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Cubic Hermite Interpolator

Source: R/interpolators.R
cubic_hermite.Rd

The cubic Hermite interpolant takes non-equispaced data and interpolates between them via cubic Hermite polynomials whose slopes must be provided.

Applications:

The interpolant is C1 and evaluation has O(log N) complexity. This interpolator is useful for solution skeletons of ODE steppers.

Usage

cubic_hermite(x, y, dydx)

Arguments

x

Numeric vector of abscissas (x-coordinates).

y

Numeric vector of ordinates (y-coordinates).

dydx

Numeric vector of derivatives (slopes) at each point.

Value

An object of class cubic_hermite with methods:

  • interpolate(xi): Evaluate the interpolator at point xi.

  • prime(xi): Evaluate the derivative of the interpolator at point xi.

  • push_back(x, y, dydx): Add a new control point to the interpolator.

  • domain(): Get the domain of the interpolator.

See also

Boost Documentation

Examples

x <- c(0, 1, 2)
y <- c(0, 1, 0)
dydx <- c(1, 0, -1)
interpolator <- cubic_hermite(x, y, dydx)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.625
interpolator$prime(xi)
#> [1] 1.25
interpolator$push_back(3, 0, 1)
interpolator$domain()
#> [1] 0 3