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Cardinal Cubic B-Spline Interpolator

Source: R/interpolators.R
cardinal_cubic_b_spline.Rd

The cardinal cubic B-spline interpolator allows for fast and accurate interpolation of a function which is known at equally spaced points.

Mathematical Properties:

It uses compactly supported basis functions constructed via iterative convolution, ensuring numerical stability. The interpolant is O(h^4) accurate for values and O(h^3) accurate for derivatives, where h is the step size.

Conditions:

Ideally, the function being interpolated should be four-times continuously differentiable. If the derivatives at the endpoints are not provided, they are estimated using one-sided finite-difference formulas.

Usage

cardinal_cubic_b_spline(
  y,
  t0,
  h,
  left_endpoint_derivative = NULL,
  right_endpoint_derivative = NULL
)

Arguments

y

Numeric vector of data points to interpolate.

t0

Numeric scalar representing the starting point of the data.

h

Numeric scalar representing the spacing between data points.

left_endpoint_derivative

Optional numeric scalar for the derivative at the left endpoint.

right_endpoint_derivative

Optional numeric scalar for the derivative at the right endpoint.

Value

An object of class cardinal_cubic_b_spline with methods:

  • interpolate(x): Evaluate the spline at point x.

  • prime(x): Evaluate the first derivative of the spline at point x.

  • double_prime(x): Evaluate the second derivative of the spline at point x.

See also

Boost Documentation

Examples

y <- c(1, 2, 0, 2, 1)
t0 <- 0
h <- 1
spline_obj <- cardinal_cubic_b_spline(y, t0, h)
x <- 0.5
spline_obj$interpolate(x)
#> [1] 2.895833
spline_obj$prime(x)
#> [1] 0.125
spline_obj$double_prime(x)
#> [1] -11.16667