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Quintic Hermite Interpolator

Source: R/interpolators.R
quintic_hermite.Rd

The quintic Hermite interpolator takes a list of possibly non-uniformly spaced abscissas, ordinates, and their velocities and accelerations.

Applications:

It constructs a quintic interpolating polynomial between segments. This is useful for taking solution skeletons from ODE steppers and turning them into a continuous function. The interpolant is C2 and its evaluation has O(log N) complexity.

Usage

quintic_hermite(x, y, dydx, d2ydx2)

Arguments

x

Numeric vector of abscissas (x-coordinates).

y

Numeric vector of ordinates (y-coordinates).

dydx

Numeric vector of first derivatives (slopes) at each point.

d2ydx2

Numeric vector of second derivatives at each point.

Value

An object of class quintic_hermite with methods:

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

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

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

  • push_back(x, y, dydx, d2ydx2): 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)
d2ydx2 <- c(0, -1, 0)
interpolator <- quintic_hermite(x, y, dydx, d2ydx2)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.640625
interpolator$prime(xi)
#> [1] 1.40625
interpolator$double_prime(xi)
#> [1] -1.25
interpolator$push_back(3, 0, 1, 0)
#> NULL
interpolator$domain()
#> [1] 0 3