# fdata2pc

##### Principal components for functional data

Compute (penalized) principal components for functional data.

- Keywords
- multivariate

##### Usage

`fdata2pc(fdataobj, ncomp = 2, norm = TRUE, lambda = 0, P = c(0, 0, 1), ...)`

##### Arguments

- fdataobj
`fdata`

class object.- ncomp
Number of principal comoponents.

- norm
=TRUE the norm of eigenvectors

`(rotation)`

is 1.- lambda
Amount of penalization. Default value is 0, i.e. no penalization is used.

- P
If P is a vector: coefficients to define the penalty matrix object. By default P=c(0,0,1) penalize the second derivative (curvature) or acceleration. If P is a matrix: the penalty matrix object.

- …
Further arguments passed to or from other methods.

##### Details

Smoothing is achieved by penalizing the integral of the square of the derivative of order m over rangeval:

m = 0 penalizes the squared difference from 0 of the function

m = 1 penalize the square of the slope or velocity

m = 2 penalize the squared acceleration

m = 3 penalize the squared rate of change of acceleration

##### Value

d The standard deviations of the functional principal components.

rotation are also known as loadings. A

`fdata`

class object whose rows contain the eigenvectors.x are also known as scores. The value of the rotated functional data is returned.

fdataobj.cen The centered

`fdataobj`

object.mean The functional mean of

`fdataobj`

object.l Vector of index of principal components.

C The matched call.

lambda Amount of penalization.

P Penalty matrix.

##### References

Venables, W. N. and B. D. Ripley (2002). *Modern Applied
Statistics with S*. Springer-Verlag.

N. Kraemer, A.-L. Boulsteix, and G. Tutz (2008). Penalized Partial Least Squares with Applications to B-Spline Transformations and Functional Data. Chemometrics and Intelligent Laboratory Systems, 94, 60 - 69. http://dx.doi.org/10.1016/j.chemolab.2008.06.009

Febrero-Bande, M., Oviedo de la Fuente, M. (2012). *Statistical
Computing in Functional Data Analysis: The R Package fda.usc.* Journal of
Statistical Software, 51(4), 1-28. http://www.jstatsoft.org/v51/i04/

##### See Also

##### Examples

```
# NOT RUN {
# }
# NOT RUN {
n= 100;tt= seq(0,1,len=51)
x0<-rproc2fdata(n,tt,sigma="wiener")
x1<-rproc2fdata(n,tt,sigma=0.1)
x<-x0*3+x1
pc=fdata2pc(x,lambda=1)
summary(pc)
# }
```

*Documentation reproduced from package fda.usc, version 2.0.1, License: GPL-2*