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An example presenting an application of Ordinary Kriging.
Loading packages
library( KRIG )
Defining objective function to approach.
m<-100 XLim<-c( -3, 6 ) x<-seq( XLim[1], XLim[2], length.out = m ) f<-function(x){ return( 1 + exp(-x^2) + 0.4 * exp(-(x-2)^2 ) - 0.5 * exp( -(x-4)^2 ) ) } z<-sapply( x, f )
Sampling function values.
n<-10 X<-matrix( runif( n, XLim[1], XLim[2] ), n, 1 ) Z<-matrix( sapply( X, f ), n, 1 ) m<-100 YLim<-c(-6,8) Y<-matrix( seq( YLim[1], YLim[2], length.out = m ), m, 1 )
Kernel definition.
s<-0.1 t<-1 Kern<-function( x, y ) { h<-sqrt( sum( ( x - y )^2 ) ) return( gaussian_kernel( h, s, t ) ) }
Computing Kriging.
K = Kov( X, X, Kern, TRUE ) k = Kov( Y, X, Kern ); KRIG<-Krig( Z = Z, K = K, k = k, G = matrix( 0, 1, 1), g = matrix( 0, 1, 1), type = "ordinary", cinv = 'syminv' )
Plotting results.
ymin<-min( z, KRIG$Z[,1], Z[,1] ) ymax<-max( z, KRIG$Z[,1], Z[,1] ) plot( x, z, type = 'l', lwd = 2, col='gold', ylim = c( ymin, ymax ), xlim = YLim ) points( Y, KRIG$Z[,1], col='darkgreen', type = 'l', lwd = 2 ) points( X, Z[,1], col = 'dodgerblue3', pch = 16, cex = 1.2 )
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