X-Git-Url: https://git.auder.net/?a=blobdiff_plain;f=src%2Fsources%2FEMGLLF.c;h=7e7a3d1d5938d22c607f20e18460a8c67d0b7c02;hb=ef67d338c7f28ba041abe40ca9a8ab69f8365a90;hp=0c39d6e05513da54c88c4a24f2918b529c7b7654;hpb=4cab944a7bf905e811d740694c39f16b2b23d7e1;p=valse.git

diff --git a/src/sources/EMGLLF.c b/src/sources/EMGLLF.c
index 0c39d6e..7e7a3d1 100644
--- a/src/sources/EMGLLF.c
+++ b/src/sources/EMGLLF.c
@@ -1,31 +1,32 @@
-#include "EMGLLF.h"
+#include "utils.h"
+#include <stdlib.h>
 #include <gsl/gsl_linalg.h>
 
 // TODO: don't recompute indexes every time......
-void EMGLLF(
+void EMGLLF_core(
 	// IN parameters
-	const double* phiInit,  // parametre initial de moyenne renormalisé
-	const double* rhoInit,  // parametre initial de variance renormalisé
-	const double* piInit,   // parametre initial des proportions
-	const double* gamInit,  // paramètre initial des probabilités a posteriori de chaque échantillon
-	int mini,      // nombre minimal d'itérations dans l'algorithme EM
-	int maxi,      // nombre maximal d'itérations dans l'algorithme EM
-	double gamma,  // valeur de gamma : puissance des proportions dans la pénalisation pour un Lasso adaptatif
-	double lambda, // valeur du paramètre de régularisation du Lasso
-	const double* X,     // régresseurs
-	const double* Y,     // réponse
-	double tau,    // seuil pour accepter la convergence
+	const Real* phiInit, // parametre initial de moyenne renormalisé
+	const Real* rhoInit, // parametre initial de variance renormalisé
+	const Real* piInit,	 // parametre initial des proportions
+	const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
+	int mini, // nombre minimal d'itérations dans l'algorithme EM
+	int maxi, // nombre maximal d'itérations dans l'algorithme EM
+	Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
+	Real lambda, // valeur du paramètre de régularisation du Lasso
+	const Real* X, // régresseurs
+	const Real* Y, // réponse
+	Real tau, // seuil pour accepter la convergence
 	// OUT parameters (all pointers, to be modified)
-	double* phi,  // parametre de moyenne renormalisé, calculé par l'EM
-	double* rho,  // parametre de variance renormalisé, calculé par l'EM
-	double* pi,   // parametre des proportions renormalisé, calculé par l'EM
-	double* LLF,   // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
-    double* S,
+	Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
+	Real* rho, // parametre de variance renormalisé, calculé par l'EM
+	Real* pi, // parametre des proportions renormalisé, calculé par l'EM
+	Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
+	Real* S,
 	// additional size parameters
-	int n,         // nombre d'echantillons
-	int p,         // nombre de covariables
-	int m,         // taille de Y (multivarié)
-	int k)         // nombre de composantes dans le mélange
+	int n, // nombre d'echantillons
+	int p, // nombre de covariables
+	int m, // taille de Y (multivarié)
+	int k) // nombre de composantes dans le mélange
 {
 	//Initialize outputs
 	copyArray(phiInit, phi, p*m*k);
@@ -35,33 +36,33 @@ void EMGLLF(
 	//S is already allocated, and doesn't need to be 'zeroed'
 
