# project.basis: Approximate Functional Data Using a Basis In fda: Functional Data Analysis

 project.basis R Documentation

## Approximate Functional Data Using a Basis

### Description

A vector or matrix of discrete data is projected into the space spanned by the values of a set of basis functions. This amounts to a least squares regression of the data on to the values of the basis functions. A small penalty can be applied to deal with situations in which the number of basis functions exceeds the number of basis points. This function is not normally used in a functional data analysis to smooth data, since function `smooth.basis` is provided for that job.

### Usage

``````project.basis(y, argvals, basisobj, penalize=FALSE)
``````

### Arguments

 `y` a vector or matrix of discrete data. `argvals` a vector containing the argument values correspond to the values in `y`. `basisobj` a basis object. `penalize` a logical variable. If TRUE, a small roughness penalty is applied to ensure that the linear equations defining the least squares solution are linearly independent or nonsingular.

### Value

the matrix of coefficients defining the least squares approximation. This matrix has as many rows are there are basis functions, as many columns as there are curves, and if the data are multivariate, as many layers as there are functions.

### References

Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009), Functional data analysis with R and Matlab, Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2005), Functional Data Analysis, 2nd ed., Springer, New York.

Ramsay, James O., and Silverman, Bernard W. (2002), Applied Functional Data Analysis, Springer, New York.

`smooth.basis`