chkginv {lazy.mat}

R Documentation

Check if the the second matrix is a generalized inverse of the first one, or vice versa.

Description

Check if the the second matrix is a generalized inverse of the first one, or vice versa.

Usage

chkginv(A, Ainv, eps = NULL, print = 0)

Arguments

A	matrix
Ainv	Possible generalized inverse of A
eps	criterion for zero
print	= 1 to print the result

Details

This function checks if the following four conditons are met.
g1) A - A %*% Ainv %*% A
g2) Ainv - Ainv %*% A %*% Ainv
g3) A %*% Ainv - t(A %*% Ainv)
g4) Ainv %*% A - t(Ainv %*% A)
In addition, when the input matrix is square, the following two conditons are added.
g01) I - A %*% Ainv
g02) I - Ainv %*% A

For each condition above, the maximum of the absolute values will be compared to eps to see if it can be regaeded as zero. The default value of eps is max(abs(c(diag(Ainv),diag(A)))) * sqrt(.Machine$double.eps) .

Value

A list of:
check=list(g1,g2,g3,g4,g01,g02) where g1, g2,... are either OK or NG
maxad=list(g1,g2,g3,g4,g01,g02) where g1, g2,... are the max absolute value of each criterion.

Examples

chkginv( demomat(3,3), matSwp(demomat(3,3)) )

# called from Ginv or matSwp
A=demomat(9,4)/100; A=t(A)%*%A; Ainv=Ginv(A,chkginv=2)

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