lmreg (version 1.2)

is.included: Whether one column space is contained in another

Description

Checks whether column space of one matrix is a subset of the column space of another matrix.

Usage

is.included(B, A, tol1=sqrt(.Machine$double.eps), tol2=sqrt(.Machine$double.eps))

Arguments

B

The matrix whose column space is to be checked for being a subset.

A

The matrix whose column space is to be checked for being a superset.

tol1

A relative tolerance to detect zero singular values while computing generalized inverse, in case A is rank deficient (default = sqrt(.Machine$double.eps)).

tol2

A relative tolerance to detect whether there is sufficient closeness between B and A.ginv(A).B (default = sqrt(.Machine$double.eps)).

Value

A logical value (TRUE if the column space of B is contained in the column space of A).

References

Sengupta and Jammalamadaka (2019), Linear Models and Regression with R: An Integrated Approach.

Examples

# NOT RUN {
A <- cbind(c(2,1,-2),c(3,1,-1))
I <- diag(1,3)
is.included(A, I, tol1=sqrt(.Machine$double.eps), tol2=1e-15)
is.included(I, A, tol1=1e-14, tol2=sqrt(.Machine$double.eps))
is.included(projector(A), A, tol1=1e-15, tol2=1e-14)
is.included(A, projector(A))
# }