From: Benjamin Auder <benjamin.auder@somewhere>
Date: Fri, 5 Jun 2020 15:36:43 +0000 (+0200)
Subject: Fix SVD error when p < m in EMGrank.c
X-Git-Url: https://git.auder.net/variants/img/current/assets/css/pieces/%7B%7B?a=commitdiff_plain;h=93dcdea364307b9d5ebe71958deb5df2a48547b3;p=valse.git

Fix SVD error when p < m in EMGrank.c
---

diff --git a/pkg/DESCRIPTION b/pkg/DESCRIPTION
index ac46366..edb3356 100644
--- a/pkg/DESCRIPTION
+++ b/pkg/DESCRIPTION
@@ -28,7 +28,7 @@ Suggests:
     roxygen2
 URL: http://git.auder.net/?p=valse.git
 License: MIT + file LICENSE
-RoxygenNote: 7.0.2
+RoxygenNote: 7.1.0
 Collate:
     'plot_valse.R'
     'main.R'
diff --git a/pkg/src/EMGrank.c b/pkg/src/EMGrank.c
index a98ff91..14b693a 100644
--- a/pkg/src/EMGrank.c
+++ b/pkg/src/EMGrank.c
@@ -5,303 +5,340 @@
 // Compute pseudo-inverse of a square matrix
 static Real* pinv(const Real* matrix, int dim)
 {
-	gsl_matrix* U = gsl_matrix_alloc(dim,dim);
-	gsl_matrix* V = gsl_matrix_alloc(dim,dim);
-	gsl_vector* S = gsl_vector_alloc(dim);
-	gsl_vector* work = gsl_vector_alloc(dim);
-	Real EPS = 1e-10; //threshold for singular value "== 0"
-	
-	//copy matrix into U
-	copyArray(matrix, U->data, dim*dim);
+  gsl_matrix* U = gsl_matrix_alloc(dim,dim);
+  gsl_matrix* V = gsl_matrix_alloc(dim,dim);
+  gsl_vector* S = gsl_vector_alloc(dim);
+  gsl_vector* work = gsl_vector_alloc(dim);
+  Real EPS = 1e-10; //threshold for singular value "== 0"
+  
+  //copy matrix into U
+  copyArray(matrix, U->data, dim*dim);
 
-	//U,S,V = SVD of matrix
-	gsl_linalg_SV_decomp(U, V, S, work);
-	gsl_vector_free(work);
+  //U,S,V = SVD of matrix
+  gsl_linalg_SV_decomp(U, V, S, work);
+  gsl_vector_free(work);
 
-	// Obtain pseudo-inverse by V*S^{-1}*t(U)
-	Real* inverse = (Real*)malloc(dim*dim*sizeof(Real));
-	for (int i=0; i<dim; i++)
-	{
-		for (int ii=0; ii<dim; ii++)
-		{
-			Real dotProduct = 0.0;
-			for (int j=0; j<dim; j++)
-				dotProduct += V->data[i*dim+j] * (S->data[j] > EPS ? 1.0/S->data[j] : 0.0) * U->data[ii*dim+j];
-			inverse[i*dim+ii] = dotProduct;
-		}
-	}
-	
-	gsl_matrix_free(U);
-	gsl_matrix_free(V);
-	gsl_vector_free(S);
-	return inverse;
+  // Obtain pseudo-inverse by V*S^{-1}*t(U)
+  Real* inverse = (Real*)malloc(dim*dim*sizeof(Real));
+  for (int i=0; i<dim; i++)
+  {
+    for (int ii=0; ii<dim; ii++)
+    {
+      Real dotProduct = 0.0;
+      for (int j=0; j<dim; j++)
+        dotProduct += V->data[i*dim+j] * (S->data[j] > EPS ? 1.0/S->data[j] : 0.0) * U->data[ii*dim+j];
+      inverse[i*dim+ii] = dotProduct;
+    }
+  }
+  
+  gsl_matrix_free(U);
+  gsl_matrix_free(V);
+  gsl_vector_free(S);
+  return inverse;
 }
 
