numeric_basis-class: Numeric representation of a function basis

In MECfda: Scalar-on-Function Regression with Measurement Error Correction

Numeric representation of a function basis

Description

A s4 class that numerically represents a basis of linear space of function.
\{\rho_k\}_{k=1}^\infty denotes a basis of function linear space. Some times the basis cannot be expressed analytically. But we can numerically store the space by the value of a finite subset of the basis functions at some certain points in the domain, \rho_k(t_j), k = 1,\dots,p, j = 1,\dots,m. The s4 class is to represent a finite sequence of functions by their values at a finite sequence of points within their domain, in which all the functions have the same domain and the domain is an interval.

Details

The units of a basis of a linear space should be linearly independent. But the program doesn't check the linear dependency of the basis function when a numeric_basis object is initialized.

Slots

basis_function

matrix of the value of the functions, (\zeta_{jk})_{m\times p}, where \zeta_{ik} = \rho_k(t_j), j = 1,\dots,m, k = 1,\dots,p. Each row of the matrix is corresponding to a point of t. Each column of the matrix is corresponding to a basis function.

t_points

a numeric atomic vector, represents the points in the domains of the function where the function values are taken. The jth element is corresponding to jth row of slot basis_function.

t_0

left end of the domain interval.

period

length of the domain interval.

Author(s)

Heyang Ji

Examples

t_0 = 0
period = 1
t_points = seq(0.05,0.95,length.out = 19)
numeric_basis(
  basis_function = cbind(1/2,cos(t_points),sin(t_points)),
  t_points       = t_points,
  t_0            = t_0,
  period         = period
)

MECfda documentation built on April 3, 2025, 10:07 p.m.