XploRe Help : DGdecompS

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library:	math
See also:	VaRDGdecomp

Quantlet:		DGdecompS
Description:		computes the square root of a positive semi-definite matrix, using an eigen value decomposition

Usage:	`B = DGdecompS(Sigma)`
Input:
	`Sigma`	p x p positive semi-definite matrix containing user-defined data.
Output:
	`B`	p x p matrix containing the square root of Sigma. Note that the solution is non-unique. B solves the equation: BB' = Sigma.

Note:

Square roots of matrices can also be computed by the Cholesky decomposition, which only works for positive definite matrices, but which is faster.

Example:

library("math") Sigma = matrix(3,3) + 10*unit(3) B=DGdecompS(Sigma) B B*B'

Result:

Contents of B
[1,]   2.2361   2.0817   -1.291
[2,]  -2.2361   2.0817   -1.291
[3,]        0   2.0817    2.582

Contents of _tmp
[1,]       11        1        1
[2,]        1       11        1
[3,]        1        1       11

Author: S. Jaschke, 20011102 license MD*Tech