R: create penalty object for two-dimensional smoothing.

laplacian {mda}

R Documentation

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 <hastie@stanford.edu

References

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