For a function \(f(t), t\in\Omega\), and a basis function sequence \(\{\rho_k\}_{k\in\kappa}\), basis expansion is to compute \(\int_\Omega f(t)\rho_k(t) dt\). Here we do basis expansion for all \(f_i(t), t\in\Omega = [t_0,t_0+T]\) in functional variable data, \(i=1,\dots,n\). We compute a matrix \((b_{ik})_{n\times p}\), where \(b_{ik} = \int_\Omega f(t)\rho_k(t) dt\). The basis we use here is numerically represented by the value of basis functions at some points in the domain.
numeric_basis_expansion(object, num_basis)# S4 method for functional_variable,numeric_basis
numeric_basis_expansion(object, num_basis)
Returns a numeric matrix, \((b_{ik})_{n\times p}\),
with an extra attribute numeric_basis, which is the numeric_basis object input
by the argument num_basis.
a functional_variable class object.
The minimum and maximum of the slot t_points should be respectively
equal to the slot t_0 and slot t_0 plus slot period.
a numeric_basis class object, representing the function basis.
See numeric_basis.
Heyang Ji