pracma (version 1.8.8)

kriging: Interpolation by Kriging

Description

Simple and ordinary Kriging interpolation and interpolating function.

Usage

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.

Value

• kriging returns a k-dim. vektor of interpolation values.

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.

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. http://apps.nrbook.com/empanel/index.html?pg=144#

See Also

akimaInterp, barylag2d, package kriging

Examples

##  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

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)

##  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
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")