numeric_basis-class {MECfda} | R Documentation |
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 oft
. 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
j
th element is corresponding toj
th row of slotbasis_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
)