0;
  z = x;
//
//  Use small value approximation if X <= A.
//
  if ( x <= a )
  {
    value = 1.0 / x / x;
    return value;
  }
//
//  Increase argument to ( X + I ) >= B.
//
  value = 0.0;

  while ( z < b )
  {
    value = value + 1.0 / z / z;
    z = z + 1.0;
  }
//
//  Apply asymptotic formula if argument is B or greater.
//
  y = 1.0 / z / z;

  value = value + 0.5 * 
      y + ( 1.0 
    + y * ( b2  
    + y * ( b4  
    + y * ( b6  
    + y *   b8 )))) / z;

  return value;
}
//****************************************************************************80

void trigamma_values ( int *n_data, double *x, double *fx )

//****************************************************************************80
//
//  Purpose:
//
//    TRIGAMMA_VALUES returns some values of the TriGamma function.
//
//  Discussion:
//
//    In Mathematica, the function can be evaluated by:
//
//      PolyGamma[1,x]
//
//    TriGamma(X) = d^2 ln ( Gamma ( X ) ) / d X^2
//
//  Modified:
//
//    16 September 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 *X, the argument of the function.
//
//    Output, double *FX, the value of the function.
//
{
# define N_MAX 11

  double fx_vec[N_MAX] = { 
    0.1644934066848226E+01, 
    0.1433299150792759E+01, 
    0.1267377205423779E+01, 
    0.1134253434996619E+01, 
    0.1025356590529597E+01, 
    0.9348022005446793E+00, 
    0.8584318931245799E+00, 
    0.7932328301639984E+00, 
    0.7369741375017002E+00, 
    0.6879720582426356E+00, 
    0.6449340668482264E+00 };

  double x_vec[N_MAX] = { 
     1.0E+00,  
     1.1E+00,  
     1.2E+00,  
     1.3E+00,  
     1.4E+00,  
     1.5E+00,  
     1.6E+00,  
     1.7E+00,  
     1.8E+00,  
     1.9E+00,  
     2.0E+00 };

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

  *n_data = *n_data + 1;

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

  return;
# undef N_MAX
}