fdars (version 0.3.3)

fdata2basis_2d: Convert 2D Functional Data to Tensor Product Basis Coefficients

Description

Projects 2D functional data (surfaces) onto a tensor product basis, which is the Kronecker product of two 1D bases.

Usage

fdata2basis_2d(
  fdataobj,
  nbasis.s = 10,
  nbasis.t = 10,
  type = c("bspline", "fourier")
)

Value

A matrix of coefficients [n x (nbasis.s * nbasis.t)].

Arguments

fdataobj

A 2D fdata object (surfaces).

nbasis.s

Number of basis functions in the s (first) direction.

nbasis.t

Number of basis functions in the t (second) direction.

type

Basis type: "bspline" (default) or "fourier".

Details

The tensor product basis is defined as: $$B_{2d}(s, t) = B_s(s) \otimes B_t(t)$$

Examples

# Create 2D surface data
s <- seq(0, 1, length.out = 20)
t <- seq(0, 1, length.out = 20)
surface <- outer(sin(2*pi*s), cos(2*pi*t))
fd2d <- fdata(array(surface, dim = c(1, 20, 20)))

# Project to tensor product basis
coefs <- fdata2basis_2d(fd2d, nbasis.s = 7, nbasis.t = 7, type = "fourier")