| is.included {lmreg} | R Documentation |
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).
Author(s)
Debasis Sengupta <shairiksengupta@gmail.com>, Jinwen Qiu <qjwsnow_ctw@hotmail.com>
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))