Added a test problem

MatlabGP/+BO/argmax.m

@@ -9,7 +9,6 @@
 
 [x,R] = fmincon(@(x) FF(Z,x),x0,[],[],[],[],lb,ub,[],opts);
 
-
 %[x,R] = VSGD(@(x) FF(Z,x),x0,'lr',0.03,'lb',lb,'ub',ub,'gamma',0.01,'iters',100,'tol',1*10^(-3));
 
 R = -1*R;

MatlabGP/+kernels/Matern12.m

@@ -0,0 +1,27 @@
+classdef Matern12<kernels.Kernel
+
+    properties
+        theta
+    end
+
+    methods
+
+        function obj = Matern12(scale,theta)
+            obj.scale = scale;
+            obj.scales{1} = scale;
+            obj.theta = theta;
+            obj.thetas{1} = theta;
+            obj.kernels{1} = obj;
+            obj.w.map = 'none';
+            obj.warping{1} = obj.w;
+        end
+
+        function [K] = forward_(obj,x1,x2,theta)
+
+            d = obj.dist(x1./theta,x2./theta);
+
+            K = exp(-d);
+        end
+
+    end
+end

MatlabGP/+kernels/Matern32.m

@@ -0,0 +1,29 @@
+classdef Matern32<kernels.Kernel
+
+    properties
+        theta
+    end
+
+    methods
+
+        function obj = Matern32(scale,theta)
+            obj.scale = scale;
+            obj.scales{1} = scale;
+            obj.theta = theta;
+            obj.thetas{1} = theta;
+            obj.kernels{1} = obj;
+            obj.w.map = 'none';
+            obj.warping{1} = obj.w;
+        end
+
+        function [K] = forward_(obj,x1,x2,theta)
+
+            d = obj.dist(x1./theta,x2./theta);
+
+            K = (1 + sqrt(3)*d);
+
+            K = K.*exp(-sqrt(3)*d);
+        end
+
+    end
+end

MatlabGP/GP.m

@@ -151,7 +151,7 @@
                 res = obj.Y - obj.mean.eval(obj.X);
             end
 
-            kkp = pinv(obj.K,0);
+            kkp = pinv(obj.K,1*10^(-4));
 
             sigp = sqrt(abs(res'*kkp*res./(size(obj.Y,1))));
 
@@ -165,7 +165,7 @@
 
             obj.K = obj.K + diag(0*xx(:,1)+obj.kernel.signn);
 
-            obj.Kinv = pinv(obj.K,0);
+            obj.Kinv = pinv(obj.K,1*10^(-4));
 
             obj.alpha = obj.Kinv*(res);
 
@@ -329,7 +329,7 @@
 
             obj.mean = obj.mean.setHPs(theta(1:ntm));
             obj.kernel = obj.kernel.setHPs(theta(ntm+1:end));
-            obj = obj.condition(obj.X,obj.Y);
+            obj = obj.condition(obj.X,obj.Y,obj.lb_x,obj.ub_x);
 
         end
 

MatlabGP/StressedPlate.m

@@ -0,0 +1,16 @@
+function [y] = StressedPlate(x,i)
+
+T = 25000;
+E = 210*10^9;
+nu = 0.3;
+rho = 7800;
+
+switch i
+    case 1
+        y = sqrt(1./(rho*x(:,3))).*sqrt(((E*x(:,3).^3)./(12*(1-nu))).*((pi^2)./x(:,1).^2 + (pi^2)./x(:,2).^2).^2 + T*((pi^2)./x(:,1).^2 + (pi^2)./x(:,2).^2)) - 120;
+    case 2
+        y = sqrt(1./(rho*x(:,3))).*sqrt(((E*x(:,3).^3)./(12*(1-nu))).*((pi^2)./x(:,1).^2 + (pi^2)./x(:,2).^2).^2) - 120;
+end
+
+
+end

