G2SWEEP: Generalized inverse matrix of type 2, g2 inverse

Description

Generalized inserve is usually not unique. Some programs use this algorithm to get a uniuqe generalized inverse matrix.

Usage

G2SWEEP(A, Augmented=FALSE, eps=1e-08)

Arguments

a matrix to be inverted

Augmented

If this is TRUE and A is a model(design) matrix X, the last column should be X'y, the last row y'X, and the last cell y'y. See the reference and example for the detail.

eps

Less than this value is considered as zero.

Value

when Augmented=FALSE

ordinary g2 inverse

when Augmented=TRUE

g2 inverse and beta hats in the last column and the last row, and sum of square error (SSE) in the last cell

attribute "rank"

the rank of input matrix

Details

Generalized inverse of g2-type is used by some softwares to do linear regression. See 'SAS Techinical Report R106, The Sweep Operator: Its importance in Statistical Computing' by J. H. Goodnight for the detail.

Examples

Run this code

# NOT RUN {
f1 =   uptake ~ Type + Treatment # formula
x = ModelMatrix(f1, CO2)  # Model matrix and relevant information
y = model.frame(f1, CO2)[,1] # observation vector
nc = ncol(x$X) # number of columns of model matrix
XpY = crossprod(x$X, y)
aXpX = rbind(cbind(crossprod(x$X), XpY), cbind(t(XpY), crossprod(y)))
ag2 = G2SWEEP(aXpX, Augmented=TRUE)
b = ag2[1:nc, (nc + 1)] ; b # Beta hat
iXpX = ag2[1:nc, 1:nc] ; iXpX # g2 inverse of X'X
SSE = ag2[(nc + 1), (nc + 1)] ; SSE # Sum of Square Error
DFr = nrow(x$X) - attr(ag2, "rank") ; DFr # Degree of freedom for the residual

# Compare the below with the above
REG(f1, CO2)
aov1(f1, CO2)
# }