Add plots to the Octave code

src/octave/DiffusionMap3dOrientations.m

@@ -25,5 +25,6 @@
     save '../../artifacts/Lambda.mat' Lambda -text;
     save '../../artifacts/c0.mat' c0 -text;
     save '../../artifacts/c.mat' c -text;
+    PlotResults(Ps,Lambda,Rotation_Axis)
 end
 

src/octave/PlotResults.m

@@ -0,0 +1,112 @@
+function PlotResults(Ps,Lambda,Rotation)
+    Plot_Eigenvalue_Eigenvector(Ps,Lambda)
+    Plot_Individual_EV(Ps,Lambda)
+    Plot_Diffusion_Statistics(Ps)
+    Plot_Corr_Ps(Ps);
+    Plot_Psi234_ColorRot(Ps,Lambda,Rotation,'Axis')
+end
+function Plot_Eigenvalue_Eigenvector(Ps,Lambda)
+    figure
+    set(gca,'NextPlot','replacechildren');
+    subplot(211)
+    imagesc(Ps)
+    colorbar
+    title('Diffusion map eigenfunctions {\psi_i}')
+    subplot(212)
+    plot(Lambda,'-*')
+    colorbar
+    title('Diffusion map eigenvalues')
+end
+function Plot_Diffusion_Statistics(Ps)
+    figure
+    set(gca,'NextPlot','replacechildren');
+    subplot(221)
+    bar(Ps(:));
+    title(['First 10 \psi, min=' num2str(min(Ps(:))) ...
+        ', Max=' num2str(max(Ps(:)))]);
+    PsNorm=Ps(:,1).^2;
+    for cntr=2:10
+        PsNorm=PsNorm+Ps(:,cntr).^2;
+    end
+    PsNorm=sqrt(PsNorm);
+    subplot(222)
+    bar(PsNorm);
+    title(['10-element norm, min=' num2str(min(PsNorm)) ...
+        ', Max=' num2str(max(PsNorm))]);
+    subplot(223)
+    histfit(PsNorm,500);
+    title('10-element norm histogram');
+    subplot(224)
+    Index=(1:size(PsNorm,1))';
+    Index=2*pi*Index/max(Index);
+    polar(Index,PsNorm,'b');
+    title('10-element norm polar histogram');
+    hold on
+    polar(Index,mean(PsNorm)*ones(size(PsNorm)),'r--');
+    hold off
+end
+function Plot_Individual_EV(Ps,Lambda)
+    figure
+    set(gca,'NextPlot','replacechildren');
+    for cntr=1:9
+        subplot(3,3,cntr)
+        plot(Ps(:,cntr+1).*Lambda(cntr+1))
+        title(['\psi_' num2str(cntr+1)])
+    end
+end
+function Plot_Psi234_ColorRot(Ps,Lambda,Rot,Text)
+    for cntr=1:size(Rot,1)
+        figure
+        set(gca,'NextPlot','replacechildren');
+
+        subplot(221)
+        scatter(Ps(:,2).*Lambda(2),Ps(:,3).*Lambda(3),20,Rot(cntr,:))
+        title(['Phase plane: \psi_2 vs. \psi_3 - Color-coded by ' ...
+            Text ' ' num2str(cntr)]);
+        colorbar
+
+        subplot(222)
+        scatter(Ps(:,2).*Lambda(2),Ps(:,4).*Lambda(4),20,Rot(cntr,:))
+        title(['Phase plane: \psi_2 vs. \psi_4 - Color-coded by ' ...
+            Text ' ' num2str(cntr)]);
+        colorbar
+
+        subplot(223)
+        scatter(Ps(:,3).*Lambda(3),Ps(:,4).*Lambda(4),20,Rot(cntr,:))
+        title(['Phase plane: \psi_3 vs. \psi_4 - Color-coded by ' ...
+            Text ' ' num2str(cntr)]);
+        colorbar
+
+        subplot(224)
+        scatter3(Ps(:,2).*Lambda(2),Ps(:,3).*Lambda(3),...
+            Ps(:,4).*Lambda(4),20,Rot(cntr,:))
+        title(['Phase plane: \psi_2-\psi_3-\psi_4 - Color-coded by ' ...
+            Text ' ' num2str(cntr)]);
+        colorbar
+    end
+    drawnow;
+end
+function Plot_Corr_Ps(Ps)
+    figure
+    subplot(4,1,1)
+    plot(real(xcov(Ps(:,2),Ps(:,2))))
+    title('Covariance of \psi_2 and \psi_2');
+    legend('Auto correlation')
+    ylim([-0.2 1.1])
+    subplot(4,1,2)
+    plot(real(xcov(Ps(:,2),Ps(:,3))))
+    title('Covariance of \psi_2 and \psi_3');
+    legend('Cross correlation')
+    ylim([-0.2 1.1])
+    subplot(4,1,3)
+    plot(real(xcov(Ps(:,2),Ps(:,4))))
+    title('Covariance of \psi_2 and \psi_4');
+    legend('Cross correlation')
+    ylim([-0.2 1.1])
+    subplot(4,1,4)
+    plot(real(xcov(Ps(:,3),Ps(:,4))))
+    title('Covariance of \psi_3 and \psi_4');
+    legend('Cross correlation')
+    ylim([-0.2 1.1])
+    drawnow;
+end