PbDlib v1.0

demos/demo_DMP01.m

@@ -155,4 +155,4 @@ view(180,-90);
 
 %print('-dpng','-r600','graphs/demo_DMP01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP02.m

@@ -35,7 +35,7 @@ addpath('./m_fcts/');
 
 %% Parameters
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-model.nbStates = 5; %Number of activation functions (i.e., number of states in the GMM)
+model.nbStates = 8; %Number of activation functions (i.e., number of states in the GMM)
 model.nbVar = 1; %Number of variables for the radial basis functions [s] (decay term)
 model.nbVarPos = 2; %Number of motion variables [x1,x2] 
 model.kP = 50; %Stiffness gain
@@ -80,7 +80,7 @@ model = init_GMM_timeBased(sIn, model);
 
 %Set Sigma 
 for i=1:model.nbStates
-	model.Sigma(:,:,i) = 1E-2; %Heuristic setting of covariance
+	model.Sigma(:,:,i) = 1E-3; %Heuristic setting of covariance
 end
 
 %Compute activation
@@ -243,4 +243,4 @@ view(180,-90);
 
 %print('-dpng','-r100','graphs/demo_DMP02.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR01.m

@@ -141,4 +141,4 @@ view(180,-90);
 
 %print('-dpng','graphs/demo_DMP_GMR01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR02.m

 function demo_DMP_GMR02
 % Enhanced dynamic movement primitive (DMP) model trained with EM by using a Gaussian mixture 
 % model (GMM) representation, with full covariance matrices coordinating the different variables 
-% in the feature space. After learning (i.e., autonomous organization of the basis functions (position 
-% and spread), Gaussian mixture regression (GMR) is used to regenerate the nonlinear force profile. 
+% in the feature space. After learning (i.e., autonomous organization of the basis functions 
+% (position and spread), Gaussian mixture regression (GMR) is used to regenerate the nonlinear force profile. 
 %
 % If this code is useful for your research, please cite the related publication:
 % @incollection{Calinon19chapter,
@@ -139,4 +139,4 @@ view(180,-90);
 
 %print('-dpng','graphs/demo_DMP_GMR02.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR03.m

@@ -139,4 +139,4 @@ view(180,-90);
 
 %print('-dpng','graphs/demo_DMP_GMR03.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR04.m

@@ -154,4 +154,4 @@ view(180,-90);
 
 %print('-dpng','graphs/demo_DMP_GMR04.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR_LQR01.m

@@ -54,8 +54,8 @@ nbData = 200; %Number of datapoints in a trajectory
 nbSamples = 4; %Number of demonstrations
 
 %Canonical system parameters
-A = kron([0 1; 0 0], eye(model.nbVarPos)); %See Eq. (5.1.1) in doc/TechnicalReport.pdf
-B = kron([0; 1], eye(model.nbVarPos)); %See Eq. (5.1.1) in doc/TechnicalReport.pdf
+A = kron([0 1; 0 0], eye(model.nbVarPos)); 
+B = kron([0; 1], eye(model.nbVarPos)); 
 C = kron([1,0],eye(model.nbVarPos));
 %Discretize system (Euler method)
 Ad = A*model.dt + eye(size(A));
@@ -64,7 +64,7 @@ Bd = B*model.dt;
 R = eye(model.nbVar) * model.rFactor;
 R = kron(eye(nbData),R);
 
-%Create transformation matrix to compute xhat = x + dx*kV/kP + ddx/kP, see Eq. (4.0.2) in doc/TechnicalReport.pdf
+%Create transformation matrix to compute xhat = x + dx*kV/kP + ddx/kP
 K1d = [1, model.kV/model.kP, 1/model.kP];
 K = kron(K1d,eye(model.nbVarPos));
 
