mgcv (version 1.6-0)

fixDependence: 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)

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.

Value

• An array of the columns of X2 which are linearly dependent on columns of X1. NULL if the two matrices are independent.

Details

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

References

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

Examples

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)