clear all;
close all;
clc;

rng(0,'twister'); % For reproducibility

% Generate data with an exponential trend
x = (0:0.5:5)';
y = 2*exp(-0.2*x) + 0.1*randn(size(x));
xpred = (0:0.02:5)';

gprMdl0 = fitrgp(x,y, 'KernelFunction','ardsquaredexponential','Sigma',1e-02,...
       'FitMethod','exact','PredictMethod','exact');
ypred0 = predict(gprMdl0,xpred);

figure
plot(x,y,'b.');
hold on;
plot(xpred,ypred0,'r','LineWidth',1.5);
xlabel('x');
ylabel('y');
legend('Data','GPR predictions');
hold off

gprMdl1 = fitrgp(x,y, 'KernelFunction','ardsquaredexponential','Sigma',0.5e-01,...
       'FitMethod','exact','PredictMethod','exact');
ypred1 = predict(gprMdl1,xpred);

figure
plot(x,y,'b.');
hold on;
plot(xpred,ypred1,'r','LineWidth',1.5);
xlabel('x');
ylabel('y');
legend('Data','GPR predictions');
hold off

gprMdl2 = fitrgp(x,y, 'KernelFunction','ardsquaredexponential',...
       'FitMethod','exact','PredictMethod','exact');
ypred2 = predict(gprMdl2,xpred);

figure
plot(x,y,'b.');
hold on;
plot(xpred,ypred2,'r','LineWidth',1.5);
xlabel('x');
ylabel('y');
legend('Data','GPR predictions');
hold off