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Functions | Variables
ROOT::Math::Cephes Namespace Reference

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]
 

Function Documentation

◆ beta()

double ROOT::Math::Cephes::beta ( double  z,
double  w 
)

Definition at line 428 of file SpecFuncCephes.cxx.

◆ erf()

double ROOT::Math::Cephes::erf ( double  x)

Definition at line 926 of file SpecFuncCephes.cxx.

◆ erfc()

double ROOT::Math::Cephes::erfc ( double  a)

Definition at line 874 of file SpecFuncCephes.cxx.

◆ gamma()

double ROOT::Math::Cephes::gamma ( double  x)

Definition at line 339 of file SpecFuncCephes.cxx.

◆ igam()

double ROOT::Math::Cephes::igam ( double  a,
double  x 
)

Definition at line 127 of file SpecFuncCephes.cxx.

◆ igamc()

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.

◆ igami()

double ROOT::Math::Cephes::igami ( double  a,
double  y 
)

Definition at line 225 of file SpecFuncCephesInv.cxx.

◆ incbcf()

double ROOT::Math::Cephes::incbcf ( double  a,
double  b,
double  x 
)

Definition at line 581 of file SpecFuncCephes.cxx.

◆ incbd()

double ROOT::Math::Cephes::incbd ( double  a,
double  b,
double  x 
)

Definition at line 674 of file SpecFuncCephes.cxx.

◆ incbet()

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.

◆ incbi()

double ROOT::Math::Cephes::incbi ( double  a,
double  b,
double  y 
)

Definition at line 411 of file SpecFuncCephesInv.cxx.

◆ lgam()

double ROOT::Math::Cephes::lgam ( double  x)

Definition at line 197 of file SpecFuncCephes.cxx.

◆ ndtri()

double ROOT::Math::Cephes::ndtri ( double  y)

Definition at line 137 of file SpecFuncCephesInv.cxx.

◆ pseries()

double ROOT::Math::Cephes::pseries ( double  a,
double  b,
double  x 
)

Definition at line 766 of file SpecFuncCephes.cxx.

◆ stirf()

static double ROOT::Math::Cephes::stirf ( double  x)
static

Definition at line 316 of file SpecFuncCephes.cxx.

Variable Documentation

◆ A

double ROOT::Math::Cephes::A[]
static
Initial value:
= {
8.11614167470508450300E-4,
-5.95061904284301438324E-4,
7.93650340457716943945E-4,
-2.77777777730099687205E-3,
8.33333333333331927722E-2
}

Definition at line 170 of file SpecFuncCephes.cxx.

◆ B

double ROOT::Math::Cephes::B[]
static
Initial value:
= {
-1.37825152569120859100E3,
-3.88016315134637840924E4,
-3.31612992738871184744E5,
-1.16237097492762307383E6,
-1.72173700820839662146E6,
-8.53555664245765465627E5
}

Definition at line 178 of file SpecFuncCephes.cxx.

◆ C

double ROOT::Math::Cephes::C[]
static
Initial value:
= {
-3.51815701436523470549E2,
-1.70642106651881159223E4,
-2.20528590553854454839E5,
-1.13933444367982507207E6,
-2.53252307177582951285E6,
-2.01889141433532773231E6
}

Definition at line 187 of file SpecFuncCephes.cxx.

◆ erfP

double ROOT::Math::Cephes::erfP[]
static
Initial value:
= {
2.46196981473530512524E-10,
5.64189564831068821977E-1,
7.46321056442269912687E0,
4.86371970985681366614E1,
1.96520832956077098242E2,
5.26445194995477358631E2,
9.34528527171957607540E2,
1.02755188689515710272E3,
5.57535335369399327526E2
}

Definition at line 813 of file SpecFuncCephes.cxx.

◆ erfQ

double ROOT::Math::Cephes::erfQ[]
static
Initial value:
= {
1.32281951154744992508E1,
8.67072140885989742329E1,
3.54937778887819891062E2,
9.75708501743205489753E2,
1.82390916687909736289E3,
2.24633760818710981792E3,
1.65666309194161350182E3,
5.57535340817727675546E2
}

Definition at line 824 of file SpecFuncCephes.cxx.

◆ erfR

double ROOT::Math::Cephes::erfR[]
static
Initial value:
= {
5.64189583547755073984E-1,
1.27536670759978104416E0,
5.01905042251180477414E0,
6.16021097993053585195E0,
7.40974269950448939160E0,
2.97886665372100240670E0
}

Definition at line 835 of file SpecFuncCephes.cxx.

◆ erfS

double ROOT::Math::Cephes::erfS[]
static
Initial value:
= {
2.26052863220117276590E0,
9.39603524938001434673E0,
1.20489539808096656605E1,
1.70814450747565897222E1,
9.60896809063285878198E0,
3.36907645100081516050E0
}

Definition at line 843 of file SpecFuncCephes.cxx.

