Triangular Decomposition of a Matrix --- Generic Function

DESCRIPTION:

Computes triangular decompositions of matrices. .LB Matrix

This function is an S Version 3 generic (see Methods); method functions can be written to handle specific S Version 3 classes of data. Classes which already have methods for this function include:
,

USAGE:

lu(x, ...) 

REQUIRED ARGUMENTS:

x
a matrix. No missing values or IEEE special values are allowed.

OPTIONAL ARGUMENTS:

...
additional arguments, such as choosing lower or upper triangular factors in the Hermitian case.

VALUE:

a representation of a triangular decomposition of x .

BACKGROUND:

If A is a matrix, then A = LU , where L is unit lower trapezoidal, and U is upper trapezoidal. At least one of L or U is triangular; both are triangular if `A" is square.

If A is a Hermitian matrix, then A can be factored as L B t(L) or t(L) B L , where L is unit lower triangular, and B is block diagonal with either 1 by 1 or 2 by 2 diagonal blocks. If A is positive semi-definite, then B is diagonal, and this factorization is a variant of the Choleski decomposition. Golub, G., and Van Loan, C. F. (1989). Matrix Computations, 2nd edition, Johns Hopkins, Baltimore.

SEE ALSO:

,

EXAMPLES:

library(Matrix) 
x <- Matrix( rnorm(9), 3, 3) 
lu(x)