fda (version 1.2.3)

eval.basis: Values of Basis Functions or their Derivatives

Description

A set of basis functions are evaluated at a vector of argument values. If a linear differential object is provided, the values are the result of applying the the operator to each basis function.

Usage

eval.basis(evalarg, basisobj, Lfdobj=0)

Arguments

evalarg

a vector of argument values.

basisobj

a basis object defining basis functions whose values are to be computed.

Lfdobj

either a nonnegative integer or a linear differential. operator object.

Value

• a matrix of basis function values with rows corresponding to argument values and columns to basis functions.

source

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

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

Details

If a linear differential operator object is supplied, the basis must be such that the highest order derivative can be computed. If a B-spline basis is used, for example, its order must be one larger than the highest order of derivative required.

See Also

getbasismatrix, eval.fd, plot.basisfd

Examples

##
## 1.  B-splines
## 
# The simplest basis currently available:
# a single step function  
str(bspl1.1 <- create.bspline.basis(norder=1, breaks=0:1))
(eval.bspl1.1 <- eval.basis(seq(0, 1, .2), bspl1.1))

# The second simplest basis:
# 2 step functions, [0, .5], [.5, 1]
str(bspl1.2 <- create.bspline.basis(norder=1, breaks=c(0,.5, 1)))
(eval.bspl1.2 <- eval.basis(seq(0, 1, .2), bspl1.2))

# Second order B-splines (degree 1:  linear splines) 
str(bspl2.3 <- create.bspline.basis(norder=2, breaks=c(0,.5, 1)))
(eval.bspl2.3 <- eval.basis(seq(0, 1, .1), bspl2.3))
# 3 bases:  order 2 = degree 1 = linear 
# (1) line from (0,1) down to (0.5, 0), 0 after
# (2) line from (0,0) up to (0.5, 1), then down to (1,0)
# (3) 0 to (0.5, 0) then up to (1,1).

##
## 2.  Fourier 
## 
# The false Fourier series with 1 basis function
falseFourierBasis <- create.fourier.basis(nbasis=1)
(eval.fFB <- eval.basis(seq(0, 1, .2), falseFourierBasis))

# Simplest real Fourier basis with 3 basis functions
fourier3 <- create.fourier.basis()
(eval.fourier3 <- eval.basis(seq(0, 1, .2), fourier3))

# 3 basis functions on [0, 365]
fourier3.365 <- create.fourier.basis(c(0, 365))
eval.F3.365 <- eval.basis(day.5, fourier3.365)

matplot(eval.F3.365, type="l")

# The next simplest Fourier basis (5  basis functions)
fourier5 <- create.fourier.basis(nbasis=5)
(eval.F5 <- eval.basis(seq(0, 1, .1), fourier5))
matplot(eval.F5, type="l")

# A more complicated example
dayrng <- c(0, 365) 

nbasis <- 51
norder <- 6 

weatherBasis <- create.fourier.basis(dayrng, nbasis)
basisMat <- eval.basis(day.5, weatherBasis) 

matplot(basisMat[, 1:5], type="l")