@@ -103,10 +103,10 @@ model = EM_tensorGMM(DataDMP, model);
 %Task-adaptive spring-damper attractor path retrieval
 r(n).p(1).A = eye(model.nbVar);
 r(n).p(1).b = s(n).p(1).b + [0; 0; 5]; %Offset added to test generalization capability
-[r(n).Mu, r(n).Sigma] = productTPGMM0(model, r(n).p); %See Eq. (6.0.5), (6.0.6) and (6.0.7) in doc/TechnicalReport.pdf
+[r(n).Mu, r(n).Sigma] = productTPGMM0(model, r(n).p); 
 r(n).Priors = model.Priors;
 r(n).nbStates = model.nbStates;
-[r(1).currTar, r(1).currSigma] = GMR(r(n), sIn, 1, 2:model.nbVar); %See Eq. (3.0.2) to (3.0.5) in doc/TechnicalReport.pdf
+[r(1).currTar, r(1).currSigma] = GMR(r(n), sIn, 1, 2:model.nbVar); 
 
 %LQR tracking (discrete version)
 Q = zeros(model.nbVarPos*2, model.nbVarPos*2);
@@ -175,4 +175,4 @@ view(180,-90);
 
 %print('-dpng','graphs/demo_DMP_GMR_LQR01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_DMP_GMR_illustr01.m

@@ -93,7 +93,7 @@ end
 
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('PaperPosition',[0 0 10 4.0],'position',[10,10,1300,450],'color',[1 1 1]); 
+figure('PaperPosition',[0 0 10 4.0],'position',[10,10,2300,900],'color',[1 1 1]); 
 clrmap = lines(model.nbStates);
 
 %Activation of the basis functions
@@ -149,7 +149,7 @@ set(gca,'xtick',[],'ytick',[sIn(end),sIn(1)],'yticklabel',{'0','1'});
 xlabel('$t$','fontsize',16,'interpreter','latex'); 
 ylabel('$s$','fontsize',16,'interpreter','latex'); 
 
-%print('-dpng','-r300','graphs/DMP_GMR01.png');
+%print('-dpng','graphs/DMP_GMR01.png');
 pause;
 close all;
 end
@@ -184,4 +184,4 @@ function hg = displaySpring(x,colTmp)
   %h = [h draw2DArrow(msh(:,25)+[0.5;-0.5], [1.2;1.1], [.7 0 0])];
   hg = [hg plot(x(1,1),x(2,1),'.','markersize',15,'color',colTmp)];
   hg = [hg plot(x(1,2),x(2,2),'.','markersize',15,'color',colTmp)];
-end
+end
\ No newline at end of file

demos/demo_GMM01.m

@@ -70,4 +70,4 @@ axis equal; set(gca,'Xtick',[]); set(gca,'Ytick',[]);
 
 %print('-dpng','graphs/demo_GMM01.png');
 %pause;
-%close all;
+%close all;
\ No newline at end of file

demos/demo_GMM_MFA01.m

@@ -80,6 +80,6 @@ for i=1:2
 	xlabel(['x_' num2str((i-1)*2+1)]); ylabel(['x_' num2str(i*2)]);
 end
 
-%print('-dpng','graphs/demo_MFA01.png');
-%pause;
-%close all;
+%print('-dpng','graphs/demo_GMM_MFA01.png');
+pause;
+close all;
\ No newline at end of file

demos/demo_GMM_MPPCA01.m

@@ -78,6 +78,6 @@ for i=1:2
 	xlabel(['x_' num2str((i-1)*2+1)]); ylabel(['x_' num2str(i*2)]);
 end
 
-%print('-dpng','graphs/demo_MPPCA01.png');
-%pause;
-%close all;
+%print('-dpng','graphs/demo_GMM_MPPCA01.png');
+pause;
+close all;
\ No newline at end of file

demos/demo_GMM_logGMM01.m

 function demo_GMM_logGMM01
-% Multivariate lognormal mixture model parameters estimation with EM algorithm
+% Multivariate lognormal mixture model parameters estimation with EM algorithm.
 %
 % If this code is useful for your research, please cite the related publication:
 % @article{Calinon16JIST,
@@ -31,7 +31,6 @@ function demo_GMM_logGMM01
 % You should have received a copy of the GNU General Public License
 % along with PbDlib. If not, see <http://www.gnu.org/licenses/>.
 