◆ erfT

double ROOT::Math::Cephes::erfT[]
static
Initial value:
= {
9.60497373987051638749E0,
9.00260197203842689217E1,
2.23200534594684319226E3,
7.00332514112805075473E3,
5.55923013010394962768E4
}

Definition at line 852 of file SpecFuncCephes.cxx.

◆ erfU

double ROOT::Math::Cephes::erfU[]
static
Initial value:
= {
3.35617141647503099647E1,
5.21357949780152679795E2,
4.59432382970980127987E3,
2.26290000613890934246E4,
4.92673942608635921086E4
}

Definition at line 859 of file SpecFuncCephes.cxx.

◆ kBig

double ROOT::Math::Cephes::kBig = 4.503599627370496e15
static

Definition at line 26 of file SpecFuncCephes.cxx.

◆ kBiginv

double ROOT::Math::Cephes::kBiginv = 2.22044604925031308085e-16
static

Definition at line 27 of file SpecFuncCephes.cxx.

◆ LS2PI

double ROOT::Math::Cephes::LS2PI = 0.91893853320467274178
static

Definition at line 30 of file SpecFuncCephes.cxx.

◆ P

double ROOT::Math::Cephes::P[]
static
Initial value:
= {
1.60119522476751861407E-4,
1.19135147006586384913E-3,
1.04213797561761569935E-2,
4.76367800457137231464E-2,
2.07448227648435975150E-1,
4.94214826801497100753E-1,
9.99999999999999996796E-1
}

Definition at line 285 of file SpecFuncCephes.cxx.

◆ P0

double ROOT::Math::Cephes::P0[5]
static
Initial value:
= {
-5.99633501014107895267E1,
9.80010754185999661536E1,
-5.66762857469070293439E1,
1.39312609387279679503E1,
-1.23916583867381258016E0,
}

Definition at line 78 of file SpecFuncCephesInv.cxx.

◆ P1

double ROOT::Math::Cephes::P1[9]
static
Initial value:
= {
4.05544892305962419923E0,
3.15251094599893866154E1,
5.71628192246421288162E1,
4.40805073893200834700E1,
1.46849561928858024014E1,
2.18663306850790267539E0,
-1.40256079171354495875E-1,
-3.50424626827848203418E-2,
-8.57456785154685413611E-4,
}

Definition at line 95 of file SpecFuncCephesInv.cxx.

◆ P2

double ROOT::Math::Cephes::P2[9]
static
Initial value:
= {
3.23774891776946035970E0,
6.91522889068984211695E0,
3.93881025292474443415E0,
1.33303460815807542389E0,
2.01485389549179081538E-1,
1.23716634817820021358E-2,
3.01581553508235416007E-4,
2.65806974686737550832E-6,
6.23974539184983293730E-9,
}

Definition at line 116 of file SpecFuncCephesInv.cxx.

◆ Q

double ROOT::Math::Cephes::Q[]
static
Initial value:
= {
-2.31581873324120129819E-5,
5.39605580493303397842E-4,
-4.45641913851797240494E-3,
1.18139785222060435552E-2,
3.58236398605498653373E-2,
-2.34591795718243348568E-1,
7.14304917030273074085E-2,
1.00000000000000000320E0
}

Definition at line 294 of file SpecFuncCephes.cxx.

◆ Q0

double ROOT::Math::Cephes::Q0[8]
static
Initial value:
= {
1.95448858338141759834E0,
4.67627912898881538453E0,
8.63602421390890590575E1,
-2.25462687854119370527E2,
2.00260212380060660359E2,
-8.20372256168333339912E1,
1.59056225126211695515E1,
-1.18331621121330003142E0,
}

Definition at line 85 of file SpecFuncCephesInv.cxx.

◆ Q1

double ROOT::Math::Cephes::Q1[8]
static
Initial value:
= {
1.57799883256466749731E1,
4.53907635128879210584E1,
4.13172038254672030440E1,
1.50425385692907503408E1,
2.50464946208309415979E0,
-1.42182922854787788574E-1,
-3.80806407691578277194E-2,
-9.33259480895457427372E-4,
}

Definition at line 106 of file SpecFuncCephesInv.cxx.

◆ Q2

double ROOT::Math::Cephes::Q2[8]
static
Initial value:
= {
6.02427039364742014255E0,
3.67983563856160859403E0,
1.37702099489081330271E0,
2.16236993594496635890E-1,
1.34204006088543189037E-2,
3.28014464682127739104E-4,
2.89247864745380683936E-6,
6.79019408009981274425E-9,
}

Definition at line 127 of file SpecFuncCephesInv.cxx.

◆ s2pi

double ROOT::Math::Cephes::s2pi = 2.50662827463100050242E0
static

Definition at line 76 of file SpecFuncCephesInv.cxx.

◆ STIR

double ROOT::Math::Cephes::STIR[5]
static
Initial value:
= {
7.87311395793093628397E-4,
-2.29549961613378126380E-4,
-2.68132617805781232825E-3,
3.47222221605458667310E-3,
8.33333333333482257126E-2,
}

Definition at line 306 of file SpecFuncCephes.cxx.