solve.gchol {bdsmatrix} | R Documentation |
This function solves the equation Ax=b for x, given b and the generalized Cholesky decompostion of A. If only the first argument is given, then a G-inverse of A is returned.
## S3 method for class 'gchol'
solve(a, b, full=TRUE, ...)
a |
a generalized cholesky decompostion of a matrix, as
returned by the |
b |
a numeric vector or matrix, that forms the right-hand side of the equation. |
full |
solve the problem for the full (orignal) matrix, or for the cholesky matrix. |
... |
other arguments are ignored |
A symmetric matrix A can be decomposed as LDL', where L is a lower
triangular matrix with 1's on the diagonal, L' is the transpose of
L, and D is diagonal.
This routine solves either the original problem Ay=b
(full
argument) or the subproblem sqrt(D)L'y=b.
If b
is missing it returns the inverse of
A or L, respectively.
if argument b
is not present, the inverse of
a
is returned, otherwise the solution to
matrix equation.
gchol
# Create a matrix that is symmetric, but not positive definite
# The matrix temp has column 6 redundant with cols 1-5
smat <- matrix(1:64, ncol=8)
smat <- smat + t(smat) + diag(rep(20,8)) #smat is 8 by 8 symmetric
temp <- smat[c(1:5, 5:8), c(1:5, 5:8)]
ch1 <- gchol(temp)
ginv <- solve(ch1, full=FALSE) # generalized inverse of ch1
tinv <- solve(ch1, full=TRUE) # generalized inverse of temp
all.equal(temp %*% tinv %*% temp, temp)