| Type: | Package |
| Title: | Functional Bases |
| Version: | 1.1.1 |
| Date: | 2022-05-17 |
| Author: | Niels Olsen |
| Maintainer: | Niels Olsen <nalo@dtu.dk> |
| Description: | Easy-to-use, very fast implementation of various functional bases. Easily used together with other packages. A functional basis is a collection of basis functions [\phi_1, ..., \phi_n] that can represent a smooth function, i.e. $f(t) = \sum c_k \phi_k(t)$. First- and second-order derivatives are also included. These are the mathematically correct ones, no approximations applied. As of version 1.1, this package includes B-splines, Fourier bases and polynomials. |
| URL: | https://github.com/naolsen/fctbases |
| License: | GPL-3 |
| Imports: | Rcpp (≥ 0.12.19) |
| Suggests: | knitr, rmarkdown, microbenchmark |
| LinkingTo: | Rcpp, RcppArmadillo |
| NeedsCompilation: | yes |
| Packaged: | 2022-05-17 14:10:06 UTC; nalo |
| Repository: | CRAN |
| Date/Publication: | 2022-05-17 17:10:02 UTC |
fctbases: Functional bases
Description
fctbases is a fast and easy implementation of functional bases in R. Simply initialize the desired basis, which returns function of class fctbasis.
Details
Internally, functions are stored as C++ objects, which are masked by the package. The package maintains the bookkeeping of fctbasis objects. Parameters are validated at initialization which also reduces some of the overhead. fctbases objects cannot be saved across sessions and must be re-initialised.
Derivatives are provided. These are the mathematically correct ones and are as fast as the non-derivatives.
See Also
Functional basis function
Description
A fctbases object is a function of class fctbasis which takes three arguments (t, x, deriv)
Arguments
t |
time points |
x |
vector or matrix of coefficients (optional) |
deriv |
Should the derivative be used and which order? Defaults to |
Details
If deriv is zero or FALSE, the function itself is evaluated.
If deriv is one or TRUE, the first derivative is evaluated.
If deriv is two, the second derivative is evaluated.
The dimension of x must match the number of basis functions.
Value
Returns a matrix of dimension length(t) times no. of bases if x is missing.
If x is provided and is a vector, it returns a vector of same length as t.
If x is provided and is a matrix, it returns a matrix of dimension length(t) times ncol(x)
Examples
## Create basis (here a b spline)
bf <- make.bspline.basis(knots = 0:12/12)
## Use a functional basis
bf(0.2)
tt <- seq(0,1, length = 50)
bf(tt) ## evaluates bf in tt
bf(tt, deriv = TRUE) ## evaluates derivative of bf in tt
## Apply bf to some coefficients
set.seed(661)
x <- runif(15)
bf(tt, x) ## Evaluate bf in tt with coefficients x.
bf(0.2, deriv = 2) ## Second derivative.
bf(0.2, x, deriv = 2) ## Second derivative with coefficients x.
Make B-spline basis
Description
Make B-spline basis
Usage
make.bspline.basis(knots, order = 4)
Arguments
knots |
Knots of the basis, including endpoints |
order |
Spline order. Defaults to 4. |
Value
Function of class "fctbasis"
See Also
Functional basis function, make.std.bspline.basis
Examples
## B-spline with equidistant knots with 13 basis function
bf <- make.bspline.basis(knots = 0:10, order = 4)
## B-spline of order 2 (ie. a linear approximation) with some uneven knots
bf <- make.bspline.basis(knots = c(-1.3, 0, 0.5, 0.7, 1.1), order = 2)
Make fourier basis
Description
Make fourier basis
Usage
make.fourier.basis(range, order, use.trig.id = FALSE)
Arguments
range |
Left and right end points. |
order |
Order of harmonics |
use.trig.id |
Use trigonometrical identities with this function? |
Details
The number of basis elements (degrees of freedom) is 2 * order + 1.
The basis functions are ordered [1, sin(t), cos(t), sin(2t), cos(2t), ...]
Using trigonometrical identities is faster, but introduces (negligible) round-off errors.
Value
Function of class "fctbasis"
See Also
Examples
## A fourier basis with period 1 and 11 basis functions.
bf <- make.fourier.basis(c(0,1), order = 5)
Make polynomial basis
Description
Make polynomial basis
Usage
make.pol.basis(order)
Arguments
order |
Order of polynomial (= degree + 1) |
Details
The polynomial basis is ordered [1, t, t^2, t^3, ..., t^n]
Value
Function of class "fctbasis"
See Also
Examples
## A four-degree polynomial
mypol <- make.pol.basis(order = 5)
'Standard' B-spline basis
Description
This initializes a bspline of order 4 with uniformly places knots. df = intervals + 3.
Usage
make.std.bspline.basis(range = c(0, 1), intervals)
Arguments
range |
End points of spline |
intervals |
Number of intervals |
Details
make.std.bspline.basis uses a different implementation than make.bspline.basis,
but is not faster in all uses.
Value
function
See Also
Functional basis function, make.bspline.basis
Examples
## 16 equidistant knots between 0 and 2 (both included)
bf <- make.std.bspline.basis(range = c(0,2), intervals = 15)
Functional basis info
Description
This function returns details about a functional basis.
Usage
object.info(fctbasis)
Arguments
fctbasis |
object of class |
Value
A named list including no. of basis, type of basis, and possibly additional information.