 // TODO: comment EMGrank purpose
 void EMGrank_core(
-	// IN parameters
-	const Real* Pi, // parametre de proportion
-	const Real* Rho, // parametre initial de variance renormalise
-	int mini, // nombre minimal d'iterations dans l'algorithme EM
-	int maxi, // nombre maximal d'iterations dans l'algorithme EM
-	const Real* X, // regresseurs
-	const Real* Y, // reponse
-	Real tau, // seuil pour accepter la convergence
-	const int* rank, // vecteur des rangs possibles
-	// OUT parameters
-	Real* phi, // parametre de moyenne renormalise, calcule par l'EM
-	Real* LLF, // log vraisemblance associe a cet echantillon, pour les valeurs estimees des parametres
-	// additional size parameters
-	int n, // taille de l'echantillon
-	int p, // nombre de covariables
-	int m, // taille de Y (multivarie)
-	int k) // nombre de composantes
+  // IN parameters
+  const Real* Pi, // parametre de proportion
+  const Real* Rho, // parametre initial de variance renormalise
+  int mini, // nombre minimal d'iterations dans l'algorithme EM
+  int maxi, // nombre maximal d'iterations dans l'algorithme EM
+  const Real* X, // regresseurs
+  const Real* Y, // reponse
+  Real tau, // seuil pour accepter la convergence
+  const int* rank, // vecteur des rangs possibles
+  // OUT parameters
+  Real* phi, // parametre de moyenne renormalise, calcule par l'EM
+  Real* LLF, // log vraisemblance associe a cet echantillon, pour les valeurs estimees des parametres
+  // additional size parameters
+  int n, // taille de l'echantillon
+  int p, // nombre de covariables
+  int m, // taille de Y (multivarie)
+  int k) // nombre de composantes
 {
-	// Allocations, initializations
-	Real* Phi = (Real*)calloc(p*m*k,sizeof(Real));
-	Real* hatBetaR = (Real*)malloc(p*m*sizeof(Real));
-	int signum;
-	Real invN = 1.0/n;
-	int deltaPhiBufferSize = 20;
-	Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
-	int ite = 0;
-	Real sumDeltaPhi = 0.0;
-	Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
-	Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
-	Real* Xr = (Real*)malloc(n*p*sizeof(Real));
-	Real* Yr = (Real*)malloc(n*m*sizeof(Real));
-	Real* tXrXr = (Real*)malloc(p*p*sizeof(Real));
-	Real* tXrYr = (Real*)malloc(p*m*sizeof(Real));
-	gsl_matrix* matrixM = gsl_matrix_alloc(p, m);
-	gsl_matrix* matrixE = gsl_matrix_alloc(m, m);
-	gsl_permutation* permutation = gsl_permutation_alloc(m);
-	gsl_matrix* V = gsl_matrix_alloc(m,m);
-	gsl_vector* S = gsl_vector_alloc(m);
-	gsl_vector* work = gsl_vector_alloc(m);
+  // Allocations, initializations
+  Real* Phi = (Real*)calloc(p*m*k,sizeof(Real));
+  Real* hatBetaR = (Real*)malloc(p*m*sizeof(Real));
+  int signum;
+  Real invN = 1.0/n;
+  int deltaPhiBufferSize = 20;
+  Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
+  int ite = 0;
+  Real sumDeltaPhi = 0.0;
+  Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
+  Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
+  Real* Xr = (Real*)malloc(n*p*sizeof(Real));
+  Real* Yr = (Real*)malloc(n*m*sizeof(Real));
+  Real* tXrXr = (Real*)malloc(p*p*sizeof(Real));
+  Real* tXrYr = (Real*)malloc(p*m*sizeof(Real));
+  gsl_matrix* matrixM = gsl_matrix_alloc(p, m);
+  gsl_matrix* matrixE = gsl_matrix_alloc(m, m);
+  gsl_permutation* permutation = gsl_permutation_alloc(m);
+  gsl_matrix* V = gsl_matrix_alloc(m,m);
+  gsl_vector* S = gsl_vector_alloc(m);
+  gsl_vector* work = gsl_vector_alloc(m);
 
-	//Initialize class memberships (all elements in class 0; TODO: randomize ?)
-	int* Z = (int*)calloc(n, sizeof(int));
+  //Initialize class memberships (all elements in class 0; TODO: randomize ?)
+  int* Z = (int*)calloc(n, sizeof(int));
 
