# R/fourier.R In fda: Functional Data Analysis

#### Documented in fourier

```fourier <- function(x, nbasis = n, period = span, nderiv = 0)
{
#  Computes the NDERIV derivative of the Fourier series basis
#    for NBASIS functions with period PERIOD, these being evaluated
#    at values in vector X
#  Returns an N by NBASIS matrix of function values
#  Note:  The number of basis functions always odd.  If the argument
#   NBASIS is even, it is increased by one.

#  Previously modified 15 December 2005

#  check x and set up range

xNames <- names(x)
#
x      <- as.vector(x)
n      <- length(x)
onen   <- rep(1,n)
xrange <- range(x)
span   <- xrange[2] - xrange[1]

#  check period and set up omega

if (period <= 0) stop("PERIOD not positive.")
omega  <- 2*pi/period
omegax <- omega*x

#  check nbasis

if (nbasis <= 0) stop("NBASIS not positive")

#  check nderiv

if (nderiv <  0) stop("NDERIV is negative.")

#  if nbasis is even, add one

if ((nbasis %/% 2)*2 == nbasis) nbasis <- nbasis + 1

#  compute basis matrix

basismat <- matrix(0,n,nbasis)
if (nderiv == 0) {
#  The fourier series itself is required.
basismat[,1] <- 1/sqrt(2)
if(nbasis>1){
j    <- seq(2,nbasis-1,2)
k    <- j/2
args <- outer(omegax,k)
basismat[,j]   <- sin(args)
basismat[,j+1] <- cos(args)
}
} else {
#  The derivative of order nderiv is required.
basismat[,1] <- 0.0
if(nbasis>1){
if (nderiv == (nderiv %/% 2)*2) {
mval  <- nderiv/2
ncase <- 1
} else {
mval <- (nderiv-1)/2
ncase <- 2
}
j    <- seq(2,nbasis-1,2)
k    <- j/2
fac  <- outer(onen,((-1)^mval)*(k*omega)^nderiv)
args <- outer(omegax,k)
if (ncase == 1) {
basismat[,j]   <-  fac * sin(args)
basismat[,j+1] <-  fac * cos(args)
} else {
basismat[,j]   <-  fac * cos(args)
basismat[,j+1] <- -fac * sin(args)
}
}
}
basismat <- basismat/sqrt(period/2)
#
fNames <- "const"
n2 <- (nbasis %/%2)
if(n2>0){
SC <- outer(c("sin", "cos"), 1:n2, paste, sep="")
fNames <- c(fNames, as.vector(SC))
}
#
dimnames(basismat) <- list(xNames, fNames)
#
return(basismat)
}
```

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fda documentation built on May 29, 2024, 11:26 a.m.