Cardinal Quintic Hermite Interpolator

Constructs a cardinal quintic Hermite interpolator given the vectors of ordinates, first derivatives, and second derivatives.

Usage

cardinal_quintic_hermite(y, dydx, d2ydx2, x0, dx)

Arguments

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.

x0

Numeric value of the first abscissa (x-coordinate).

dx

Numeric value of the spacing between abscissas.

Value

An object of class cardinal_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.

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

Examples

y <- c(0, 1, 0)
dydx <- c(1, 0, -1)
d2ydx2 <- c(0, -1, 0)
x0 <- 0
dx <- 1
interpolator <- cardinal_quintic_hermite(y, dydx, d2ydx2, x0, dx)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.640625
interpolator$prime(xi)
#> [1] 1.40625
interpolator$double_prime(xi)
#> [1] -1.25
interpolator$domain()
#> [1] 0 2