-
 addpath('./m_fcts/');
 
 
@@ -42,9 +41,6 @@ model.nbVar = 2; %Number of variables [x1,x2]
 nbData = 500; %Number of datapoints
 
 
-figure('PaperPosition',[0 0 24 4],'position',[10,10,1000,600]); hold on;
-% for nb=1:20
-
 %% Generate data
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % model.Mu(:,1) = [1; 0.5];
@@ -69,12 +65,8 @@ end
 
 %% Parameters estimation
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% model.Mu
-% model.Sigma
 model = init_GMM_kmeans(Data, model);
 model = EM_logGMM(Data, model);
-% model.Mu
-% model.Sigma
 
 nbX = 100;
 [X0,Y0] = meshgrid(linspace(min(Data(1,:)),max(Data(1,:)),nbX), linspace(min(Data(2,:)),max(Data(2,:)),nbX));
@@ -91,17 +83,11 @@ hmix = sum(h,1);
 
 %% Plot
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-clf; hold on; axis off;
-for i=1:model.nbStates
-	%plot(DataIn, h(i,:), '-','color',[.7 .7 .7]);
-end
+figure('PaperPosition',[0 0 24 4],'position',[10,10,1600,900]); hold on; hold on; axis off;
 pcolor(X0,Y0,reshape(hmix,nbX,nbX)); shading flat;
-
 plot(Data(1,:), Data(2,:), '.','markersize',6,'color',[0 0 0]);
 axis([min(Data(1,:)), max(Data(1,:)), min(Data(2,:)), max(Data(2,:))]); 
-% pause
-% end %nb
 
 %print('-dpng','graphs/demo_logGMM01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_GMM_logNormal01.m

 function demo_GMM_logNormal01
-%Conditional probability with multivariate log-normal distribution
+% Conditional probability with multivariate log-normal distribution
 %
 % If this code is useful for your research, please cite the related publication:
 % @article{Calinon16JIST,
@@ -42,21 +42,15 @@ model0.nbStates = 1;
 model0.Priors = 1;
 model = model0;
 
-figure('position',[10 10 1300 500],'color',[1 1 1]);
-% disp('Press enter to regenerate data...');
-% for nb=1:5
-	
 	
 %% Multivariate normal distribution
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 model0.Mu = zeros(model0.nbVar,1);
 %model0.Mu = rand(model0.nbVar,1)*10;
 
-%if nb<2
 V0 = rand(model0.nbVar,1);
 model0.Sigma = V0*V0' + diag(rand(model0.nbVar,1))*1E-1;
 [V,D] = eigs(model0.Sigma);
-%end
 Data0 = V*D^.5 * randn(model0.nbVar,nbData) + repmat(model0.Mu,1,nbData);
 
 
@@ -86,7 +80,8 @@ DataOut = exp(DataOut0);
 
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-clf;
+figure('position',[10 10 2300 1200],'color',[1 1 1]);
+
 %Normal distribution
 subplot(1,2,1); hold on; grid on; title('Normal distribution');
 plot(Data0(1,:), Data0(2,:), '.','markersize',8,'color',[.7 .7 .7]);
@@ -102,10 +97,8 @@ set(gca,'xtick',model0.Mu(1),'ytick',model0.Mu(2));
 % X = R * [cos(t); sin(t)] + repmat(model0.Mu, 1, nbDrawingSeg);
 % gaussPDF(X, model0.Mu, model0.Sigma)
 
-
 %Log-normal distribution
 subplot(1,2,2); hold on; grid on; title('Log-normal distribution');
-
 nbX = 50;
 [X0,Y0] = meshgrid(linspace(min(Data(1,:)),max(Data(1,:)),nbX), linspace(min(Data(2,:)),max(Data(2,:)),nbX));
 X = reshape(X0,1,nbX^2);
@@ -129,9 +122,7 @@ plot(model.Mu(1,:), model.Mu(2,:), '.', 'markersize', 6, 'color', [.4 0 0]);
 axis equal; axis([min(Data(1,:)), max(Data(1,:)), min(Data(2,:)), max(Data(2,:))]); 
 xlabel('exp(x_1)'); ylabel('exp(x_2)');
 set(gca,'xtick',exp(model0.Mu(1)),'ytick',exp(model0.Mu(2)));
+%print('-dpng','graphs/demo_GMM_logNormal01.png');
 
