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asa103.cpp
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asa103.cpp
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/*
* asa103.cpp
*
* Created on: Feb 19, 2019
* Author: tfmehdi
*/
# include <cmath>
# include <cstdlib>
# include <ctime>
# include <iostream>
# include <iomanip>
using namespace std;
# include "asa103.hpp"
//****************************************************************************80
double digamma ( double x, int *ifault )
//****************************************************************************80
//
// Purpose:
//
// DIGAMMA calculates DIGAMMA ( X ) = d ( LOG ( GAMMA ( X ) ) ) / dX
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 20 March 2016
//
// Author:
//
// Original FORTRAN77 version by Jose Bernardo.
// C++ version by John Burkardt.
//
// Reference:
//
// Jose Bernardo,
// Algorithm AS 103:
// Psi ( Digamma ) Function,
// Applied Statistics,
// Volume 25, Number 3, 1976, pages 315-317.
//
// Parameters:
//
// Input, double X, the argument of the digamma function.
// 0 < X.
//
// Output, int *IFAULT, error flag.
// 0, no error.
// 1, X <= 0.
//
// Output, double DIGAMMA, the value of the digamma function at X.
//
{
static double c = 8.5;
static double euler_mascheroni = 0.57721566490153286060;
double r;
double value;
double x2;
//
// Check the input.
//
if ( x <= 0.0 )
{
value = 0.0;
*ifault = 1;
return value;
}
//
// Initialize.
//
*ifault = 0;
//
// Use approximation for small argument.
//
if ( x <= 0.000001 )
{
value = - euler_mascheroni - 1.0 / x + 1.6449340668482264365 * x;
return value;
}
//
// Reduce to DIGAMA(X + N).
//
value = 0.0;
x2 = x;
while ( x2 < c )
{
value = value - 1.0 / x2;
x2 = x2 + 1.0;
}
//
// Use Stirling's (actually de Moivre's) expansion.
//
r = 1.0 / x2;
value = value + log ( x2 ) - 0.5 * r;
r = r * r;
value = value
- r * ( 1.0 / 12.0
- r * ( 1.0 / 120.0
- r * ( 1.0 / 252.0
- r * ( 1.0 / 240.0
- r * ( 1.0 / 132.0 ) ) ) ) );
return value;
}
//****************************************************************************80
void psi_values ( int *n_data, double *x, double *fx )
//****************************************************************************80
//
// Purpose:
//
// PSI_VALUES returns some values of the Psi or Digamma function.
//
// Discussion:
//
// In Mathematica, the function can be evaluated by:
//
// PolyGamma[x]
//
// or
//
// Polygamma[0,x]
//
// PSI(X) = d ln ( Gamma ( X ) ) / d X = Gamma'(X) / Gamma(X)
//
// PSI(1) = - Euler's constant.
//
// PSI(X+1) = PSI(X) + 1 / X.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 August 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] = {
-0.5772156649015329E+00,
-0.4237549404110768E+00,
-0.2890398965921883E+00,
-0.1691908888667997E+00,
-0.6138454458511615E-01,
0.3648997397857652E-01,
0.1260474527734763E+00,
0.2085478748734940E+00,
0.2849914332938615E+00,
0.3561841611640597E+00,
0.4227843350984671E+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
}
//****************************************************************************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 GNU LGPL license.
//
// 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
}