mroot {mgcv}  R Documentation 
Find a square root of a positive semidefinite 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 semidefinite 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, B with as many columns as the rank of A, and such that A=BB'.
Simon N. Wood simon.wood@rproject.org
require(mgcv) set.seed(0) a < matrix(runif(24),6,4) A < a%*%t(a) ## A is +ve semidefinite, rank 4 B < mroot(A) ## default pivoted choleski method tol < 100*.Machine$double.eps chol.err < max(abs(AB%*%t(B)));chol.err if (chol.err>tol) warning("mroot (chol) suspect") B < mroot(A,method="svd") ## svd method svd.err < max(abs(AB%*%t(B)));svd.err if (svd.err>tol) warning("mroot (svd) suspect")