laplacian: create penalty object for two-dimensional smoothing.

In mda: Mixture and Flexible Discriminant Analysis

create penalty object for two-dimensional smoothing.

Description

Creates a penalty matrix for use by gen.ridge for two-dimensional smoothing.

Usage

laplacian(size, compose)
laplacian(size = 16, compose = FALSE)

Arguments

size	dimension of the image is size x size; default is 16.
compose	default is compose=FALSE, which means the penalty is returned as an eigen-decomposition. If compose=TRUE, a penalty matrix is returned.

Details

Formulas are used to construct a laplacian for smoothing a square image.

Value

If compose=FALSE, an eigen-decomposition object is returned. The vectors component is a size^2 x size^2 orthogonal matrix, and the $values component is a size^2 vector of non-negative eigen-values. If compose=TRUE, these are multiplied together to form a single matrix.

Author(s)

Trevor Hastie <[e-mail]

References

Here we follow very closely the material on page 635 in JASA 1991 of O'Sullivan's article on discretized Laplacian Smoothing

See Also

gen.ridge,fda

mda documentation built on July 9, 2023, 7:14 p.m.