The PCHIP (Piecewise Cubic Hermite Interpolating Polynomial) interpolant takes non-equispaced data
and interpolates between them via cubic Hermite polynomials whose slopes are chosen to preserve monotonicity.
Details:
The interpolant is C1 and evaluation has O(log N) complexity.
See Fritsch and Carlson for details.
Usage
pchip(x, y, left_endpoint_derivative = NULL, right_endpoint_derivative = NULL)
Arguments
- x
Numeric vector of abscissas (x-coordinates).
- y
Numeric vector of ordinates (y-coordinates).
- left_endpoint_derivative
Optional numeric value of the derivative at the left endpoint.
- right_endpoint_derivative
Optional numeric value of the derivative at the right endpoint.
Value
An object of class pchip 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): Add a new control point
Examples
x <- c(0, 1, 2, 3)
y <- c(0, 1, 0, 1)
interpolator <- pchip(x, y)
xi <- 0.5
interpolator$interpolate(xi)
#> [1] 0.625
interpolator$prime(xi)
#> [1] 1.25
interpolator$push_back(4, 1)