-% pause;
-% end %nb
-
-%print('-dpng','graphs/demo_logNormal01.png');
-close all;
+pause;
+close all;
\ No newline at end of file

demos/demo_GMM_profileGMM01.m

 function demo_GMM_profileGMM01
-% Example of univariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm.
+% Univariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm.
 % The approach shares links with radial basis function networks (RBFN), but adapts the Gaussian basis functions with EM 
 % based on the distribution profiles instead of considering a simple clustering of the input space.
 %
@@ -41,35 +41,19 @@ addpath('./m_fcts/');
 model.nbStates = 40; %Number of states in the GMM
 model.nbVar = 1; %Number of variables [x1]
 nbData = 1000; %Length of each trajectory
-nbSamples = 1; %Number of samples
 
 
 %% Load data
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% demos=[];
-% load('data/2Dletters/W.mat');
-% Data=[]; w=[];
-% for n=1:nbSamples
-% 	s(n).w = spline(1:size(demos{n}.vel(1:model.nbVar,:),2), demos{n}.vel(1:model.nbVar,:), linspace(1,size(demos{n}.pos,2),nbData)); %Resampling
-% 	Data = [Data, 1:nbData];
-% 	w = [w, s(n).w];
-% end
-% w = w-min(w);
-% w = w/max(w);
-
-% Data = 1:nbData;
-% load('data/lognormal03.mat');
-
 load('data/velprofile01.mat');
 Data = spline(1:size(Data,2),Data,linspace(1,size(Data,2),nbData)); %Resample data
 tlist = Data(1,:) + 1E-8; %The first value should be non-zero
 w = Data(2,:);
 Data = tlist;
 
-
 %Rescale data and make it positive to represent a probability density function
-w = w-min(w);
-w = w/max(w);
+w = w - min(w);
+w = w / max(w);
 
 
 %% Parameters estimation
@@ -81,8 +65,7 @@ model = EM_weighted_univariateGMM(Data, w, model);
 for i=1:model.nbStates
 	Phi(:,i) = gaussPDF(Data, model.Mu(:,i), model.Sigma(:,:,i));
 end
-model.Priors = (Phi'*Phi)\Phi'*w';
-%sum(model.Priors)
+model.Priors = (Phi' * Phi) \ Phi' * w';
 
 %Probability density function of normal distributions
 for i=1:model.nbStates
@@ -90,28 +73,23 @@ for i=1:model.nbStates
 end
 hmix = sum(h,1);
 
+disp(['Error: ' num2str(norm(hmix-w))]);
+
+
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('PaperPosition',[0 0 24 4],'position',[10,10,1200,200]); hold on; box on; 
+figure('position',[10,10,2300,500]); hold on; box on; 
 %[~,hmix] = plotGMM1D(model, [.8 0 0], [tlist(1) 0 tlist(end) 1], .8, nbData);
+hf(1) = plot(tlist, w, '-','linewidth',2,'color',[.7 .7 .7]);
 for i=1:model.nbStates
-	plot(tlist, h(i,:),'-','linewidth',4,'color',[1 .7 .7]);
+	plot(tlist, h(i,:),'-','linewidth',2,'color',[1 .7 .7]);
 end
-for n=1:nbSamples
-	plot(tlist, w((n-1)*nbData+1:n*nbData), '-','linewidth',6,'color',[.7 .7 .7]);
-end
-plot(tlist, hmix,'-','linewidth',2,'color',[.8 0 0]);
-
+hf(2) = plot(tlist, hmix,'-','linewidth',2,'color',[.8 0 0]);
 axis([tlist(1) tlist(end) 0 1.05]); set(gca,'Xtick',[]); set(gca,'Ytick',[]);
 xlabel('$t$','fontsize',18,'interpreter','latex'); 
 ylabel('$|\dot{x}|$','fontsize',18,'interpreter','latex');
+legend(hf, {'Reference','Reconstructed'});
+% print('-dpng','graphs/demo_GMM_profileGMM01.png');
 
