# Interpolation by Kriging Simple and ordinary Kriging interpolation and interpolating function. ```r kriging(u, v, u0, type = c("ordinary", "simple")) ``` ## Arguments - `u`: an `nxm`-matrix of n points in the m-dimensional space. - `v`: an `n`-dim. (column) vector of interpolation values. - `u0`: a `kxm`-matrix of k points in `R^m` to be interpolated. - `type`: character; values `simple' or `ordinary'; no partial matching. ## Details Kriging is a geo-spatial estimation procedure that estimates points based on the variations of known points in a non-regular grid. It is especially suited for surfaces. ## Note In the literature, different versions and extensions are discussed. ## Returns `kriging` returns a `k`-dim. vektor of interpolation values. ## References Press, W. H., A. A. Teukolsky, W. T. Vetterling, and B. P. Flannery (2007). Numerical recipes: The Art of Scientific Computing (3rd Ed.). Cambridge University Press, New York, Sect. 3.7.4, pp. 144-147. ## See Also `akimaInterp`, `barylag2d`, package `kriging` ## Examples ```r ## Interpolate the Saddle Point function f <- function(x) x[1]^2 - x[2]^2 # saddle point function set.seed(8237) n <- 36 x <- c(1, 1, -1, -1, runif(n-4, -1, 1)) # add four vertices y <- c(1, -1, 1, -1, runif(n-4, -1, 1)) u <- cbind(x, y) v <- numeric(n) for (i in 1:n) v[i] <- f(c(x[i], y[i])) kriging(u, v, c(0, 0)) #=> 0.006177183 kriging(u, v, c(0, 0), type = "simple") #=> 0.006229557 ## Not run: xs <- linspace(-1, 1, 101) # interpolation on a diagonal u0 <- cbind(xs, xs) yo <- kriging(u, v, u0, type = "ordinary") # ordinary kriging ys <- kriging(u, v, u0, type = "simple") # simple kriging plot(xs, ys, type = "l", col = "blue", ylim = c(-0.1, 0.1), main = "Kriging interpolation along the diagonal") lines(xs, yo, col = "red") legend( -1.0, 0.10, c("simple kriging", "ordinary kriging", "function"), lty = c(1, 1, 1), lwd = c(1, 1, 2), col=c("blue", "red", "black")) grid() lines(c(-1, 1), c(0, 0), lwd = 2) ## End(Not run) ## Find minimum of the sphere function f <- function(x, y) x^2 + y^2 + 100 v <- bsxfun(f, x, y) ff <- function(w) kriging(u, v, w) ff(c(0, 0)) #=> 100.0317 ## Not run: optim(c(0.0, 0.0), ff) # $par: [1] 0.04490075 0.01970690 # $value: [1] 100.0291 ezcontour(ff, c(-1, 1), c(-1, 1)) points(0.04490075, 0.01970690, col = "red") ## End(Not run) ```

kriging function