Get Multivariate Functional Data from a list of matrices

  grid = NULL,
  n_basis = 30,
  n_order = 4,
  basisobj = NULL,
  Lfdobj = 2,
  lambda = NULL,
  lambda_grid = 10^seq(-10, 1, length.out = 10),
  ncores = 1



A named list of matrices. Names of the elements in the list denote the functional variable names. Each matrix in the list corresponds to a functional variable. All matrices must have the same dimension, where the number of rows corresponds to replications, while the number of columns corresponds to the argument values at which functions are evaluated.


A numeric vector, containing the argument values at which functions are evaluated. Its length must be equal to the number of columns in each matrix in data_list. Default is NULL, in this case a vector equally spaced numbers between 0 and 1 is created, with as many numbers as the number of columns in each matrix in data_list.


An integer variable specifying the number of basis functions; default value is 30. See details on basis functions.


An integer specifying the order of B-splines, which is one higher than their degree. The default of 4 gives cubic splines.


An object of class basisfd defining the B-spline basis function expansion. Default is NULL, which means that a basisfd object is created by doing create.bspline.basis(rangeval = domain, nbasis = n_basis, norder = n_order)


An object of class Lfd defining a linear differential operator of order m. It is used to specify a roughness penalty through fdPar. Alternatively, a nonnegative integer specifying the order m can be given and is passed as Lfdobj argument to the function fdPar, which indicates that the derivative of order m is penalized. Default value is 2, which means that the integrated squared second derivative is penalized.


A non-negative real number. If you want to use a single specified smoothing parameter for all functional data objects in the dataset, this argument is passed to the function fda::fdPar. Default value is NULL, in this case the smoothing parameter is chosen by minimizing the generalized cross-validation (GCV) criterion over the grid of values given by the argument. See details on how smoothing parameters work.


A vector of non-negative real numbers. If lambda is provided as a single number, this argument is ignored. If lambda is NULL, then this provides the grid of values over which the optimal smoothing parameter is searched. Default value is 10^seq(-10,1,l=20).




An object of class mfd. See also mfd for additional details on the multivariate functional data class.


Basis functions are created with fda::create.bspline.basis(domain, n_basis), i.e. B-spline basis functions of order 4 with equally spaced knots are used to create mfd objects.

The smoothing penalty lambda is provided as fda::fdPar(bs, 2, lambda), where bs is the basis object and 2 indicates that the integrated squared second derivative is penalized.

Rather than having a list of matrices, you may have a data frame with long format, i.e. with all functional observations in a single column for each functional variable. In this case, see get_mfd_df.

See also

mfd, get_mfd_list, get_mfd_array


# Only take first 5 multivariate functional observations
# and only two variables from air
air_small <- lapply(air[c("NO2", "CO")], function(x) x[1:5, ])
mfdobj <- get_mfd_list(data_list = air_small)