-	//Initialize phi to zero, because some M loops might exit before phi affectation
-	zeroArray(phi, p*m*k);
+  //Initialize phi to zero, because some M loops might exit before phi affectation
+  zeroArray(phi, p*m*k);
 
-	while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
-	{
-		/////////////
-		// Etape M //
-		/////////////
-		
-		//M step: Mise a jour de Beta (et donc phi)
-		for (int r=0; r<k; r++)
-		{
-			//Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
-			int cardClustR=0;
-			for (int i=0; i<n; i++)
-			{
-				if (Z[i] == r)
-				{
-					for (int j=0; j<p; j++)
-						Xr[mi(cardClustR,j,n,p)] = X[mi(i,j,n,p)];
-					for (int j=0; j<m; j++)
-						Yr[mi(cardClustR,j,n,m)] = Y[mi(i,j,n,m)];
-					cardClustR++;
-				}
-			}
-			if (cardClustR == 0)
-				continue;
+  while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
+  {
+    /////////////
+    // Etape M //
+    /////////////
+    
+    //M step: Mise a jour de Beta (et donc phi)
+    for (int r=0; r<k; r++)
+    {
+      //Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
+      int cardClustR=0;
+      for (int i=0; i<n; i++)
+      {
+        if (Z[i] == r)
+        {
+          for (int j=0; j<p; j++)
+            Xr[mi(cardClustR,j,n,p)] = X[mi(i,j,n,p)];
+          for (int j=0; j<m; j++)
+            Yr[mi(cardClustR,j,n,m)] = Y[mi(i,j,n,m)];
+          cardClustR++;
+        }
+      }
+      if (cardClustR == 0)
+        continue;
 
-			//Compute tXrXr = t(Xr) * Xr
-			for (int j=0; j<p; j++)
-			{
-				for (int jj=0; jj<p; jj++)
-				{
-					Real dotProduct = 0.0;
-					for (int u=0; u<cardClustR; u++)
-						dotProduct += Xr[mi(u,j,n,p)] * Xr[mi(u,jj,n,p)];
-					tXrXr[mi(j,jj,p,p)] = dotProduct;
-				}
-			}
+      //Compute tXrXr = t(Xr) * Xr
+      for (int j=0; j<p; j++)
+      {
+        for (int jj=0; jj<p; jj++)
+        {
+          Real dotProduct = 0.0;
+          for (int u=0; u<cardClustR; u++)
+            dotProduct += Xr[mi(u,j,n,p)] * Xr[mi(u,jj,n,p)];
+          tXrXr[mi(j,jj,p,p)] = dotProduct;
+        }
+      }
 
-			//Get pseudo inverse = (t(Xr)*Xr)^{-1}
-			Real* invTXrXr = pinv(tXrXr, p);
-			
-			// Compute tXrYr = t(Xr) * Yr
-			for (int j=0; j<p; j++)
-			{
-				for (int jj=0; jj<m; jj++)
-				{
-					Real dotProduct = 0.0;
-					for (int u=0; u<cardClustR; u++)
-						dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,jj,n,m)];
-					tXrYr[mi(j,jj,p,m)] = dotProduct;
-				}
-			}
+      //Get pseudo inverse = (t(Xr)*Xr)^{-1}
+      Real* invTXrXr = pinv(tXrXr, p);
 
-			//Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
-			for (int j=0; j<p; j++)
-			{
-				for (int jj=0; jj<m; jj++)
-				{
-					Real dotProduct = 0.0;
-					for (int u=0; u<p; u++)
-						dotProduct += invTXrXr[mi(j,u,p,p)] * tXrYr[mi(u,jj,p,m)];
-					matrixM->data[j*m+jj] = dotProduct;
-				}
-			}
-			free(invTXrXr);
+      // Compute tXrYr = t(Xr) * Yr
+      for (int j=0; j<p; j++)
+      {
+        for (int jj=0; jj<m; jj++)
+        {
+          Real dotProduct = 0.0;
+          for (int u=0; u<cardClustR; u++)
+            dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,jj,n,m)];
+          tXrYr[mi(j,jj,p,m)] = dotProduct;
+        }
+      }
 
