| matSwp {lazy.mat} | R Documentation |
Matrix Sweep Operator
Description
Matrix Sweep Operator
Usage
matSwp(
A,
loc = c(1:nrow(A)),
eps = 1e-08,
nopermute = 0,
chkginv = 0,
debug = 0,
history = 0
)
Arguments
A |
a matrix to be sweeped. |
loc |
vector consisting of the pivot locations. |
eps |
small value to check if the pivot is 0. |
nopermute |
=1 to avoid permuting rows/cols when inverting A. |
chkginv |
= 1 to check if the resulting g-inverse is genuine. |
debug |
= 1 to print intermediate result. |
history |
= 1 to return the permutation matrix RR and CC. |
Details
By default, inv(A) will be calculated by permuting columns
and rows of A
in order to avoid zero pivots as much as possible.
In this case, if RR and CC are the permutation matrix,
inv(A) = CC %*% inv(RR %*% A %*% CC) %*% RR
If history=1 is given, a list of A=matSwp(A) and RR and CC will be
returned.
For a symbolic matrix, use matSweep in lazy.symbolic package.
Value
A matrix swept
or a list of A matrix swept and permutation matrix.
References
Beaton, A.E. (1964) The use of special matrix operators in statistical
calculus. Ed. D thesis, Harvard University.
Reprinted as Educational Testing Service Research Bulletin 64-51.
Princeton, N.J.
Goodnight, J.H. (1979) Tutorial on the SWEEP operator.
The Amarican Statistician, 33, 3, 149-158.
Dempster,A.P. (1969) Elements of Continuous Multivariate Analysis.
Addison- Wesley Publishing Co.,Inc.
Examples
M <- matrix(c(1,2,3,3,2,1,4,5,2),3,3)
Minv <- matSwp(M)
Minv-matSwp(M,1:3)
Minv-matSwp(M,c(3,1,2))
M-matSwp( matSwp(M,1), 1 )
#' # zeros in diagonal
M <- pmat(4,1,3)%*%pmat(4,2,3)
# wrong result
Minv0 <- matSwp(M, nopermute=1) # same as matSwp(M,1:4)
M%*%Minv0
Minv0%*%M
# correct result
res <- matSwp(M, history=1)
res
Minv <- res$inv
M%*%Minv
Minv%*%M
# correct result 2
M1 <- res$RR %*% M %*% res$CC
Minv1 <- res$CC %*% matSwp(M1, 1:4) %*% res$RR
M%*%Minv1
Minv1%*%M
# g2 inverse
M <- matrix(c(1,2,3,3,2,1,4,5,2),3,3)
M[1,] <- 0
matSwp(M,chkginv=1)
# g2 inverse of a rectangular matrix by augmenting with 0s.
G <- matrix(c(1,2,3,3,2,1),3,2)
ginvG <- matSwp(cbind(G,0))[1:2,1:3]
chkginv( G, ginvG, print=1 )