Hypergeom2F1Mat: The Gauss hypergeometric function of matrix argument X

In gajdosandrej/CharFunToolR: Numerical Computation Cumulative Distribution Function and Probability Density Function from Characteristic Function

The Gauss hypergeometric function of matrix argument X

Description

Hypergeom2F1Mat(a, b, c, X, MAX) computes the The Gauss hypergeometric function 2F1(a,b;c;X) of a (p x p)-matrix argument X. Hypergeom2F1Mat is defined for the complex parameters a, b, and c with Re(a) > (p-1)/2 and Re(c-a) > (p-1)/2, and a real symmetric matrix argument X, with Re(X) < I.

For more details and definition of the hypergeometric functions with matrix argument see, e.g., Koev and Edelman (2006) or Muirhead (2009).

Usage

Hypergeom2F1Mat(a, b, c, X, MAX)

Arguments

a	complex vector of parameters of the hypergeometric function 2F1(a,b;c;X).
b	complex vector of parameters of the hypergeometric function 2F1(a,b;c;X).
c	complex vector of parameters of the hypergeometric function 2F1(a,b;c;X).
X	real symmetric (p x p)-matrix argument (alternatively can be specified as a (p x p)-diagonal matrix or a p-vector of the eigenvalues of X).
MAX	maximum number of partitions, |\kappa| <= MAX, default value is MAX = 20.

Value

Hypergeometric sum, 2F1(a,b;c;X).

Note

Ver.: 18-Oct-2018 13:52:32 (consistent with Matlab CharFunTool v1.3.0, 22-Aug-2018 12:23:08).

References

[1] Koev, P. and Edelman, A., 2006. The efficient evaluation of the hypergeometric function of a matrix argument. Mathematics of Computation, 75(254), 833-846.

[2] Muirhead RJ. Aspects of multivariate statistical theory. John Wiley & Sons; 2009 Sep 25.

[3] Butler RW, Wood AT. Laplace approximations for hypergeometric functions with matrix argument. The Annals of Statistics. 2002;30(4):1155-77.

See Also

Other Utility Function: ChebCoefficients(), ChebPoints(), ChebPolyValues(), ChebPoly(), ChebValues(), GammaLog(), GammaMultiLog(), GammaMulti(), GammaZX(), Hypergeom1F1MatApprox(), Hypergeom1F1Mat(), Hypergeom2F1(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1(), interpBarycentric()

Examples

## EXAMPLE
a <- 3
b <- 2.5
c <- 1.5
# X <- c(1, 2, 3) / 5
X <- t(c(1, 2, 3) / 5)
MAX <- 50
f <- Hypergeom2F1Mat(a, b, c, X, MAX)

# a <- 3
# b <- c(1,2,3,4,5)
# c <- c(5,4,3,2,1)
# X <-  t(c(1, 2, 3)) / 5
# MAX <- 10
# f <- Hypergeom2F1Mat(a, b, c, X, MAX)

gajdosandrej/CharFunToolR documentation built on June 3, 2024, 7:46 p.m.