# mroot: Smallest square root of matrix In mgcv: Mixed GAM Computation Vehicle with Automatic Smoothness Estimation

 mroot R Documentation

## Smallest square root of matrix

### Description

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.

### Usage

mroot(A,rank=NULL,method="chol")


### Arguments

 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. NULL or <1 imply that it should be estimated. 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.

### 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@r-project.org

### Examples

  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")


mgcv documentation built on July 26, 2023, 5:38 p.m.