Documentation
¶
Overview ¶
Package cephes implements functions originally in the Netlib code by Stephen Mosher.
Index ¶
- Variables
- func Hyp2f1(a, b, c, x float64) float64
- func Hys2f1(a, b, c, x float64) (s, loss float64)
- func Igam(a, x float64) float64
- func IgamC(a, x float64) float64
- func IgamI(a, p float64) float64
- func Incbet(aa, bb, xx float64) float64
- func Incbi(aa, bb, yy0 float64) float64
- func Ndtri(y0 float64) float64
- func Zeta(x, q float64) float64
Constants ¶
This section is empty.
Variables ¶
var P0 = [5]float64{
-5.99633501014107895267e1,
9.80010754185999661536e1,
-5.66762857469070293439e1,
1.39312609387279679503e1,
-1.23916583867381258016e0,
}
approximation for 0 <= |y - 0.5| <= 3/8
var P1 = [9]float64{
4.05544892305962419923e0,
3.15251094599893866154e1,
5.71628192246421288162e1,
4.40805073893200834700e1,
1.46849561928858024014e1,
2.18663306850790267539e0,
-1.40256079171354495875e-1,
-3.50424626827848203418e-2,
-8.57456785154685413611e-4,
}
Approximation for interval z = math.Sqrt(-2 log y ) between 2 and 8 i.e., y between exp(-2) = .135 and exp(-32) = 1.27e-14.
var P2 = [9]float64{
3.23774891776946035970e0,
6.91522889068984211695e0,
3.93881025292474443415e0,
1.33303460815807542389e0,
2.01485389549179081538e-1,
1.23716634817820021358e-2,
3.01581553508235416007e-4,
2.65806974686737550832e-6,
6.23974539184983293730e-9,
}
Approximation for interval z = math.Sqrt(-2 log y ) between 8 and 64 i.e., y between exp(-32) = 1.27e-14 and exp(-2048) = 3.67e-890.
var Q0 = [8]float64{
1.95448858338141759834e0,
4.67627912898881538453e0,
8.63602421390890590575e1,
-2.25462687854119370527e2,
2.00260212380060660359e2,
-8.20372256168333339912e1,
1.59056225126211695515e1,
-1.18331621121330003142e0,
}
var Q1 = [8]float64{
1.57799883256466749731e1,
4.53907635128879210584e1,
4.13172038254672030440e1,
1.50425385692907503408e1,
2.50464946208309415979e0,
-1.42182922854787788574e-1,
-3.80806407691578277194e-2,
-9.33259480895457427372e-4,
}
var Q2 = [8]float64{
6.02427039364742014255e0,
3.67983563856160859403e0,
1.37702099489081330271e0,
2.16236993594496635890e-1,
1.34204006088543189037e-2,
3.28014464682127739104e-4,
2.89247864745380683936e-6,
6.79019408009981274425e-9,
}
Functions ¶
func Hyp2f1 ¶ added in v0.17.0
hyp2f1.c * * Gauss hypergeometric function F * 2 1 * * * SYNOPSIS: * * double a, b, c, x, y, hyp2f1(); * * y = hyp2f1( a, b, c, x ); * * * DESCRIPTION: * * * hyp2f1( a, b, c, x ) = F ( a, b; c; x ) * 2 1 * * inf. * - a(a+1)...(a+k) b(b+1)...(b+k) k+1 * = 1 + > ----------------------------- x . * - c(c+1)...(c+k) (k+1)! * k = 0 * * Cases addressed are * Tests and escapes for negative integer a, b, or c * Linear transformation if c - a or c - b negative integer * Special case c = a or c = b * Linear transformation for x near +1 * Transformation for x < -0.5 * Psi function expansion if x > 0.5 and c - a - b integer * Conditionally, a recurrence on c to make c-a-b > 0 * * |x| > 1 is rejected. * * The parameters a, b, c are considered to be integer * valued if they are within 1.0e-14 of the nearest integer * (1.0e-13 for IEEE arithmetic). * * ACCURACY: * * * Relative error (-1 < x < 1): * arithmetic domain # trials peak rms * IEEE -1,7 230000 1.2e-11 5.2e-14 * * Several special cases also tested with a, b, c in * the range -7 to 7. * * ERROR MESSAGES: * * A "partial loss of precision" message is printed if * the internally estimated relative error exceeds 1^-12. * A "singularity" message is printed on overflow or * in cases not addressed (such as x < -1).
func Hys2f1 ¶ added in v0.17.0
Defining power series expansion of Gauss hypergeometric function
loss estimates loss of significance upon return.
func Igam ¶
Igam computes the incomplete Gamma integral.
Igam(a,x) = (1/ Γ(a)) \int_0^x e^{-t} t^{a-1} dt
The input argument a must be positive and x must be non-negative or Igam will panic.
func IgamC ¶
IgamC computes the complemented incomplete Gamma integral.
IgamC(a,x) = 1 - Igam(a,x)
= (1/ Γ(a)) \int_0^\infty e^{-t} t^{a-1} dt
The input argument a must be positive and x must be non-negative or IgamC will panic.
func IgamI ¶
IgamI computes the inverse of the incomplete Gamma function. That is, it returns the x such that:
IgamC(a, x) = p
The input argument a must be positive and p must be between 0 and 1 inclusive or IgamI will panic. IgamI should return a positive number, but can return 0 even with non-zero y due to underflow.
func Ndtri ¶
Ndtri returns the argument, x, for which the area under the Gaussian probability density function (integrated from minus infinity to x) is equal to y.
func Zeta ¶
Zeta computes the Riemann zeta function of two arguments.
Zeta(x,q) = \sum_{k=0}^{\infty} (k+q)^{-x}
Note that Zeta returns +Inf if x is 1 and will panic if x is less than 1, q is either zero or a negative integer, or q is negative and x is not an integer.
Note that:
zeta(x,1) = zetac(x) + 1
Types ¶
This section is empty.
Source Files