matinv: Total and Partial Matrix Inversion using Gauss-Jordan Sweep Operator

Description

This function inverts or partially inverts a matrix using pivoting (the sweep operator). It is useful for sequential model-building.

Usage

matinv(a, which, negate=TRUE, eps=1e-12)

Arguments

square matrix to invert or partially invert. May have been inverted or partially inverted previously by matinv, in which case its "swept" attribute is updated. Will un-invert if already inverted.

which

vector of column/row numbers in a to invert. Default is all, for total inverse.

negate

So that the algorithm can keep track of which pivots have been swept as well as roundoff errors, it actually returns the negative of the inverse or partial inverse. By default, these elements are negated to give the usual expected result. Set negate=FAL

eps

singularity criterion

Value

a square matrix, with attributes "rank" and "swept".

References

Clarke MRB (1982). Algorithm AS 178: The Gauss-Jordan sweep operator with detection of collinearity. Appl Statist 31:166--9.

Ridout MS, Cobb JM (1986). Algorithm AS R78 : A remark on algorithm AS 178: The Gauss-Jordan sweep operator with detection of collinearity. Appl Statist 38:420--2.

Examples

Run this code

a      <- diag(1:3)
a.inv1 <- matinv(a, 1, negate=FALSE)	     #Invert with respect to a[1,1]
a.inv1
a.inv  <- -matinv(a.inv1, 2:3, negate=FALSE) #Finish the job
a.inv
solve(a)