GP example

UaUtilities/GaussianProcessRegressionExample2D.m

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+
+
+%%
+%
+% Example of how to use Gaussian Process Regression model on two-dimentional (spatial) data
+%
+
+
+
+
+nx=50;  ny=nx; 
+x=linspace(-5,5,nx); 
+y=linspace(-5,5,ny); 
+[X,Y]=ndgrid(x,x) ;
+
+Z=exp(-X.*X-Y.*Y) + 0.01*randn(nx,ny)  ;
+
+
+
+
+xy=[X(:) Y(:)] ; z=Z(:); 
+
+tic
+%gprMdl=fitrgp(xy,z,PredictorNames={'x','y'},ResponseName="z");
+gprMdl=fitrgam(xy,z,PredictorNames={'x','y'},ResponseName="z",FitStandardDeviation=true,OptimizeHyperparameters="auto");
+toc
+
+% Here the prediction is evaluated at the data locations
+tic
+[zpred,~,zint] = predict(gprMdl,xy);
+toc
+
+Zpred=reshape(zpred,nx,ny);
+
+
+
+
+figure(100)
+surf(x,y,Z)
+title("data")
+
+
+figure(150)
+surf(x,y,Zpred)
+title("fit to data")
+
+Residuals=Zpred-Z; 
+
+figure(200) ; surf(x,y,Residuals)  ; title("Residuals")
+
+
+figure(300) ; histogram(Residuals)
+
+
+%%