mroot | 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 |
method |
|
The function uses SVD, or a pivoted Choleski routine. It is primarily of use for turning penalized regression problems into ordinary regression problems.
A matrix, {\bf B}
with as many columns as the rank of
{\bf A}
, and such that {\bf A} = {\bf BB}^\prime
.
Simon N. Wood simon.wood@r-project.org
require(mgcv)
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")
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