Compute functional derivative

Compute the numerical derivative of functional data. Uses finite differences for fast computation via Rust.

Usage

deriv(
  fdataobj,
  nderiv = 1,
  method = "diff",
  class.out = "fdata",
  nbasis = NULL,
  ...
)

Arguments

fdataobj

An object of class 'fdata'.

nderiv

Derivative order (1, 2, ...). Default is 1. For 2D data, only first-order derivatives are currently supported.

method

Method for computing derivatives. Currently only "diff" (finite differences) is supported.

class.out

Output class, either "fdata" or "fd". Default is "fdata".

nbasis

Not used (for compatibility with fda.usc).

...

Additional arguments (ignored).

Value

For 1D data: an 'fdata' object containing the derivative values. For 2D data: a list with components ds, dt, and dsdt, each an 'fdata' object containing the respective partial derivative.

Details

For 1D functional data (curves), computes the nth derivative. For 2D functional data (surfaces), computes partial derivatives:

• ds: partial derivative with respect to s (first argument)

• dt: partial derivative with respect to t (second argument)

• dsdt: mixed partial derivative

Examples

# Create smooth curves
t <- seq(0, 2*pi, length.out = 100)
X <- matrix(0, 10, 100)
for (i in 1:10) X[i, ] <- sin(t + i/5)
fd <- fdata(X, argvals = t)

# First derivative (should be approximately cos)
fd_deriv <- deriv(fd, nderiv = 1)