R: Smallest square root of matrix

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@stats.gla.ac.uk

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