MFPCA (version 1.3-10)

univExpansion: Calculate a univariate basis expansion

Description

This function calculates a univariate basis expansion based on given scores (coefficients) and basis functions.

Usage

univExpansion(
  type,
  scores,
  argvals = ifelse(!is.null(functions), functions@argvals, NULL),
  functions,
  params = NULL
)

Value

An object of class funData with N observations on

argvals, corresponding to the linear combination of the basis functions.

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.

Warning

The options type = "spline2Dpen", type = "DCT2D" and type = "DCT3D" have not been tested with ATLAS/MKL/OpenBLAS.

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.

See Also

MFPCA, splineFunction1D, splineFunction2D, splineFunction2Dpen, dctFunction2D, dctFunction3D, expandBasisFunction

Examples

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)