mroot {mgcv}  R Documentation 
Smallest square root of matrix
Description
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.
Usage
mroot(A,rank=NULL,method="chol")
Arguments
A 
The positive semidefinite matrix, a square root of which is to be found. 
rank 
if the rank of the matrix 
method 

Details
The function uses SVD, or a pivoted Choleski routine. It is primarily of use for turning penalized regression problems into ordinary regression problems.
Value
A matrix, {\bf B}
with as many columns as the rank of
{\bf A}
, and such that {\bf A} = {\bf BB}^\prime
.
Author(s)
Simon N. Wood simon.wood@rproject.org
Examples
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")