gchol-class {bdsmatrix}R Documentation

Class "gchol"


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.

Objects from the Class

These objects are created by the gchol function.



A numeric vector containing the results of the decompostion


An integer vector of length 2, the dimension of the matrix


A list of length 2 containing the dimnames. These default to the dimnames of the matrix A


The rank of the matrix



signature(x = "gchol", y = "matrix"): multiply the cholesky decomposition by a matrix. That is, if A=LDL' is the decomposition, then gchol(A) %*% B will return L D^.5 B.


signature(x = "matrix", y = "gchol"): multiply by a matrix on the left


signature(x = "gchol"): if a square portion from the upper left corner is selected, then the result will be a gchol object, otherwise an ordinary matrix is returned. The latter most often occurs when printing part of the matrix at the command line.


signature(from = "gchol", to = "matrix"): Use of the as.matrix function will return L


signature(x = "gchol"): Use of the diag function will return D


signature(x = "gchol"): returns the dimension of the matrix


signature(x = "gchol"): returns the dimnames


signature(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. This is very useful inside modeling functions such as coxph, since the X matrix can often contain a redundant column.


Terry Therneau

See Also




[Package bdsmatrix version 1.3-7 Index]