projector {dae}

Create projectors

Description

The class "projector" is the subclass of the class "matrix" in which matrices are square, symmetric and idempotent.

The function projector tests whether a matrix satisfies these criteria and if it does creates a "projector" object, computing the projector's degrees of freedom and adding them to the object.

Usage

projector(Q)

Arguments

Q

The matrix to be made into a projector.

Details

In checking that the matrix is square, symmetric and idempotent, the equality of the matrix with either its transpose or square is tested. In this, a difference in elements is considered to be zero if it is less than daeTolerance, which is initially set to .Machine$double.eps ^ 0.5 (about 1.5E-08). The function set.daeTolerance can be used to change daeTolerance.

Value

An object of Class "projector" that consists of a square, summetric, idempotent matrix and degrees of freedom (rank) of the matrix.

Author(s)

Chris Brien

See Also

degfree, correct.degfree in package dae.

projector for further information about this class.

Examples

## set up a 2 x 2 mean operator that takes the mean of a vector of 2 values
m <- matrix(rep(0.5,4), nrow=2)

## create an object of class projector
proj.m <- projector(m)

## check that it is a valid projector
is.projector(proj.m)