Script for area-to-point kriging (A2PK)

This script shows you how to use the function A2PK.m

The same examples as in ./exemples/ folder are given below with less details.

addpath('./FastGaussianSimulation');
addpath('./functions');

Unconditional simulation

Generating input data

covar.model='spherical'; covar.range=[20 20]; covar.var=1; covar.azimuth=0;
covar = covarIni(covar);
z.x=1:100;
z.y=1:100;
[z.X,z.Y] = meshgrid(z.x, z.y);
z.nxy = numel(z.X);
z.s = [numel(z.x) numel(z.y)];
z.true = FGS(z, covar);
z.true = z.true{1};
Z.dx=4;Z.dy=4;
Z.x = mean(z.x(1:Z.dx)):Z.dx:mean(z.x(end-Z.dx+1:end));
Z.y = mean(z.y(1:Z.dy)):Z.dy:mean(z.y(end-Z.dy+1:end));
[Z.X,Z.Y] = meshgrid(Z.x, Z.y);
G = zeros(numel(Z.X),z.nxy);
[~,id] = min(bsxfun(@minus,Z.X(:), z.X(:)').^2 + bsxfun(@minus, Z.Y(:), z.Y(:)').^2);
G(sub2ind(size(G), id, 1:z.nxy)) = 1/(Z.dx*Z.dy);
Z.true = reshape(G * z.true(:), numel(Z.y), numel(Z.x));
z.pt = sampling_pt(z,z.true,2,0);
n_real=1;

Run function

[zcs] = A2PK(z.x,z.y,z.pt,Z.true,G,covar,n_real);

Figure

figure('pos',[0 0 800 330]); c_axis=[-3 3];

subplot(1,2,1); imagesc(z.x, z.y, z.true); caxis(c_axis); title('True fine-scale');

subplot(1,2,2);imagesc(z.x, z.y, zcs); caxis(c_axis); title('Conditional realization');

Conditional Simulation

z.pt = sampling_pt(z,z.true,2,5);

Run function

[zcs,zh,S] = A2PK(z.x,z.y,z.pt,Z.true,G,covar,n_real);

Figure

figure('pos',[0 0 800 800]); c_axis=[-3 3];

subplot(2,2,1); hold on; imagesc(z.x, z.y, z.true); scatter(z.pt.x,z.pt.y,[],z.pt.d,'s','filled','MarkerEdgeColor','k'); axis tight; caxis(c_axis); title('True fine-scale'); axis ij

subplot(2,2,2); imagesc(z.x, z.y, zcs); caxis(c_axis); title('Conditional realization');

subplot(2,2,3); imagesc(z.x, z.y, zh); caxis(c_axis); title('Kriging estimation');

subplot(2,2,4); imagesc(z.x, z.y, S); title('Variance of estimation');