-			//U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
-			gsl_linalg_SV_decomp(matrixM, V, S, work);
+      //Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
+      for (int j=0; j<p; j++)
+      {
+        for (int jj=0; jj<m; jj++)
+        {
+          Real dotProduct = 0.0;
+          for (int u=0; u<p; u++)
+            dotProduct += invTXrXr[mi(j,u,p,p)] * tXrYr[mi(u,jj,p,m)];
+          matrixM->data[j*m+jj] = dotProduct;
+        }
+      }
+      free(invTXrXr);
 
-			//Set m-rank(r) singular values to zero, and recompose
-			//best rank(r) approximation of the initial product
-			for (int j=rank[r]; j<m; j++)
-				S->data[j] = 0.0;
-			
-			//[intermediate step] Compute hatBetaR = U * S * t(V)
-			double* U = matrixM->data; //GSL require double precision
-			for (int j=0; j<p; j++)
-			{
-				for (int jj=0; jj<m; jj++)
-				{
-					Real dotProduct = 0.0;
-					for (int u=0; u<m; u++)
-						dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
-					hatBetaR[mi(j,jj,p,m)] = dotProduct;
-				}
-			}
+      //U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
+      if (p >= m)
+        gsl_linalg_SV_decomp(matrixM, V, S, work);
+      else
+      {
+        gsl_matrix* matrixM_ = gsl_matrix_alloc(m, p);
+        for (int j=0; j<m; j++)
+        {
+          for (int jj=0; jj<p; jj++)
+            matrixM_->data[jj*m+j] = matrixM->data[j*p +jj];
+        }
+        gsl_matrix* V_ = gsl_matrix_alloc(p,p);
+        gsl_vector* S_ = gsl_vector_alloc(p);
+        gsl_vector* work_ = gsl_vector_alloc(p);
+        gsl_linalg_SV_decomp(matrixM_, V_, S_, work_);
+        gsl_vector_free(work_);
+        for (int j=0; j<m; j++)
+        {
+          if (j < p)
+            S->data[j] = S_->data[j];
+          else
+            S->data[j] = 0.0;
+          for (int jj=0; jj<m; jj++)
+          {
+            if (j < p && jj < p)
+              V->data[jj * m + j] = V_->data[jj * m + j];
+            else
+              V->data[jj * m + j] = 0.0;
+          }
+        }
+        for (int j=0; j<m; j++)
+        {
+          for (int jj=0; jj<p; jj++)
+            matrixM->data[j*p+jj] = matrixM_->data[jj*m +j];
+        }
+        gsl_matrix_free(matrixM_);
+        gsl_matrix_free(V_);
+        gsl_vector_free(S_);
+      }
 
-			//Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
-			for (int j=0; j<p; j++)
-			{
-				for (int jj=0; jj<m; jj++)
-				{
-					Real dotProduct=0.0;
-					for (int u=0; u<m; u++)
-						dotProduct += hatBetaR[mi(j,u,p,m)] * Rho[ai(u,jj,r,m,m,k)];
-					phi[ai(j,jj,r,p,m,k)] = dotProduct;
-				}
-		}
-		}
+      //Set m-rank(r) singular values to zero, and recompose
+      //best rank(r) approximation of the initial product
+      for (int j=rank[r]; j<m; j++)
+        S->data[j] = 0.0;
+      
+      //[intermediate step] Compute hatBetaR = U * S * t(V)
+      double* U = matrixM->data; //GSL require double precision
+      for (int j=0; j<p; j++)
+      {
+        for (int jj=0; jj<m; jj++)
+        {
+          Real dotProduct = 0.0;
+          for (int u=0; u<m; u++)
+            dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
+          hatBetaR[mi(j,jj,p,m)] = dotProduct;
+        }
+      }
 