MatlabGP/TestAppliedAviationProblem.asv

@@ -0,0 +1,110 @@
+
+clear all
+clc
+
+lb = [0.5 0.5 2.5*10^(-3)];
+ub = [1.5 1.5 7.5*10^(-3)];
+
+xx = lb + (ub - lb).*lhsdesign(50000,3);
+yy = StressedPlate(xx,1);
+
+x1 = lb + (ub - lb).*lhsdesign(5,3);
+y1 = StressedPlate(x1,1);
+
+x2 = [lb + (ub - lb).*lhsdesign(100,3)];
+y2 = StressedPlate(x2,2);
+
+x{1} = x1;
+x{2} = x2;
+
+y{1} = y1;
+y{2} = y2;
+
+%%
+ma = means.linear([1 1 1 1]);
+mb = means.linear([1 1 1]);
+
+a = kernels.Matern52(1,[0.1 0.2 0.1 0.3]);%.periodic(1,10);
+b = kernels.EQ(1,[0.2 0.2 0.2]);
+a.signn = 0;
+b.signn = 0;
+
+%%
+tic
+for i = 1:2
+    Z{i} = GP(mb,b);
+    Z{i} = Z{i}.condition(x{i},y{i},lb,ub);
+    Z{i} = Z{i}.train();
+end
+toc
+
+%%
+tic
+MF = NLMFGP(Z,ma,a);
+MF = MF.condition();
+MF = MF.train();
+toc
+
+
+%%
+figure
+hold on
+utils.plotLineOut(Z{1},(lb+ub)/2,1,'color','r')
+utils.plotLineOut(Z{2},(lb+ub)/2,1,'color','b')
+
+%%
+
+figure
+hold on
+utils.plotLineOut(MF,(lb+ub)/2,1)
+
+%%
+
+1 - mean((yy - Z{1}.eval_mu(xx)).^2)./var(yy)
+max(abs(yy - Z{1}.eval_mu(xx)))./std(yy)
+
+1 - mean((yy - MF.eval_mu(xx)).^2)./var(yy)
+max(abs(yy - MF.eval_mu(xx)))./std(yy)
+
+%%
+for jj = 1:40
+
+    [xn,Rn] = BO.argmax(@BO.maxVAR,MF);
+
+    x{1} = [x{1}; xn];
+    x{2} = [x{2}; xn];
+
+    y{1} = [y{1}; StressedPlate(xn,1)];
+    y{2} = [y{2}; StressedPlate(xn,2)];
+
+    for ii = 1:2
+        %Z{ii} = GP(mb,b);
+        Z{i} = Z{i}.condition(x{i},y{i},lb,ub);
+        %Z{ii} = Z{ii}.train();
+    end
+
+    MF.GPs = Z;
+    MF = MF.condition();
+    MF = MF.train();
+
+    R2z(jj) = 1 - mean((yy - Z{1}.eval_mu(xx)).^2)./var(yy);
+    RMAEz(jj) = max(abs(yy - Z{1}.eval_mu(xx)))./std(yy);
+
+    R2MF(jj) = 1 - mean((yy - MF.eval_mu(xx)).^2)./var(yy);
+    RMAEMF(jj) = max(abs(yy - MF.eval_mu(xx)))./std(yy);
+
+    figure(1)
+    clf(1)
+    hold on
+    plot(1:jj,R2z)
+    plot(1:jj,R2MF)
+
+    figure(2)
+    clf(2)
+    hold on
+    plot(1:jj,RMAEz)
+    plot(1:jj,RMAEMF)
+
+    drawnow
+
+end

MatlabGP/TestAppliedAviationProblem.m

@@ -0,0 +1,107 @@
+
+clear all
+clc
+
+lb = [0.5 0.5 2.5*10^(-3)];
+ub = [1.5 1.5 7.5*10^(-3)];
+
+xx = lb + (ub - lb).*lhsdesign(50000,3);
+yy = StressedPlate(xx,1);
+
+x1 = lb + (ub - lb).*lhsdesign(5,3);
+y1 = StressedPlate(x1,1);
+
+x2 = [lb + (ub - lb).*lhsdesign(20,3)];
+y2 = StressedPlate(x2,2);
+
+x{1} = x1;
+x{2} = x2;
+
+y{1} = y1;
+y{2} = y2;
+
+%%
+ma = means.linear([1 1 1 1]);
+mb = means.linear([1 1 1]);
+
+a = kernels.EQ(1,[0.1 0.2 0.1 0.3]);%.periodic(1,10);
+b = kernels.EQ(1,[0.2 0.2 0.2]);
+a.signn = 0;
+b.signn = 0;
+
+%%
+tic
+for i = 1:2
+    Z{i} = GP(mb,b);
+    Z{i} = Z{i}.condition(x{i},y{i},lb,ub);
+    Z{i} = Z{i}.train();
+end
+toc
+
+%%
+tic
+MF = NLMFGP(Z,ma,a);
+MF = MF.condition();
+MF = MF.train();
+toc
+
+
+%%
+figure
+hold on
+utils.plotLineOut(Z{1},(lb+ub)/2,1,'color','r')
+utils.plotLineOut(Z{2},(lb+ub)/2,1,'color','b')
+
+%%
+
+figure
+hold on
+utils.plotLineOut(MF,(lb+ub)/2,1)
+
+%%
+
+1 - mean((yy - Z{1}.eval_mu(xx)).^2)./var(yy)
+max(abs(yy - Z{1}.eval_mu(xx)))./std(yy)
+
+1 - mean((yy - MF.eval_mu(xx)).^2)./var(yy)
+max(abs(yy - MF.eval_mu(xx)))./std(yy)
+
+%%
+for jj = 1:50
+
+    [xn,Rn] = BO.argmax(@BO.maxVAR,MF);
+
+    x{1} = [x{1}; xn];
+    x{2} = [x{2}; xn];
+
+    y{1} = [y{1}; StressedPlate(xn,1)];
+    y{2} = [y{2}; StressedPlate(xn,2)];
+
+    for ii = 1:2
+        Z{ii} = Z{ii}.condition(x{ii},y{ii},lb,ub);
+    end
+
+    MF.GPs = Z;
+    MF = MF.condition();
+
+    R2z(jj) = 1 - mean((yy - Z{1}.eval_mu(xx)).^2)./var(yy);
+    RMAEz(jj) = max(abs(yy - Z{1}.eval_mu(xx)))./std(yy);
+
+    R2MF(jj) = 1 - mean((yy - MF.eval_mu(xx)).^2)./var(yy);
+    RMAEMF(jj) = max(abs(yy - MF.eval_mu(xx)))./std(yy);
+
+    figure(1)
+    clf(1)
+    hold on
+    plot(1:jj,R2z)
+    plot(1:jj,R2MF)
+
+    figure(2)
+    clf(2)
+    hold on
+    plot(1:jj,RMAEz)
+    plot(1:jj,RMAEMF)
+
+    drawnow
+
+end