mroot {mgcv} | 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. |

`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 routine uses an LAPACK SVD routine, or the LINPACK 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

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")

[Package

*mgcv* version 1.3-23

Index]