-		/////////////
-		// Etape E //
-		/////////////
-		
-		Real sumLogLLF2 = 0.0;
-		for (int i=0; i<n; i++)
-		{
-			Real sumLLF1 = 0.0;
-			Real maxLogGamIR = -INFINITY;
-			for (int r=0; r<k; r++)
-			{
-				//Compute
-				//Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
-				//*phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
-				//split in several sub-steps
-				
-				//compute det(Rho(:,:,r)) [TODO: avoid re-computations]
-				for (int j=0; j<m; j++)
-				{
-					for (int jj=0; jj<m; jj++)
-						matrixE->data[j*m+jj] = Rho[ai(j,jj,r,m,m,k)];
-				}
-				gsl_linalg_LU_decomp(matrixE, permutation, &signum);
-				Real detRhoR = gsl_linalg_LU_det(matrixE, signum);
+      //Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
+      for (int j=0; j<p; j++)
+      {
+        for (int jj=0; jj<m; jj++)
+        {
+          Real dotProduct=0.0;
+          for (int u=0; u<m; u++)
+            dotProduct += hatBetaR[mi(j,u,p,m)] * Rho[ai(u,jj,r,m,m,k)];
+          phi[ai(j,jj,r,p,m,k)] = dotProduct;
+        }
+      }
+    }
 
-				//compute Y(i,:)*Rho(:,:,r)
-				for (int j=0; j<m; j++)
-				{
-					YiRhoR[j] = 0.0;
-					for (int u=0; u<m; u++)
-						YiRhoR[j] += Y[mi(i,u,n,m)] * Rho[ai(u,j,r,m,m,k)];
-				}
+    /////////////
+    // Etape E //
+    /////////////
+    
+    Real sumLogLLF2 = 0.0;
+    for (int i=0; i<n; i++)
+    {
+      Real sumLLF1 = 0.0;
+      Real maxLogGamIR = -INFINITY;
+      for (int r=0; r<k; r++)
+      {
+        //Compute
+        //Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
+        //*phi(:,:,r)) * transpose( Y(i,:)*Rho(:,:,r) - X(i,:)*phi(:,:,r) ) );
+        //split in several sub-steps
+        
+        //compute det(Rho(:,:,r)) [TODO: avoid re-computations]
+        for (int j=0; j<m; j++)
+        {
+          for (int jj=0; jj<m; jj++)
+            matrixE->data[j*m+jj] = Rho[ai(j,jj,r,m,m,k)];
+        }
+        gsl_linalg_LU_decomp(matrixE, permutation, &signum);
+        Real detRhoR = gsl_linalg_LU_det(matrixE, signum);
 
-				//compute X(i,:)*phi(:,:,r)
-				for (int j=0; j<m; j++)
-				{
-					XiPhiR[j] = 0.0;
-					for (int u=0; u<p; u++)
-						XiPhiR[j] += X[mi(i,u,n,p)] * phi[ai(u,j,r,p,m,k)];
-				}
+        //compute Y(i,:)*Rho(:,:,r)
+        for (int j=0; j<m; j++)
+        {
+          YiRhoR[j] = 0.0;
+          for (int u=0; u<m; u++)
+            YiRhoR[j] += Y[mi(i,u,n,m)] * Rho[ai(u,j,r,m,m,k)];
+        }
 
-				//compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
-				Real dotProduct = 0.0;
-				for (int u=0; u<m; u++)
-					dotProduct += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
-				Real logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
+        //compute X(i,:)*phi(:,:,r)
+        for (int j=0; j<m; j++)
+        {
+          XiPhiR[j] = 0.0;
+          for (int u=0; u<p; u++)
+            XiPhiR[j] += X[mi(i,u,n,p)] * phi[ai(u,j,r,p,m,k)];
+        }
 
-				//Z(i) = index of max (gam(i,:))
-				if (logGamIR > maxLogGamIR)
-				{
-					Z[i] = r;
-					maxLogGamIR = logGamIR;
-				}
-				sumLLF1 += exp(logGamIR) / pow(2*M_PI,m/2.0);
-			}
+        //compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
+        Real dotProduct = 0.0;
+        for (int u=0; u<m; u++)
+          dotProduct += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+        Real logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
 
-			sumLogLLF2 += log(sumLLF1);
-		}
+        //Z(i) = index of max (gam(i,:))
+        if (logGamIR > maxLogGamIR)
+        {
+          Z[i] = r;
+          maxLogGamIR = logGamIR;
+        }
+        sumLLF1 += exp(logGamIR) / pow(2*M_PI,m/2.0);
+      }
 
-		// Assign output variable LLF
-		*LLF = -invN * sumLogLLF2;
+      sumLogLLF2 += log(sumLLF1);
+    }
 
