# 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, B with as many columns as the rank of A, and such that A=BB'.

### 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 March 29, 2022, 5:06 p.m.