ROOT 6.14/05 Reference Guide |
Functions | |
double | beta (double z, double w) |
double | erf (double x) |
double | erfc (double a) |
double | gamma (double x) |
double | igam (double a, double x) |
double | igamc (double a, double x) |
incomplete complementary gamma function igamc(a, x) = 1 - igam(a, x) More... | |
double | igami (double a, double y) |
double | incbcf (double a, double b, double x) |
double | incbd (double a, double b, double x) |
double | incbet (double aa, double bb, double xx) |
DESCRIPTION: More... | |
double | incbi (double a, double b, double y) |
double | lgam (double x) |
double | ndtri (double y) |
double | pseries (double a, double b, double x) |
static double | stirf (double x) |
Variables | |
static double | A [] |
static double | B [] |
static double | C [] |
static double | erfP [] |
static double | erfQ [] |
static double | erfR [] |
static double | erfS [] |
static double | erfT [] |
static double | erfU [] |
static double | kBig = 4.503599627370496e15 |
static double | kBiginv = 2.22044604925031308085e-16 |
static double | LS2PI = 0.91893853320467274178 |
static double | P [] |
static double | P0 [5] |
static double | P1 [9] |
static double | P2 [9] |
static double | Q [] |
static double | Q0 [8] |
static double | Q1 [8] |
static double | Q2 [8] |
static double | s2pi = 2.50662827463100050242E0 |
static double | STIR [5] |
double ROOT::Math::Cephes::beta | ( | double | z, |
double | w | ||
) |
Definition at line 428 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::erf | ( | double | x | ) |
Definition at line 926 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::erfc | ( | double | a | ) |
Definition at line 874 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::gamma | ( | double | x | ) |
Definition at line 339 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::igam | ( | double | a, |
double | x | ||
) |
Definition at line 127 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::igamc | ( | double | a, |
double | x | ||
) |
incomplete complementary gamma function igamc(a, x) = 1 - igam(a, x)
Definition at line 51 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::igami | ( | double | a, |
double | y | ||
) |
Definition at line 225 of file SpecFuncCephesInv.cxx.
double ROOT::Math::Cephes::incbcf | ( | double | a, |
double | b, | ||
double | x | ||
) |
Definition at line 581 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::incbd | ( | double | a, |
double | b, | ||
double | x | ||
) |
Definition at line 674 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::incbet | ( | double | aa, |
double | bb, | ||
double | xx | ||
) |
DESCRIPTION:
Returns incomplete beta integral of the arguments, evaluated from zero to x. The function is defined as
x - -
| (a+b) | | a-1 b-1
--------— | t (1-t) dt. |
---|---|
(a) | (b) - |
0
The domain of definition is 0 <= x <= 1. In this implementation a and b are restricted to positive values. The integral from x to 1 may be obtained by the symmetry relation
1 - incbet( a, b, x ) = incbet( b, a, 1-x ).
The integral is evaluated by a continued fraction expansion or, when b*x is small, by a power series.
ACCURACY:
Tested at uniformly distributed random points (a,b,x) with a and b in "domain" and x between 0 and 1. Relative error arithmetic domain # trials peak rms IEEE 0,5 10000 6.9e-15 4.5e-16 IEEE 0,85 250000 2.2e-13 1.7e-14 IEEE 0,1000 30000 5.3e-12 6.3e-13 IEEE 0,10000 250000 9.3e-11 7.1e-12 IEEE 0,100000 10000 8.7e-10 4.8e-11 Outputs smaller than the IEEE gradual underflow threshold were excluded from these statistics.
ERROR MESSAGES: message condition value returned incbet domain x<0, x>1 0.0 incbet underflow 0.0
Cephes Math Library, Release 2.8: June, 2000 Copyright 1984, 1995, 2000 by Stephen L. Moshier
Definition at line 484 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::incbi | ( | double | a, |
double | b, | ||
double | y | ||
) |
Definition at line 411 of file SpecFuncCephesInv.cxx.
double ROOT::Math::Cephes::lgam | ( | double | x | ) |
Definition at line 197 of file SpecFuncCephes.cxx.
double ROOT::Math::Cephes::ndtri | ( | double | y | ) |
Definition at line 137 of file SpecFuncCephesInv.cxx.
double ROOT::Math::Cephes::pseries | ( | double | a, |
double | b, | ||
double | x | ||
) |
Definition at line 766 of file SpecFuncCephes.cxx.
|
static |
Definition at line 316 of file SpecFuncCephes.cxx.
|
static |
Definition at line 170 of file SpecFuncCephes.cxx.
|
static |
Definition at line 178 of file SpecFuncCephes.cxx.
|
static |
Definition at line 187 of file SpecFuncCephes.cxx.
|
static |
Definition at line 813 of file SpecFuncCephes.cxx.
|
static |
Definition at line 824 of file SpecFuncCephes.cxx.
|
static |
Definition at line 835 of file SpecFuncCephes.cxx.
|
static |
Definition at line 843 of file SpecFuncCephes.cxx.
|
static |
Definition at line 852 of file SpecFuncCephes.cxx.
|
static |
Definition at line 859 of file SpecFuncCephes.cxx.
|
static |
Definition at line 26 of file SpecFuncCephes.cxx.
|
static |
Definition at line 27 of file SpecFuncCephes.cxx.
|
static |
Definition at line 30 of file SpecFuncCephes.cxx.
|
static |
Definition at line 285 of file SpecFuncCephes.cxx.
|
static |
Definition at line 78 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 95 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 116 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 294 of file SpecFuncCephes.cxx.
|
static |
Definition at line 85 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 106 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 127 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 76 of file SpecFuncCephesInv.cxx.
|
static |
Definition at line 306 of file SpecFuncCephes.cxx.