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Basis Representation Functions for Functional Data

Source: R/basis.R
basis2fdata.Rd

Functions for representing functional data using basis expansions, including B-splines, Fourier bases, and P-splines with penalization. Reconstruct Functional Data from Basis Coefficients

Usage

basis2fdata(
  coefs,
  argvals,
  nbasis = NULL,
  type = c("bspline", "fourier"),
  rangeval = NULL
)

Arguments

coefs

Coefficient matrix [n x nbasis] where n is the number of curves and nbasis is the number of basis functions. Can also be a vector for a single curve.

argvals

Numeric vector of evaluation points for reconstruction.

nbasis

Number of basis functions. If NULL, inferred from ncol(coefs).

type

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

rangeval

Range of argvals. Default: range(argvals).

Value

An fdata object with reconstructed curves.

Details

Given basis coefficients, reconstruct the functional data by evaluating the basis expansion at specified argument values.

The reconstruction computes X(t) = sum(coef_k * B_k(t)) where B_k are the basis functions evaluated at argvals.

Examples

# Create some functional data
t <- seq(0, 1, length.out = 100)
X <- matrix(sin(2 * pi * t), nrow = 1)
fd <- fdata(X, argvals = t)

# Project to basis and reconstruct
coefs <- fdata2basis(fd, nbasis = 15, type = "fourier")
fd_recon <- basis2fdata(coefs, argvals = t, type = "fourier")