R: Detect linear dependencies of one matrix on another

fixDependence {mgcv} | R Documentation

## Detect linear dependencies of one matrix on another

### Description

Identifies columns of a matrix `X2` which are linearly dependent on columns of a matrix `X1`. Primarily of use in setting up identifiability constraints for nested GAMs.

### Usage

    fixDependence(X1,X2,tol=.Machine$double.eps^.5,rank.def=0,strict=FALSE)

### Arguments

`X1` | A matrix.
`X2` | A matrix, the columns of which may be partially linearly dependent on the columns of `X1`.
`tol` | The tolerance to use when assessing linear dependence.
`rank.def` | If the degree of rank deficiency in `X2`, given `X1`, is known, then it can be supplied here, and `tol` is then ignored. Unused unless positive and not greater than the number of columns in `X2`.
`strict` | if `TRUE` then only columns individually dependent on `X1` are detected, if `FALSE` then enough columns to make the reduced `X2` full rank and independent of `X1` are detected.

### Details

The algorithm uses a simple approach based on QR decomposition: see Wood (2006, section 4.10.2) for details.

### Value

A vector of the columns of `X2` which are linearly dependent on columns of `X1` (or which need to be deleted to acheive independence and full rank if `strict==FALSE`). `NULL` if the two matrices are independent.

### Author(s)

Simon N. Wood simon.wood@r-project.org

### References

Wood S.N. (2006) Generalized Additive Models: An Introduction with R. Chapman and Hall/CRC Press.

### Examples

    library(mgcv)
    n<-20;c1<-4;c2<-7
    X1<-matrix(runif(n*c1),n,c1)
    X2<-matrix(runif(n*c2),n,c2)
    X2[,3]<-X1[,2]+X2[,4]*.1
    X2[,5]<-X1[,1]*.2+X1[,2]*.04
    fixDependence(X1,X2)
    fixDependence(X1,X2,strict=TRUE)

[Package mgcv version 1.8-3 Index]