Internal function that implements the MFPCA algorithm for given univariate decompositions
calcMFPCA(
N,
p,
Bchol,
M,
type,
weights,
npc,
argvals,
uniBasis,
fit = FALSE,
approx.eigen = FALSE
)
A list containing the following components:
A vector of estimated eigenvalues \(\hat \nu_1 , \ldots , \hat \nu_M\).
A
multiFunData
object containing the estimated
multivariate functional principal components \(\hat \psi_1, \ldots, \hat
\psi_M\).
A matrix of dimension N x M
containing the
estimated scores \(\hat \rho_{im}\).
A matrix representing the eigenvectors associated with the combined univariate score vectors. This might be helpful for calculating predictions.
The normalizing factors used for calculating the multivariate eigenfunctions and scores. This might be helpful when calculation predictions.
A multivariate functional
data object, corresponding to the mean function. The MFPCA is applied to
the de-meaned functions in mFData
.
A
multiFunData
object containing estimated
trajectories for each observation based on the truncated Karhunen-Loeve
representation and the estimated scores and eigenfunctions.
Number of observations.
Number of elements in multivariate functional data.
Cholesky decomposition of B = block diagonal of Cholesky decompositions.
The number of multivariate functional principal components to calculate.
Vector of univariate decompositions to use.
Vector of weights.
Vector giving the number of univariate basis functions used.
List of argument values for each of the univariate basis functions.
List of univariate basis functions.
Logical. If TRUE
, a truncated multivariate Karhunen-Loeve
representation for the data is calculated based on the estimated scores and
eigenfunctions.
Logical. If TRUE
, the eigenanalysis problem for
the estimated covariance matrix is solved approximately using the
irlba package, which is much faster. If the number M
of
eigenvalues to calculate is high with respect to the number of observations
in mFData
or the number of estimated univariate eigenfunctions, the
approximation may be inappropriate. In this case, approx.eigen is set to
FALSE
and the function throws a warning. Defaults to FALSE
.