-		//newDeltaPhi = max(max((abs(phi-Phi))./(1+abs(phi))));
-		Real newDeltaPhi = 0.0;
-		for (int j=0; j<p; j++)
-		{
-			for (int jj=0; jj<m; jj++)
-			{
-				for (int r=0; r<k; r++)
-				{
-					Real tmpDist = fabs(phi[ai(j,jj,r,p,m,k)]-Phi[ai(j,jj,r,p,m,k)])
-						/ (1.0+fabs(phi[ai(j,jj,r,p,m,k)]));
-					if (tmpDist > newDeltaPhi)
-						newDeltaPhi = tmpDist;
-				}
-			}
-		}
+    // Assign output variable LLF
+    *LLF = -invN * sumLogLLF2;
 
-		//update distance parameter to check algorithm convergence (delta(phi, Phi))
-		//TODO: deltaPhi should be a linked list for perf.
-		if (ite < deltaPhiBufferSize)
-			deltaPhi[ite] = newDeltaPhi;
-		else
-		{
-			sumDeltaPhi -= deltaPhi[0];
-			for (int u=0; u<deltaPhiBufferSize-1; u++)
-				deltaPhi[u] = deltaPhi[u+1];
-			deltaPhi[deltaPhiBufferSize-1] = newDeltaPhi;
-		}
-		sumDeltaPhi += newDeltaPhi;
+    //newDeltaPhi = max(max((abs(phi-Phi))./(1+abs(phi))));
+    Real newDeltaPhi = 0.0;
+    for (int j=0; j<p; j++)
+    {
+      for (int jj=0; jj<m; jj++)
+      {
+        for (int r=0; r<k; r++)
+        {
+          Real tmpDist = fabs(phi[ai(j,jj,r,p,m,k)]-Phi[ai(j,jj,r,p,m,k)])
+            / (1.0+fabs(phi[ai(j,jj,r,p,m,k)]));
+          if (tmpDist > newDeltaPhi)
+            newDeltaPhi = tmpDist;
+        }
+      }
+    }
 
-		// update other local variables
-		for (int j=0; j<m; j++)
-		{
-			for (int jj=0; jj<p; jj++)
-			{
-				for (int r=0; r<k; r++)
-					Phi[ai(jj,j,r,p,m,k)] = phi[ai(jj,j,r,p,m,k)];
-			}
-		}
-		ite++;
-	}
+    //update distance parameter to check algorithm convergence (delta(phi, Phi))
+    //TODO: deltaPhi should be a linked list for perf.
+    if (ite < deltaPhiBufferSize)
+      deltaPhi[ite] = newDeltaPhi;
+    else
+    {
+      sumDeltaPhi -= deltaPhi[0];
+      for (int u=0; u<deltaPhiBufferSize-1; u++)
+        deltaPhi[u] = deltaPhi[u+1];
+      deltaPhi[deltaPhiBufferSize-1] = newDeltaPhi;
+    }
+    sumDeltaPhi += newDeltaPhi;
 
-	//free memory
-	free(hatBetaR);
-	free(deltaPhi);
-	free(Phi);
-	gsl_matrix_free(matrixE);
-	gsl_matrix_free(matrixM);
-	gsl_permutation_free(permutation);
-	gsl_vector_free(work);
-	gsl_matrix_free(V);
-	gsl_vector_free(S);
-	free(XiPhiR);
-	free(YiRhoR);
-	free(Xr);
-	free(Yr);
-	free(tXrXr);
-	free(tXrYr);
-	free(Z);
+    // update other local variables
+    for (int j=0; j<m; j++)
+    {
+      for (int jj=0; jj<p; jj++)
+      {
+        for (int r=0; r<k; r++)
+          Phi[ai(jj,j,r,p,m,k)] = phi[ai(jj,j,r,p,m,k)];
+      }
+    }
+    ite++;
+  }
+
+  //free memory
+  free(hatBetaR);
+  free(deltaPhi);
+  free(Phi);
+  gsl_matrix_free(matrixE);
+  gsl_matrix_free(matrixM);
+  gsl_permutation_free(permutation);
+  gsl_vector_free(work);
+  gsl_matrix_free(V);
+  gsl_vector_free(S);
+  free(XiPhiR);
+  free(YiRhoR);
+  free(Xr);
+  free(Yr);
+  free(tXrXr);
+  free(tXrYr);
+  free(Z);
 }