kriging: Interpolation by Kriging

In pracma: Practical Numerical Math Functions

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.

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.

Value

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

Note

In the literature, different versions and extensions are discussed.

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

##  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)

pracma documentation built on Nov. 10, 2023, 1:14 a.m.