# laplacian

From mda v0.4-10
by Trevor Hastie

##### create penalty object for two-dimensional smoothing.

Creates a penalty matrix for use by `gen.ridge`

for
two-dimensional smoothing.

- Keywords
- regression

##### 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.

##### 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

*Documentation reproduced from package mda, version 0.4-10, License: GPL-2*

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