gchol-class {bdsmatrix} | R Documentation |
The result of a generalized Cholesky decomposition A=LDL' where A is a symmetric matrix, L is lower triangular with 1s on the diagonal, and D is a diagonal matrix.
These objects are created by the gchol
function.
.Data
:Dim
:Dimnames
:rank
:signature(from = "gchol", to = "matrix")
: Use of
the as.matrix
function will return Lsignature(x = "gchol")
: Use of the diag
function
will return Dsignature(x = "gchol")
: returns the dimension of the
matrix signature(x = "gchol")
: returns the dimnamessignature(object = "gchol")
: By default a triangular
matrix is printed showing D on the diagonal and L off the diagonal
signature(x= "matrix")
: create a generalized
Cholesky decompostion of the matrix
The primary advantages of the genearlized decomposition, as compared to
the standard chol function
, has to do with redundant columns
and generalized inverses (g-inverse).
The lower triangular matrix L is always of full rank. The diagonal matrix
D has a 0 element at position j if and only if the jth column of A is
linearly dependent on columns 1 to j-1 preceding it.
The g-inverse of A involves the inverse of L and a g-inverse of D.
The g-inverse of D retains the zeros and inverts non-zero elements
of D.
All this makes manipulation of the result particularly convenient.
Terry Therneau
showClass("gchol")