warp_knots: Piecewise-linear monotone warping with knots (Xiong et al....

In rlibkriging: Kriging Models using the 'libKriging' Library

Piecewise-linear monotone warping with knots (Xiong et al. 2007)

Description

Implements the non-stationary input warping of Xiong, Chen, Apley & Ding (2007, Int. J. Numer. Meth. Engng). The domain [0,1] is split into K+1 intervals by K interior knots, each carrying a learnable positive slope s_k = \exp(r_k). The warp is:

w(x) = \sum_{j<k} s_j (t_{j+1}-t_j) + s_k (x-t_k)

for x \in [t_k, t_{k+1}), giving a continuous, monotone piecewise-linear function with K+1 free parameters.

This is the same construction as the knots argument in DiceKriging.

Usage

warp_knots(n_knots = 3, knot_positions = NULL)

Arguments

n_knots	number of interior knots K \ge 1 (default 3)
knot_positions	optional numeric vector of K knot positions strictly inside (0,1), in increasing order. When NULL (default), knots are placed uniformly at 1/(K+1), 2/(K+1), \ldots, K/(K+1).

Value

warp specification string, e.g. "knots(3)" or "knots(0.25:0.5:0.75)"

References

Xiong, Y., Chen, W., Apley, D. & Ding, X. (2007). A non-stationary covariance-based Kriging method for metamodelling in engineering design. International Journal for Numerical Methods in Engineering, 71(6), 733–756.

See Also

WarpKriging

rlibkriging documentation built on May 14, 2026, 1:06 a.m.