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

In lmreg: Data and Functions Used in Linear Models and Regression with R: An Integrated Approach

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).

Author(s)

Debasis Sengupta <[e-mail]>, Jinwen Qiu <[e-mail]>

References

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

Examples

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))

lmreg documentation built on May 2, 2019, 9:29 a.m.