solve.gchol {kinship} | 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=T, ...)
a |
a generalized cholesky decompostion of a matrix, as
returned by the gchol function.
|
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. |
... |
an argument to achieve compatibility with solve from R base |
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.
## Not run: # 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) print(as.matrix(ch1)) # print out L print(diag(ch1)) # print out D aeq <- function(x,y) all.equal(as.vector(x), as.vector(y)) aeq(diag(ch1)[6], 0) # Check that it has a zero in the proper place ginv <- solve(ch1) # see if I get a generalized inverse aeq(temp %*% ginv %*% temp, temp) aeq(ginv %*% temp %*% ginv, ginv) ## End(Not run)