-% w=hmix;
-% save('data/lognormal03.mat','w');
-% return
-
-disp(['Error: ' num2str(norm(hmix-w))]);
-
-% print('-dpng','graphs/demo_profileGMM01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_GMM_profileGMM_multivariate01.m

 function demo_GMM_profileGMM_multivariate01
-% Example of multivariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm
+% Multivariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm
 %
 % If this code is useful for your research, please cite the related publication:
 % @article{Calinon16JIST,
@@ -36,25 +36,13 @@ addpath('./m_fcts/');
 
 %% Parameters
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-model.nbStates = 4; %Number of states in the GMM
+model.nbStates = 8; %Number of states in the GMM
 model.nbVar = 2; %Number of variables [x1]
 nbData = 200; %Length of each trajectory
-nbSamples = 1; %Number of samples
 
 
 %% Load data
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% demos=[];
-% load('data/2Dletters/W.mat');
-% Data=[]; w=[];
-% for n=1:nbSamples
-% 	s(n).w = spline(1:size(demos{n}.vel(1:model.nbVar,:),2), demos{n}.vel(1:model.nbVar,:), linspace(1,size(demos{n}.pos,2),nbData)); %Resampling
-% 	Data = [Data, repmat(1:nbData,model.nbVar,1)];
-% 	w = [w, s(n).w];
-% end
-% w = w - repmat(min(w,[],2),1,nbData*nbSamples);
-% w = w ./ repmat(max(w,[],2),1,nbData*nbSamples);
-
 Data = repmat(1:nbData,model.nbVar,1);
 load('data/lognormal05.mat'); %load 'w'
 
@@ -68,24 +56,24 @@ model = EM_weighted_multivariateGMM(Data, w, model);
 
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('position',[10,10,1000,500]); 
+figure('position',[10,10,2000,900]); 
 for k=1:model.nbVar
 	subplot(model.nbVar,1,k); hold on; box on; 
 	mtmp.nbStates = model.nbStates; 
 	mtmp.Priors = model.Priors(k,:);
 	mtmp.Mu(1,:) = model.Mu(k,:);
 	mtmp.Sigma(1,1,:) = model.Sigma(k,k,:);
+	hf(1) = plot(1:nbData, w(k,:), '-','linewidth',2,'color',[.7 .7 .7]);
 	[~,hmix(k,:)] = plotGMM1D(mtmp, [1 nbData 0 1], [.8 0 0], .2);
-	for n=1:nbSamples
-		plot(1:nbData, w(k,(n-1)*nbData+1:n*nbData), '-','linewidth',2,'color',[.7 .7 .7]);
-	end
+	hf(2) = plot(1:nbData, hmix(k,:),'-','linewidth',2,'color',[.8 0 0]);
 	axis([1 nbData 0 1.05]); set(gca,'Xtick',[]); set(gca,'Ytick',[]);
 	xlabel('$t$','fontsize',18,'interpreter','latex'); 
 	ylabel(['$\dot{x}_' num2str(k) '$'],'fontsize',18,'interpreter','latex');
 end
+legend(hf, {'Reference','Reconstructed'});
+%print('-dpng','graphs/demo_GMM_profileGMM_multivariate01.png');
 
-norm(hmix-w)
+disp(['Error: ' num2str(norm(hmix-w))]);
 
-%print('-dpng','graphs/demo_profileGMM_multivariate01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_GMM_profileLogGMM01.m

 function demo_GMM_profileLogGMM01
-% Example of univariate velocity profile fitting with a lognormal mixture model and a weighted EM algorithm
+% Univariate velocity profile fitting with a lognormal mixture model and a weighted EM algorithm
 % 
 % If this code is useful for your research, please cite the related publication:
 % @article{Calinon16JIST,
@@ -39,40 +39,19 @@ addpath('./m_fcts/');
 model.nbStates = 40; %Number of states in the GMM
 model.nbVar = 1; %Number of variables [x1]
 nbData = 1000; %Length of each trajectory
-nbSamples = 1; %Number of samples
 
