Gabriele Cosmo
85 lines
2.8 KiB
C++
85 lines
2.8 KiB
C++
/*********************************************************************
|
|
Returns the exponential integral function
|
|
|
|
E_n(x) = int_1^infinity e^( -x * t ) / t^n dt, for x > 0.
|
|
|
|
C.A. Bertulani May/15/2000
|
|
*********************************************************************/
|
|
|
|
#include "nf_specialFunctions.h"
|
|
|
|
#if defined __cplusplus
|
|
#include <cmath>
|
|
#include "G4Exp.hh"
|
|
#include "G4Log.hh"
|
|
namespace GIDI {
|
|
using namespace GIDI;
|
|
using namespace std;
|
|
#endif
|
|
|
|
#define EULER 0.57721566490153286 /* Euler's constant gamma */
|
|
#define MAXIT 100 /* Maximum allowed number of iterations. */
|
|
#define FPMIN 1.0e-300 /* close to the smallest representable floting-point number. */
|
|
#define EPS 1.0e-15 /* Desired relative error, not smaller than the machine precision. */
|
|
|
|
/*
|
|
************************************************************
|
|
*/
|
|
double nf_exponentialIntegral( int n, double x, nfu_status *status ) {
|
|
|
|
int i, ii, nm1;
|
|
double a, b, c, d, del, fact, h, psi;
|
|
double ans = 0.0;
|
|
|
|
*status = nfu_badInput;
|
|
if( !isfinite( x ) ) return( x );
|
|
*status = nfu_Okay;
|
|
|
|
nm1 = n - 1;
|
|
if( ( n < 0 ) || ( x < 0.0 ) || ( ( x == 0.0 ) && ( ( n == 0 ) || ( n == 1 ) ) ) ) {
|
|
*status = nfu_badInput; }
|
|
else {
|
|
if( n == 0 ) {
|
|
ans = G4Exp( -x ) / x; } /* Special case */
|
|
else if( x == 0.0 ) {
|
|
ans = 1.0 / nm1; } /* Another special case */
|
|
else if( x > 1.0 ) { /* Lentz's algorithm */
|
|
b = x + n;
|
|
c = 1.0 / FPMIN;
|
|
d = 1.0 / b;
|
|
h = d;
|
|
for( i = 1; i <= MAXIT; i++ ) {
|
|
a = -i * ( nm1 + i );
|
|
b += 2.0;
|
|
d = 1.0 / ( a * d + b ); /* Denominators cannot be zero */
|
|
c = b + a / c;
|
|
del = c * d;
|
|
h *= del;
|
|
if( fabs( del - 1.0 ) < EPS ) return( h * G4Exp( -x ) );
|
|
}
|
|
*status = nfu_failedToConverge; }
|
|
else {
|
|
ans = ( nm1 != 0 ) ? 1.0 / nm1 : -G4Log(x) - EULER; /* Set first term */
|
|
fact = 1.0;
|
|
for( i = 1; i <= MAXIT; i++ ) {
|
|
fact *= -x / i;
|
|
if( i != nm1 ) {
|
|
del = -fact / ( i - nm1 ); }
|
|
else {
|
|
psi = -EULER; /* Compute psi(n) */
|
|
for( ii = 1; ii <= nm1; ii++ ) psi += 1.0 / ii;
|
|
del = fact * ( -G4Log( x ) + psi );
|
|
}
|
|
ans += del;
|
|
if( fabs( del ) < fabs( ans ) * EPS ) return( ans );
|
|
}
|
|
*status = nfu_failedToConverge;
|
|
}
|
|
}
|
|
return( ans );
|
|
}
|
|
|
|
#if defined __cplusplus
|
|
}
|
|
#endif
|