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mda (version 0.5-4)

laplacian: 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)

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.

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.

Author

Trevor Hastie <hastie@stanford.edu

Details

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

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