Qm: Projection Matrix Q

In DCCA: Detrended Fluctuation and Detrended Cross-Correlation Analysis

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

Q = Qm(m = 3, nu = 0)
Q
# same as
P = Pm(m = 3, nu = 0)
Q = Qm(P = P)
Q

DCCA documentation built on Jan. 1, 2020, 5:06 p.m.