% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/WarpKrigingClass.R
\name{warp_knots}
\alias{warp_knots}
\title{Piecewise-linear monotone warping with knots (Xiong et al. 2007)}
\usage{
warp_knots(n_knots = 3, knot_positions = NULL)
}
\arguments{
\item{n_knots}{number of interior knots \eqn{K \ge 1} (default 3)}

\item{knot_positions}{optional numeric vector of \eqn{K} knot positions
strictly inside \eqn{(0,1)}, in increasing order.
When \code{NULL} (default), knots are placed uniformly at
\eqn{1/(K+1), 2/(K+1), \ldots, K/(K+1)}.}
}
\value{
warp specification string, e.g. \code{"knots(3)"} or
  \code{"knots(0.25:0.5:0.75)"}
}
\description{
Implements the non-stationary input warping of Xiong, Chen, Apley & Ding (2007,
\emph{Int. J. Numer. Meth. Engng}).  The domain \eqn{[0,1]} is split into
\eqn{K+1} intervals by \eqn{K} interior knots, each carrying a learnable
positive slope \eqn{s_k = \exp(r_k)}.  The warp is:
\deqn{w(x) = \sum_{j<k} s_j (t_{j+1}-t_j) + s_k (x-t_k)}
for \eqn{x \in [t_k, t_{k+1})}, giving a continuous, monotone
piecewise-linear function with \eqn{K+1} free parameters.

This is the same construction as the \code{knots} argument in
\pkg{DiceKriging}.
}
\references{
Xiong, Y., Chen, W., Apley, D. & Ding, X. (2007).
  A non-stationary covariance-based Kriging method for metamodelling
  in engineering design.
  \emph{International Journal for Numerical Methods in Engineering},
  71(6), 733--756.
}
\seealso{
\code{\link{WarpKriging}}
}
