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nf_incompleteGammaFunctions.cc File Reference
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Functions

double nf_incompleteGammaFunctionComplementary (double a, double x, nfu_status *status)
 
double nf_incompleteGammaFunction (double a, double x, nfu_status *status)
 

Variables

static double big = 4.503599627370496e15
 
static double biginv = 2.22044604925031308085e-16
 

Function Documentation

double nf_incompleteGammaFunction ( double  a,
double  x,
nfu_status status 
)

Definition at line 155 of file nf_incompleteGammaFunctions.cc.

155  {
156 /* left tail of incomplete gamma function:
157 *
158 * inf. k
159 * a -x - x
160 * x e > ----------
161 * - -
162 * k=0 | (a+k+1)
163 */
164  double ans, ax, c, r;
165 
166  *status = nfu_badInput;
167  if( !isfinite( x ) ) return( x );
168  *status = nfu_Okay;
169 
170  if( ( x <= 0 ) || ( a <= 0 ) ) return( 0.0 );
171  if( ( x > 1.0 ) && ( x > a ) ) return( nf_gammaFunction( a, status ) - nf_incompleteGammaFunctionComplementary( a, x, status ) );
172 
173  ax = G4Exp( a * G4Log( x ) - x ); /* Compute x**a * exp(-x) */
174  if( ax == 0. ) return( 0.0 );
175 
176  r = a; /* power series */
177  c = 1.0;
178  ans = 1.0;
179  do {
180  r += 1.0;
181  c *= x / r;
182  ans += c;
183  } while( c > ans * DBL_EPSILON ); // Loop checking, 11.06.2015, T. Koi
184 
185  return( ans * ax / a );
186 }
#define DBL_EPSILON
Definition: templates.hh:87
#define isfinite
G4double G4Log(G4double x)
Definition: G4Log.hh:230
G4double G4Exp(G4double initial_x)
Exponential Function double precision.
Definition: G4Exp.hh:183
double nf_incompleteGammaFunctionComplementary(double a, double x, nfu_status *status)
double nf_gammaFunction(double x, nfu_status *status)

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double nf_incompleteGammaFunctionComplementary ( double  a,
double  x,
nfu_status status 
)

Definition at line 88 of file nf_incompleteGammaFunctions.cc.

88  {
89 
90  double ans, ax, c, yc, r, t, y, z;
91  double pk, pkm1, pkm2, qk, qkm1, qkm2;
92 
93  *status = nfu_badInput;
94  if( !isfinite( x ) ) return( x );
95  *status = nfu_Okay;
96 
97  if( ( x <= 0 ) || ( a <= 0 ) ) return( 1.0 );
98  if( ( x < 1.0 ) || ( x < a ) ) return( nf_gammaFunction( a, status ) - nf_incompleteGammaFunction( a, x, status ) );
99 
100  ax = G4Exp( a * G4Log( x ) - x );
101  if( ax == 0. ) return( 0.0 );
102 
103  if( x < 10000. ) {
104  y = 1.0 - a; /* continued fraction */
105  z = x + y + 1.0;
106  c = 0.0;
107  pkm2 = 1.0;
108  qkm2 = x;
109  pkm1 = x + 1.0;
110  qkm1 = z * x;
111  ans = pkm1 / qkm1;
112 
113  do {
114  c += 1.0;
115  y += 1.0;
116  z += 2.0;
117  yc = y * c;
118  pk = pkm1 * z - pkm2 * yc;
119  qk = qkm1 * z - qkm2 * yc;
120  if( qk != 0 ) {
121  r = pk / qk;
122  t = fabs( ( ans - r ) / r );
123  ans = r; }
124  else {
125  t = 1.0;
126  }
127  pkm2 = pkm1;
128  pkm1 = pk;
129  qkm2 = qkm1;
130  qkm1 = qk;
131  if( fabs( pk ) > big ) {
132  pkm2 *= biginv;
133  pkm1 *= biginv;
134  qkm2 *= biginv;
135  qkm1 *= biginv;
136  }
137  } while( t > DBL_EPSILON ); } // Loop checking, 11.06.2015, T. Koi
138  else { /* Asymptotic expansion. */
139  y = 1. / x;
140  r = a;
141  c = 1.;
142  ans = 1.;
143  do {
144  a -= 1.;
145  c *= a * y;
146  ans += c;
147  } while( fabs( c ) > 100 * ans * DBL_EPSILON ); // Loop checking, 11.06.2015, T. Koi
148  }
149 
150  return( ans * ax );
151 }
static double biginv
#define DBL_EPSILON
Definition: templates.hh:87
#define isfinite
G4double G4Log(G4double x)
Definition: G4Log.hh:230
G4double G4Exp(G4double initial_x)
Exponential Function double precision.
Definition: G4Exp.hh:183
double nf_incompleteGammaFunction(double a, double x, nfu_status *status)
static double big
double nf_gammaFunction(double x, nfu_status *status)

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Variable Documentation

double big = 4.503599627370496e15
static

Definition at line 82 of file nf_incompleteGammaFunctions.cc.

double biginv = 2.22044604925031308085e-16
static

Definition at line 83 of file nf_incompleteGammaFunctions.cc.