Functional Bases.

fctbases

R-package: Easy-to-use, efficient implementations of functional bases for use in functional data analysis and elsewhere.

fctbases is a package for R, which implements some of the common linear functional bases such as B-splines and Fourier bases and stores these internally as C++ objects, accesssed from R as normal functions. In this way there is no need for initializing an R object every time a basis is used in R. One simply initializes the desired basis, which is returned as an R function that one calls with desired time point and possibly coefficients. All calculations are implemented in C++. By moving some of computations to the time when objects are initialized, this speeds up some of the computations the even more. The package takes care of the internal bookkeeping of C++ objects and ensures the validity of these.

In short what you can do is:

• Calculate the values of a basis at desired time point(s)
• Evaluate a basis with coefficients at desired time point(s)
• Both of the above, but also for first and second order derivatives.

Usage

Initialize a basis function by calling an appropiate initialization function, e.g.

knots <- 0:10 / 10

f <- make.bspline.basis(knots, order = 4) (or just f <- make.bspline.basis(knots)

will return a bspline of order 4 (standard) with equidistant knots from 0 to 1.

endpoints <- c(0, 1)

f <- make.fourier.basis(endpoints, 10)

will return a Fourier basis with harmonics up to order 10 (that is, 21 degress of freedom) anchored in 0 and 1.

The resulting function takes three arguments: t is a vector of time points, x are optional coefficients to be multiplied, and deriv is whether the derivative in time should be evaluated or not (defaults to false). All fctbases functions follow this pattern.

f(t): Returns a matrix of the basis function evaluted at time points t.

f(t, x): Returns a vector of the basis function evaluted at time points t, multiplied by coefficients x. Equal to f(t) %*% x

f(t, deriv = T): Returns first derivative, d/dt f(t).

f(t, x, deriv = T): Returns first derivative, d/dt f(t) %*% x.

f(t, deriv = 2): Returns second derivative, d^2/dt^2 f(t).

f(t, x, deriv = 2): Returns second derivative, d^2/dt^2 f(t) %*% x.

Installation

Download and install the package as a source package or use devtools, e.g. devtools::install_github("naolsen/fctbases"). A C++ compiler is required to compile the source. The package is also available from CRAN install.package("fctbases") (the version on Github may be newer).

Issues

It is currently not possible to save fctbasis objects as .RData objects (and likely will not be).
Using a fctbasis object from a previous session will return an error.

Other

Feel free to contribute and add suggestions. There are some bases, that I think would be nice to add: natural cubic splines, hermitian polynomials, wavelets bases and possibly others.