Hypergeom1F1Mat: The confluent hypergeometric function of matrix argument

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

The confluent hypergeometric function of matrix argument

Description

Hypergeom1F1Mat(a, b, X, MAX) computes the confluent hypergeometric function 1F1(a;b;X) of a (p x p)-matrix argument X. Hypergeom1F1Mat is defined for the complex parameters a and b, with Re(a) > (p-1)/2 and Re(b-a) > (p-1)/2, and a REAL symmetric matrix argument X.

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

Usage

Hypergeom1F1Mat(a, b, X, MAX)

Arguments

a	complex vector of parameters of the hypergeometric function 1F1^alpha(a;b;X).
b	complex vector of parameters of the hypergeometric function 1F1^alpha(a;b;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, 1F1(a;b;X).

Note

Ver.: 18-Oct-2018 13:16:53 (consistent with Matlab CharFunTool v1.3.0, 25-Oct-2017 14:56:37).

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(), Hypergeom2F1Mat(), Hypergeom2F1(), HypergeompFqMat(), InterpChebValues(), hypergeom1F1(), interpBarycentric()

Examples

## EXAMPLE
a <- 3
b <- 5
X <- c(1, 2, 3)
MAX <- 10
f <- Hypergeom1F1Mat(a, b, X, MAX)

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