Added LSIM-based ECG fiducial-point extraction tool

external/chmm-lsim-matlab-toolbox/README.md

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+# chmm-lsim-karimi-toolbox
+A MATLAB toolbox for HMMs, CHMMs & LSIMs in multi-channel data processing, modeling & classification  

external/chmm-lsim-matlab-toolbox/chmm/chmm_cartesian_product.m

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+
+function [pi_0_ehmm , coupling_tetha_ehmm ,  transition_ehmm  ,ehmm_gmm_para, index_matrix ] = chmm_cartesian_product( pi_0_chmm ,  transition_chmm  ,chmm_gmm_para  )
+
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+% Converting CHMM to equivalent HMM
+% ehmm stand for equivalent HMM 
+%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
+
+
+
+coupling_tetha_ehmm = 1;
+
+
+C = size(pi_0_chmm , 1);
+
+temp =1;
+for c=1:C    
+    temp = kron(temp , pi_0_chmm{c,1});
+end
+
+pi_0_ehmm{1,1} = temp;
+
+if size(chmm_gmm_para{1,1}.gmm_para(1).sigma(1).x,2)==1
+    sigma_diag = 1;
+else
+    sigma_diag = 0;
+end
+
+dim_observation = zeros(C , 1);
+state_numbers = zeros(C , 1);
+num_gmm_component =  zeros(C , 1);
+
+
+
+for zee = 1:C
+
+    dim_observation(zee,1)  = length( chmm_gmm_para{zee,1}.gmm_para(1).mu(1).x );
+    state_numbers(zee,1)  = size( pi_0_chmm{zee,1} ,1);
+    num_gmm_component(zee,1)  = length(chmm_gmm_para{zee,1}.gmm_para(1).P);    
+
+end
+
+
+A_cartesian = zeros( prod(state_numbers) , prod(state_numbers) );
+
+for row_num = 1:size(A_cartesian,1)
+
+    temp =1;    
+    for c=1:C        
+        temp = kron(temp , transition_chmm{c,1}(row_num,:));
+    end
+
+    A_cartesian(row_num , :) = temp;
+
+end
+
+transition_ehmm{1,1} = A_cartesian;
+
+
+index_matrix = zeros(C , prod(state_numbers));
+index_matrix_gmm = zeros(C , prod(num_gmm_component));
+
+for c = 1:C
+
+    tempIndex = state_numbers;
+    tempIndex(1:c)=[];    
+    tempRaw = kron(1:state_numbers(c)  , ones(1,prod(tempIndex)));    
+    tempIndex = state_numbers;
+    tempIndex(c:end)=[];
+    index_matrix(c,:)=repmat(tempRaw , 1 , prod(tempIndex) );
+
+    tempIndex = num_gmm_component;
+    tempIndex(1:c)=[];    
+    tempRaw = kron(1:num_gmm_component(c)  , ones(1,prod(tempIndex)));    
+    tempIndex = num_gmm_component;
+    tempIndex(c:end)=[];
+    index_matrix_gmm(c,:)=repmat(tempRaw , 1 , prod(tempIndex) );
+
+end
+
+
+
+dimension_numbers_index =  ( [0;cumsum(dim_observation(:))] );
+
+
+channel_num_states = prod(state_numbers);
+num_gmm_component_hmm = prod(num_gmm_component);
+P_all_hmm = ones( 1 , max(channel_num_states) , max(num_gmm_component_hmm)  );
+mu_all_hmm = zeros(  sum(dim_observation)  , max(channel_num_states) , max(num_gmm_component_hmm)   );
+
+if sigma_diag
+    sigma_all_hmm =  zeros(  sum(dim_observation)  , max(channel_num_states) , max(num_gmm_component_hmm) );
+else
+    sigma_all_hmm =  zeros(  sum(dim_observation)  , sum(dim_observation) , max(channel_num_states) , max(num_gmm_component_hmm) );
+end
+
+
+
+for i = 1:channel_num_states
+    this_set =index_matrix(:,i);
+    for k=1:num_gmm_component_hmm
+        this_gmm = index_matrix_gmm(:,k);
+        for c=1:C
+            mu_all_hmm(dimension_numbers_index(c)+1:dimension_numbers_index(c+1),i,k) = chmm_gmm_para{c, 1}.gmm_para(this_set(c)).mu(this_gmm(c)).x;
+             if sigma_diag
+                sigma_all_hmm( dimension_numbers_index(c)+1:dimension_numbers_index(c+1) ,  i , k) = chmm_gmm_para{c, 1}.gmm_para(this_set(c)).sigma(this_gmm(c)).x;
+            else
+               sigma_all_hmm( dimension_numbers_index(c)+1:dimension_numbers_index(c+1), dimension_numbers_index(c)+1:dimension_numbers_index(c+1), i , k) = chmm_gmm_para{c, 1}.gmm_para(this_set(c)).sigma(this_gmm(c)).x;
+             end
+             P_all_hmm(1,i,k) = P_all_hmm(1,i,k)* chmm_gmm_para{c, 1}.gmm_para(this_set(c)).P(this_gmm(c));
+        end
+    end
+end
+
+
+
+
+gmm_para=[];
+
+for i=1:channel_num_states
+
+    for k=1:num_gmm_component_hmm
+
+        gmm_para(i).P(k,1)=P_all_hmm(1,i,k);
+        if sigma_diag
+            gmm_para(i).sigma(k).x = sigma_all_hmm( : ,  i , k)  ;
+        else
+            gmm_para(i).sigma(k).x = sigma_all_hmm( :,:, i , k)  ;
+        end
+        gmm_para(i).mu(k).x =  mu_all_hmm( : ,  i , k);
+    end
+
+end
+
+
+ehmm_gmm_para{1,1}.gmm_para = gmm_para;
+
+
+
+
+
+end
+
+
+
+
+
+
+