| mroot {mgcv} | R Documentation |
Find a square root of a positive semi-definite matrix, having as few columns as possible. Uses either pivoted choleski decomposition or singular value decomposition to do this.
mroot(A,rank=NULL,method="chol")
A |
The positive semi-definite matrix, a square root of which is to be found. |
rank |
if the rank of the matrix A is known then it should
be supplied. |
method |
"chol" to use pivoted choloeski decompositon,
which is fast but tends to over-estimate rank. "svd" to use
singular value decomposition, which is slow, but is the most accurate way
to estimate rank. |
The routine uses an LAPACK SVD routine, or the LINPACK pivoted Choleski routine. It is primarily of use for turning penalized regression problems into ordinary regression problems.
A matrix, B with as many columns as the rank of A, and such that A=BB'.
Simon N. Wood simon.wood@r-project.org
set.seed(0)
a <- matrix(runif(24),6,4)
A <- a%*%t(a) ## A is +ve semi-definite, rank 4
B <- mroot(A) ## default pivoted choleski method
tol <- 100*.Machine$double.eps
chol.err <- max(abs(A-B%*%t(B)));chol.err
if (chol.err>tol) warning("mroot (chol) suspect")
B <- mroot(A,method="svd") ## svd method
svd.err <- max(abs(A-B%*%t(B)));svd.err
if (svd.err>tol) warning("mroot (svd) suspect")