# S.basis: Smoothing matrix with roughness penalties by basis... In fda.usc: Functional Data Analysis and Utilities for Statistical Computing

 S.basis R Documentation

## Smoothing matrix with roughness penalties by basis representation.

### Description

Provides the smoothing matrix `S` with roughness penalties.

### Usage

```S.basis(tt, basis, lambda = 0, Lfdobj = vec2Lfd(c(0, 0)), w = NULL, ...)
```

### Arguments

 `tt` Discretization points. `basis` Basis to use. See create.basis. `lambda` A roughness penalty. By default, no penalty `lambda`=0. `Lfdobj` See eval.penalty. `w` Optional case weights. `...` Further arguments passed to or from other methods. Arguments to be passed by default to create.basis

### Details

Provides the smoothing matrix S for the discretization points `tt` and b`basis` with roughness penalties. If `lambda=0` is not used penalty, else a basis roughness penalty matrix is caluclated using getbasispenalty.

### Value

Return the smoothing matrix `S`.

### Author(s)

Manuel Febrero-Bande, Manuel Oviedo de la Fuente manuel.oviedo@udc.es

### References

Ramsay, James O. and Silverman, Bernard W. (2006). Functional Data Analysis, 2nd ed., Springer, New York.

Wasserman, L. All of Nonparametric Statistics. Springer Texts in Statistics, 2006.

See Also as `S.np`

### Examples

```## Not run:
np=101
tt=seq(0,1,len=np)

nbasis=11
base1 <- create.bspline.basis(c(0, np), nbasis)
base2 <- create.fourier.basis(c(0, np), nbasis)

S1<-S.basis(tt,basis=base1,lambda=3)
image(S1)
S2<-S.basis(tt,basis=base2,lambda=3)
image(S2)

## End(Not run)
```

fda.usc documentation built on Oct. 17, 2022, 9:06 a.m.