# Calculate a univariate basis expansion This function calculates a univariate basis expansion based on given scores (coefficients) and basis functions. ```r univExpansion( type, scores, argvals = ifelse(!is.null(functions), functions@argvals, NULL), functions, params = NULL ) ``` ## Arguments - `type`: A character string, specifying the basis for which the decomposition is to be calculated. - `scores`: A matrix of scores (coefficients) for each observation based on the given basis functions. - `argvals`: A list, representing the domain of the basis functions. If `functions` is not `NULL`, the usual default is `functions@argvals`. See funData and the underlying expansion functions for details. - `functions`: A functional data object, representing the basis functions. Can be `NULL` if the basis functions are not estimated from observed data, but have a predefined form. See Details. - `params`: A list containing the parameters for the particular basis to use. ## Returns An object of class `funData` with `N` observations on `argvals`, corresponding to the linear combination of the basis functions. ## Details This function calculates functional data $X_i(t), i= 1 \ldots N$ that is represented as a linear combination of basis functions $b_k(t)$ $$ X_i(t) = \sum_{k = 1}^K \theta_{ik} b_k(t), i = 1,\ldots, N. $$ The basis functions may be prespecified (such as spline basis functions or Fourier bases) or can be estimated from observed data (e.g. by functional principal component analysis). If `type = "default"` (i.e. a linear combination of arbitrary basis functions is to be calculated), both scores and basis functions must be supplied. ## Warning The options `type = "spline2Dpen"`, `type = "DCT2D"` and `type = "DCT3D"` have not been tested with ATLAS/MKL/OpenBLAS. ## Examples ```r oldPar <- par(no.readonly = TRUE) par(mfrow = c(1,1)) set.seed(1234) ### Spline basis ### # simulate coefficients (scores) for N = 10 observations and K = 8 basis functions N <- 10 K <- 8 scores <- t(replicate(n = N, rnorm(K, sd = (K:1)/K))) dim(scores) # expand spline basis on [0,1] funs <- univExpansion(type = "splines1D", scores = scores, argvals = list(seq(0,1,0.01)), functions = NULL, # spline functions are known, need not be given params = list(bs = "ps", m = 2, k = K)) # params for mgcv plot(funs, main = "Spline reconstruction") ### PCA basis ### # simulate coefficients (scores) for N = 10 observations and K = 8 basis functions N <- 10 K <- 8 scores <- t(replicate(n = N, rnorm(K, sd = (K:1)/K))) dim(scores) # Fourier basis functions as eigenfunctions eFuns <- eFun(argvals = seq(0,1,0.01), M = K, type = "Fourier") # expand eigenfunction basis funs <- univExpansion(type = "uFPCA", scores = scores, argvals = NULL, # use argvals of eFuns (default) functions = eFuns) plot(funs, main = "PCA reconstruction") par(oldPar) ``` ## See Also `MFPCA`, `splineFunction1D`, `splineFunction2D`, `splineFunction2Dpen`, `dctFunction2D`, `dctFunction3D`, `expandBasisFunction`

univExpansion function