 
 %% Load data
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% demos=[];
-% load('data/2Dletters/W.mat');
-% Data=[]; w=[];
-% for n=1:nbSamples
-% 	s(n).w = spline(1:size(demos{n}.vel(1:model.nbVar,:),2), demos{n}.vel(1:model.nbVar,:), linspace(1,size(demos{n}.pos,2),nbData)); %Resampling
-% 	Data = [Data, log(1:nbData)]; %log data are collected
-% 	w = [w, s(n).w];
-% end
-% w = w-min(w);
-% w = w/max(w);
-
-% Data = log(1:nbData);
-% load('data/lognormal03.mat');
-
-% s = importdata('data/2cold_vel_orig.csv');
-% Data = s.data';
-% save('data/velprofile01.mat','Data');
-% return
-
 load('data/velprofile01.mat');
 Data = spline(1:size(Data,2),Data,linspace(1,size(Data,2),nbData)); %Resample data
 tlist = Data(1,:) + 1E-8; %The first value should be non-zero
 w = Data(2,:);
-%Data = tlist;
 Data = log(tlist);
 
 %Rescale data and make it positive to represent a probability density function
-w = w-min(w);
-w = w/max(w);
+w = w - min(w);
+w = w / max(w);
 
 
 %% Parameters estimation
@@ -96,27 +75,21 @@ for i=1:model.nbStates
 end
 hmix = sum(h,1);
 
+disp(['Error: ' num2str(norm(hmix-w))]);
 
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('PaperPosition',[0 0 24 4],'position',[10,10,1200,200]); hold on; box on; 
+figure('position',[10,10,2300,500]); hold on; box on; 
+hf(1) = plot(tlist, w, '-','linewidth',2,'color',[.7 .7 .7]);
 for i=1:model.nbStates
-	plot(tlist, h(i,:),'-','linewidth',4,'color',[1 .7 .7]);
+	plot(tlist, h(i,:),'-','linewidth',2,'color',[1 .7 .7]);
 end
-for n=1:nbSamples
-	plot(tlist,w((n-1)*nbData+1:n*nbData), '-','linewidth',6,'color',[.7 .7 .7]);
-end
-plot(tlist, hmix,'-','linewidth',2,'color',[.8 0 0]);
+hf(2) = plot(tlist, hmix,'-','linewidth',2,'color',[.8 0 0]);
 axis([tlist(1) tlist(end) 0 1.05]); set(gca,'Xtick',[]); set(gca,'Ytick',[]);
 xlabel('$t$','fontsize',18,'interpreter','latex'); 
 ylabel('$|\dot{x}|$','fontsize',18,'interpreter','latex');
+legend(hf, {'Reference','Reconstructed'});
+%print('-dpng','graphs/demo_GMM_profileLogGMM01.png');
 
-% w=hmix;
-% save('data/lognormal04.mat','w');
-% return
-
-disp(['Error: ' num2str(norm(hmix-w))]);
-
-%print('-dpng','graphs/demo_profileLogGMM01.png');
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_GMM_profileLogGMM_multivariate01.m

 function demo_GMM_profileLogGMM_multivariate01
-%Example of multivariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm
+% Multivariate velocity profile fitting with a Gaussian mixture model (GMM) and a weighted EM algorithm
 %
 % If this code is useful for your research, please cite the related publication:
 % @article{Calinon16JIST,
@@ -36,10 +36,9 @@ addpath('./m_fcts/');
 
 %% Parameters
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-model.nbStates = 4; %Number of states in the GMM
+model.nbStates = 8; %Number of states in the GMM
 model.nbVar = 2; %Number of variables [x1]
 nbData = 200; %Length of each trajectory
-nbSamples = 1; %Number of samples
 
 
 %% Load data
@@ -78,28 +77,26 @@ hmix = hmix ./ repmat(max(hmix,[],2), [1,nbData]);
 
