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

### See Also

`gen.ridge`,`fda`

[Package mda version 0.5-2 Index]