DCCA (version 0.1.1)

Qm: Projection Matrix Q

Description

Creates the \(m+1\) by \(m+1\) projection matrix defined by \(Q = I-P\) where \(I\) is the the \(m+1\) by \(m+1\) identity matrix and \(P\) is the \(m+1\) by \(m+1\) projection matrix into the space generated by polynomials of degree \(nu + 1\).

Usage

Qm(m = 2, nu = 0, P = NULL)

Arguments

nu

the degree of the polinomial fit.

m

a positive integer satisfying \(m >= nu\) indicating the size of the window for the polinomial fit.

P

optional: the projection matrix such that \(Q = I - P\) (see function Pm). If this matrix is provided \(m\) and \(nu\) are ignored.

Value

an \(m+1\) by \(m+1\) matrix.

See Also

Pm which generates the projection matrix \(P\).

Examples

# NOT RUN {
Q = Qm(m = 3, nu = 0)
Q
# same as
P = Pm(m = 3, nu = 0)
Q = Qm(P = P)
Q
# }