 %% Plots
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('position',[10,10,1000,500]); 
+figure('position',[10,10,2000,900]); 
 for k=1:model.nbVar
 	subplot(model.nbVar,1,k); hold on; box on; 
 	mtmp.nbStates = model.nbStates; 
 	mtmp.Priors = model.Priors(k,:);
 	mtmp.Mu(1,:) = model.Mu(k,:);
 	mtmp.Sigma(1,1,:) = model.Sigma(k,k,:);
-	for n=1:nbSamples
-		plot(1:nbData, w(k,(n-1)*nbData+1:n*nbData), '-','linewidth',2,'color',[.7 .7 .7]);
-	end
+	hf(1) = plot(1:nbData, w(k,:), '-','linewidth',2,'color',[.7 .7 .7]);
 	for i=1:model.nbStates
-		plot(1:nbData, squeeze(h(k,i,:)), '-','linewidth',4,'color',[1 .7 .7]);
+		plot(1:nbData, squeeze(h(k,i,:)), '-','linewidth',2,'color',[1 .7 .7]);
 	end
-	plot(1:nbData, hmix(k,:), '-','linewidth',2,'color',[.8 0 0]);
-
+	hf(2) = plot(1:nbData, hmix(k,:),'-','linewidth',2,'color',[.8 0 0]);
 	axis([1 nbData 0 1.05]); set(gca,'Xtick',[]); set(gca,'Ytick',[]);
 	xlabel('$t$','fontsize',18,'interpreter','latex'); 
 	ylabel(['$\dot{x}_' num2str(k) '$'],'fontsize',18,'interpreter','latex');
 end
+legend(hf, {'Reference','Reconstructed'});
+%print('-dpng','graphs/demo_GMM_profileLogGMM_multivariate01.png');
 
-norm(hmix-w)
+disp(['Error: ' num2str(norm(hmix-w))]);
 
-%print('-dpng','graphs/demo_profileLogGMM_multivariate01.png');
 pause;
 close all;
\ No newline at end of file

demos/demo_GMM_semiTied01.m

@@ -72,6 +72,6 @@ for i=1:model.nbStates
 end
 view(-40,6); axis equal;
 
-%print('-dpng','graphs/demo_semitiedGMM01.png');
+%print('-dpng','graphs/demo_GMM_semitiedGMM01.png');
 pause;
 close all;
\ No newline at end of file

demos/demo_GPR01.m

@@ -102,7 +102,13 @@ end
 set(gca,'xtick',[],'ytick',[]); axis equal; axis square;
 xlabel(['$x_1$'],'interpreter','latex','fontsize',18);
 ylabel(['$x_2$'],'interpreter','latex','fontsize',18);
-
 %print('-dpng','graphs/demo_GPR01.png');
+
+% figure; hold on; axis off; 
+% colormap(flipud(gray));
+% imagesc(abs(Kdd));
+% axis tight; axis square; axis ij;
+% print('-dpng','graphs/GPR_kernel_RBF01.png');
+
 pause;
-close all;
+close all;
\ No newline at end of file

demos/demo_GPR02.m

@@ -161,7 +161,4 @@ function K = covFct(x1, x2, p, flag_noiseObs)
 	if flag_noiseObs==1
 		K = K + eye(size(K)) .* p(3); %Consideration of noisy observation y
 	end
-end
-
-
-
+end
\ No newline at end of file

demos/demo_GPR03.m

@@ -83,9 +83,9 @@ end
 
 %% Plot
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('PaperPosition',[0 0 12 4],'position',[10 10 1300 600]); 
+figure('PaperPosition',[0 0 22 4],'position',[10 10 2300 600]); 
 %Prior samples
-subplot(1,3,1); hold on; title('Samples from prior','fontsize',14);
+subplot(1,4,1); hold on; title('Samples from prior','fontsize',14);
 for n=2:nbRepros/2
 	plot(r(n).Data(1,:), r(n).Data(2,:), '-','lineWidth',3.5,'color',[.9 .9 .9]*rand(1));
 end
@@ -96,7 +96,7 @@ xlabel('$x^{\scriptscriptstyle\mathcal{I}}_1$','interpreter','latex','fontsize',
 ylabel('$x^{\scriptscriptstyle\mathcal{O}}_1$','interpreter','latex','fontsize',18);
 
