eval.fd.Rd

\name{eval.fd}
\alias{eval.fd}
\alias{predict.fd}
\alias{predict.fdPar}
\alias{predict.fdSmooth}
\alias{fitted.fdSmooth}
\alias{residuals.fdSmooth}
\title{
  Values of a Functional Data Object
}
\description{
  Evaluate a functional data object at specified argument values, or
  evaluate a derivative or the result of applying a linear differential
  operator to the functional object.
}
\usage{
eval.fd(evalarg, fdobj, Lfdobj=0, returnMatrix=FALSE)
\method{predict}{fd}(object, newdata=NULL, Lfdobj=0, returnMatrix=FALSE,
                     ...)
\method{predict}{fdPar}(object, newdata=NULL, Lfdobj=0,
                     returnMatrix=FALSE, ...)
\method{predict}{fdSmooth}(object, newdata=NULL, Lfdobj=0,
                     returnMatrix=FALSE, ...)
\method{fitted}{fdSmooth}(object, returnMatrix=FALSE, ...)
\method{residuals}{fdSmooth}(object, returnMatrix=FALSE, ...)
}
\arguments{
  \item{evalarg, newdata}{
    a vector or matrix of argument values at which the functional data
    object is to be evaluated.  If a matrix with more than one column,
    the number of columns must match ncol(dfobj[['coefs']]).

  }
  \item{fdobj}{
    a functional data object to be evaluated.
  }
  \item{Lfdobj}{
    either a nonnegative integer or a linear differential operator
    object.  If present, the derivative or the value of applying the
    operator is evaluated rather than the functions themselves.
  }
  \item{object}{
    an object of class \code{fd}
  }
  \item{returnMatrix}{
    logical:  Should a 2-dimensional array to be returned using a
    special class from the Matrix package if appropriate?
  }
  \item{\dots}{
    optional arguments for \code{predict}, not currently used
  }
}
\details{
  \code{eval.fd} evaluates \code{Lfdobj} of \code{fdobj} at
  \code{evalarg}.

  \code{predict.fd} is a convenience wrapper for
  \code{eval.fd}.  If \code{newdata} is NULL and
  \code{fdobj[['basis']][['type']]} is \code{bspline}, \code{newdata} =
  \code{unique(knots(fdojb,interior=FALSE))};  otherwise, \code{newdata}
  = \code{fdobj[['basis']][['rangeval']]}.

  \code{predict.fdSmooth}, \code{fitted.fdSmooth} and
  \code{residuals.fdSmooth} are other wrappers for \code{eval.fd}.
}
\value{
  an array of 2 or 3 dimensions containing the function
  values.  The first dimension corresponds to the argument values in
  \code{evalarg},
  the second to replications, and the third if present to functions.
}
\author{
  Soren Hosgaard wrote an initial version of \code{predict.fdSmooth},
  \code{fitted.fdSmooth}, and \code{residuals.fdSmooth}.
}
\references{
  Ramsay, James O., Hooker, Giles, and Graves, Spencer (2009),
    \emph{Functional data analysis with R and Matlab}, Springer, New York.
  
  Ramsay, James O., and Silverman, Bernard W. (2005), 
    \emph{Functional Data Analysis, 2nd ed.}, Springer, New York.
  
  Ramsay, James O., and Silverman, Bernard W. (2002), 
    \emph{Applied Functional Data Analysis}, Springer, New York.
}
\seealso{
  \code{\link{getbasismatrix}},
  \code{\link{eval.bifd}},
  \code{\link{eval.penalty}},
  \code{\link{eval.monfd}},
  \code{\link{eval.posfd}}
}
\examples{
oldpar <- par(no.readonly=TRUE)
##
## eval.fd
##
#    set up the fourier basis
daybasis <- create.fourier.basis(c(0, 365), nbasis=65)
#  Make temperature fd object
#  Temperature data are in 12 by 365 matrix tempav
#  See analyses of weather data.
#  Set up sampling points at mid days
#  Convert the data to a functional data object
tempfd <- smooth.basis(day.5,  CanadianWeather$dailyAv[,,"Temperature.C"],
                       daybasis)$fd
#   set up the harmonic acceleration operator
Lbasis  <- create.constant.basis(c(0, 365))
Lcoef   <- matrix(c(0,(2*pi/365)^2,0),1,3)
bfdobj  <- fd(Lcoef,Lbasis)
bwtlist <- fd2list(bfdobj)
harmaccelLfd <- Lfd(3, bwtlist)
#   evaluate the value of the harmonic acceleration
#   operator at the sampling points
Ltempmat <- eval.fd(day.5, tempfd, harmaccelLfd)

#  Confirm that it still works with
#  evalarg = a matrix with only one column
#  when fdobj[['coefs']] is a matrix with multiple columns

Ltempmat. <- eval.fd(matrix(day.5, ncol=1), tempfd, harmaccelLfd)
#  confirm that the two answers are the same

\dontshow{stopifnot(}
all.equal(Ltempmat, Ltempmat.)
\dontshow{)}

#  Plot the values of this operator
matplot(day.5, Ltempmat, type="l")

##
## predict.fd
##
predict(tempfd) # end points only at 35 locations
str(predict(tempfd, day.5)) # 365 x 35 matrix
str(predict(tempfd, day.5, harmaccelLfd))

# cublic splie with knots at 0, .5, 1
bspl3 <- create.bspline.basis(c(0, .5, 1))
plot(bspl3) # 5 bases
fd.bspl3 <- fd(c(0, 0, 1, 0, 0), bspl3)
pred3 <- predict(fd.bspl3)

pred3. <- matrix(c(0, .5, 0), 3)
dimnames(pred3.) <- list(NULL, 'reps 1')
\dontshow{stopifnot(}
all.equal(pred3, pred3.)
\dontshow{)}

pred.2 <- predict(fd.bspl3, c(.2, .8))

pred.2. <- matrix(.176, 2, 1)
dimnames(pred.2.) <- list(NULL, 'reps 1')
\dontshow{stopifnot(}
all.equal(pred.2, pred.2.)
\dontshow{)}

##
## predict.fdSmooth
##
lipSm9 <- smooth.basisPar(liptime, lip, lambda=1e-9)$fd
plot(lipSm9)

##
## with evalarg of class Date and POSIXct
##
# Date
July4.1776 <- as.Date('1776-07-04')
Apr30.1789 <- as.Date('1789-04-30')
AmRev <- c(July4.1776, Apr30.1789)
BspRevolution <- create.bspline.basis(AmRev)

AmRevYears <- seq(July4.1776, Apr30.1789, length.out=14)
(AmRevLinear <- as.numeric(AmRevYears-July4.1776))
fitLin <- smooth.basis(AmRevYears, AmRevLinear, BspRevolution)
AmPred <- predict(fitLin, AmRevYears)

# POSIXct
AmRev.ct <- as.POSIXct1970(c('1776-07-04', '1789-04-30'))
BspRev.ct <- create.bspline.basis(AmRev.ct)
AmRevYrs.ct <- seq(AmRev.ct[1], AmRev.ct[2], length.out=14)
(AmRevLin.ct <- as.numeric(AmRevYrs.ct-AmRev.ct[2]))
fitLin.ct <- smooth.basis(AmRevYrs.ct, AmRevLin.ct, BspRev.ct)
AmPred.ct <- predict(fitLin.ct, AmRevYrs.ct)
par(oldpar)
}
% docclass is function
\keyword{smooth}