## 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)
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