 %Posterior samples
-subplot(1,3,2); hold on;  title('Samples from posterior','fontsize',14);
+subplot(1,4,2); hold on;  title('Samples from posterior','fontsize',14);
 for n=nbRepros/2+1:nbRepros
 	plot(r(n).Data(1,:), r(n).Data(2,:), '-','lineWidth',3.5,'color',[.9 .9 .9]*rand(1));
 end
@@ -108,7 +108,7 @@ xlabel('$x^{\scriptscriptstyle\mathcal{I}}_1$','interpreter','latex','fontsize',
 ylabel('$x^{\scriptscriptstyle\mathcal{O}}_1$','interpreter','latex','fontsize',18);
 
 %Trajectory distribution
-subplot(1,3,3); hold on;  title('Trajectory distribution','fontsize',14);
+subplot(1,4,3); hold on;  title('Trajectory distribution','fontsize',14);
 patch([r(1).Data(1,:), r(1).Data(1,end:-1:1)], ...
 	[r(1).Data(2,:)+squeeze(r(1).SigmaOut.^.5)', r(1).Data(2,end:-1:1)-squeeze(r(1).SigmaOut(:,:,end:-1:1).^.5)'], ...
 	[.8 .8 .8],'edgecolor','none');
@@ -120,6 +120,20 @@ set(gca,'xtick',[],'ytick',[]); axis([0, 1, -0.7 0.7]);
 xlabel('$x^{\scriptscriptstyle\mathcal{I}}_1$','interpreter','latex','fontsize',18);
 ylabel('$x^{\scriptscriptstyle\mathcal{O}}_1$','interpreter','latex','fontsize',18);
 
+%Plot covariance
+subplot(1,4,4); hold on; axis off; title('Covariance','fontsize',14);
+colormap(flipud(gray));
+imagesc(abs(Kdd));
+axis tight; axis square; axis ij;
 %print('-dpng','-r300','graphs/GPR03.png');
+
+% figure; hold on; axis off; 
+% colormap(flipud(gray));
+% imagesc(abs(Kdd));
+% axis tight; axis square; axis ij;
+% print('-dpng','graphs/GPR_kernel_periodic01.png');
+
 pause;
 close all;
+
+

demos/demo_GPR04.m

@@ -82,10 +82,10 @@ end
 
 %% Plot
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-figure('PaperPosition',[0 0 12 4],'position',[10 10 1300 600]); 
+figure('PaperPosition',[0 0 22 4],'position',[10 10 2300 600]); 
 limAxes = [0, 1, -.5 .5];
 %Prior samples
-subplot(1,3,1); hold on; title('Samples from prior','fontsize',14);
+subplot(1,4,1); hold on; title('Samples from prior','fontsize',14);
 for n=2:nbRepros/2
 	plot(r(n).Data(1,:), r(n).Data(2,:), '-','lineWidth',3.5,'color',[.9 .9 .9]*rand(1));
 end
@@ -96,7 +96,7 @@ xlabel('$x^{\scriptscriptstyle\mathcal{I}}_1$','interpreter','latex','fontsize',
 ylabel('$x^{\scriptscriptstyle\mathcal{O}}_1$','interpreter','latex','fontsize',18);
 
 %Posterior samples
-subplot(1,3,2); hold on;  title('Samples from posterior','fontsize',14);
+subplot(1,4,2); hold on;  title('Samples from posterior','fontsize',14);
 for n=nbRepros/2+1:nbRepros
 	plot(r(n).Data(1,:), r(n).Data(2,:), '-','lineWidth',3.5,'color',[.9 .9 .9]*rand(1));
 end
@@ -108,7 +108,7 @@ xlabel('$x^{\scriptscriptstyle\mathcal{I}}_1$','interpreter','latex','fontsize',
 ylabel('$x^{\scriptscriptstyle\mathcal{O}}_1$','interpreter','latex','fontsize',18);
 
 %Trajectory distribution
-subplot(1,3,3); hold on;  title('Trajectory distribution','fontsize',14);
+subplot(1,4,3); hold on;  title('Trajectory distribution','fontsize',14);
 patch([r(1).Data(1,:), r(1).Data(1,end:-1:1)], ...