#' Calculate univariate functional PCA

#' 

#' This function is a slightly adapted version of the 

#' calculating univariate functional principal components based on a smoothed 

#' covariance function. The smoothing basis functions are penalized splines.

#' 

#'   covariance estimate? Defaults to \code{FALSE}.

#' @param cov.weight.type The type of weighting used for the smooth covariance

#'   estimate. Defaults to \code{"none"}, i.e. no weighting. Alternatively, 

#'   by the number of observation points.

#'   

#' @return \item{fit}{The approximation of \code{Y.pred} (if \code{NULL}, the 

#'   were calculated.} \item{sigma2}{The estimated variance of the measurement 

#'   error.}  \item{estVar}{The estimated smooth variance function of the data.}

#'   

#'   

#' @references Di, C., Crainiceanu, C., Caffo, B., and Punjabi, N. (2009). 

#'   Multilevel functional principal component analysis. Annals of Applied 

#' 

#' This function calculates a univariate functional principal components 

#' analysis by smoothed covariance based on code from 

#' 

#' @section Warning: This function works only for univariate functional data 

#'   observed on one-dimensional domains.

#' @param nbasis An integer, representing the number of  B-spline basis 

#'   functions used for estimation of the mean function and bivariate smoothing 

#'   of the covariance surface. Defaults to \code{10} (cf. 

#' @param pve A numeric value between 0 and 1, the proportion of variance 

#'   explained: used to choose the number of principal components. Defaults to 

#' @param npc An integer, giving a prespecified value for the number of 

#'   principal components. Defaults to \code{NULL}. If given, this overrides 

#' @param makePD Logical: should positive definiteness be enforced for the 

#'   covariance surface estimate? Defaults to \code{FALSE} (cf. 

#' @param cov.weight.type The type of weighting used for the smooth covariance 

#'   estimate. Defaults to \code{"none"}, i.e. no weighting. Alternatively, 

#'   pointwise estimates of the covariance function by the number of observation

#'   points.

#'   

#'   (if \code{predData} is \code{NULL}).} \item{npc}{The number of functional 

#'   principal components: either the supplied \code{npc}, or the minimum number

#'   of basis functions needed to explain proportion \code{pve} of the variance 

#'   \item{sigma2}{The estimated measurement error variance (cf. 

#'   variance function of the data.}

#'   

#'   \code{\link{fpcaBasis}}, \code{\link{univDecomp}}

#'   

#' @export PACE

#' This function calculates a functional principal component basis

#' representation for functional data on one-dimensional domains. The FPCA is

#' calculated via the \code{\link{PACE}} function, which is built on

#' 

#' @param funDataObject An object of class \code{\link[funData]{funData}} 

#'   containing the observed functional data samples and for which the FPCA is 

#' @param nbasis An integer, representing the number of  B-spline basis 

#'   functions used for estimation of the mean function and bivariate smoothing 

#'   of the covariance surface. Defaults to \code{10} (cf. 

#' @param pve A numeric value between 0 and 1, the proportion of variance 

#'   explained: used to choose the number of principal components. Defaults to 

#' @param npc An integer, giving a prespecified value for the number of 

#'   principal components. Defaults to \code{NULL}. If given, this overrides 

#' @param makePD Logical: should positive definiteness be enforced for the 

#'   covariance surface estimate? Defaults to \code{FALSE} (cf. 

#' @param cov.weight.type The type of weighting used for the smooth covariance

#'   estimate in \code{\link{PACE}}. Defaults to \code{"none"}, i.e. no weighting. Alternatively, 

#'   by the number of observation points.

#'   

#' @return \item{scores}{A matrix of scores (coefficients) with dimension