 	//Other local variables
-	//NOTE: variables order is always [maxi],n,p,m,k
-	double* gam = (double*)malloc(n*k*sizeof(double));
+	Real* gam = (Real*)malloc(n*k*sizeof(Real));
 	copyArray(gamInit, gam, n*k);
-	double* b = (double*)malloc(k*sizeof(double));
-	double* Phi = (double*)malloc(p*m*k*sizeof(double));
-	double* Rho = (double*)malloc(m*m*k*sizeof(double));
-	double* Pi = (double*)malloc(k*sizeof(double));
-	double* gam2 = (double*)malloc(k*sizeof(double));
-	double* pi2 = (double*)malloc(k*sizeof(double));
-	double* Gram2 = (double*)malloc(p*p*k*sizeof(double));
-	double* ps = (double*)malloc(m*k*sizeof(double));
-	double* nY2 = (double*)malloc(m*k*sizeof(double));
-	double* ps1 = (double*)malloc(n*m*k*sizeof(double));
-	double* ps2 = (double*)malloc(p*m*k*sizeof(double));
-	double* nY21 = (double*)malloc(n*m*k*sizeof(double));
-	double* Gam = (double*)malloc(n*k*sizeof(double));
-	double* X2 = (double*)malloc(n*p*k*sizeof(double));
-	double* Y2 = (double*)malloc(n*m*k*sizeof(double));
+	Real* b = (Real*)malloc(k*sizeof(Real));
+	Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
+	Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
+	Real* Pi = (Real*)malloc(k*sizeof(Real));
+	Real* gam2 = (Real*)malloc(k*sizeof(Real));
+	Real* pi2 = (Real*)malloc(k*sizeof(Real));
+	Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
+	Real* ps = (Real*)malloc(m*k*sizeof(Real));
+	Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
+	Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
+	Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
+	Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
+	Real* Gam = (Real*)malloc(n*k*sizeof(Real));
+	Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
+	Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
+	Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
 	gsl_matrix* matrix = gsl_matrix_alloc(m, m);
 	gsl_permutation* permutation = gsl_permutation_alloc(m);
-	double* YiRhoR = (double*)malloc(m*sizeof(double));
-	double* XiPhiR = (double*)malloc(m*sizeof(double));
-	double dist = 0.;
-	double dist2 = 0.;
+	Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
+	Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
+	Real dist = 0.;
+	Real dist2 = 0.;
 	int ite = 0;
-	double EPS = 1e-15;
-	double* dotProducts = (double*)malloc(k*sizeof(double));
+	const Real EPS = 1e-15;
+	const Real gaussConstM = pow(2.*M_PI,m/2.);
 
 	while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
 	{
@@ -74,33 +75,33 @@ void EMGLLF(
 		{
 			for (int mm=0; mm<m; mm++)
 			{
-				//Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
+				//Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
 				for (int u=0; u<n; u++)
 					Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
 			}
 			for (int i=0; i<n; i++)
 			{
-				//X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
+				//X2[i,,r] = sqrt(gam[i,r]) * X[i,]
 				for (int u=0; u<p; u++)
-					X2[ai(i,u,r,n,m,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
+					X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
 			}
 			for (int mm=0; mm<m; mm++)
 			{
-				//ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
+				//ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
 				for (int u=0; u<p; u++)
 				{
-					double dotProduct = 0.;
+					Real dotProduct = 0.;
 					for (int v=0; v<n; v++)
 						dotProduct += X2[ai(v,u,r,n,m,k)] * Y2[ai(v,mm,r,n,m,k)];
-					ps2[ai(u,mm,r,n,m,k)] = dotProduct;
+					ps2[ai(u,mm,r,p,m,k)] = dotProduct;
 				}
 			}
 			for (int j=0; j<p; j++)
 			{
 				for (int s=0; s<p; s++)
 				{
-					//Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
-					double dotProduct = 0.;
+					//Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
+					Real dotProduct = 0.;
 					for (int u=0; u<n; u++)
 						dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
 					Gram2[ai(j,s,r,p,p,k)] = dotProduct;
@@ -115,26 +116,26 @@ void EMGLLF(
 		// Pour pi
 		for (int r=0; r<k; r++)
 		{
-			//b(r) = sum(sum(abs(phi(:,:,r))));
-			double sumAbsPhi = 0.;
+			//b[r] = sum(abs(phi[,,r]))
+			Real sumAbsPhi = 0.;
 			for (int u=0; u<p; u++)
 				for (int v=0; v<m; v++)
 					sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
 			b[r] = sumAbsPhi;
 		}
-		//gam2 = sum(gam,1);
+		//gam2 = colSums(gam)
 		for (int u=0; u<k; u++)
 		{
-			double sumOnColumn = 0.;
+			Real sumOnColumn = 0.;
 			for (int v=0; v<n; v++)
 				sumOnColumn += gam[mi(v,u,n,k)];
 			gam2[u] = sumOnColumn;
 		}
-		//a=sum(gam*transpose(log(pi)));
-		double a = 0.;
+		//a = sum(gam %*% log(pi))
+		Real a = 0.;
 		for (int u=0; u<n; u++)
 		{
-			double dotProduct = 0.;
+			Real dotProduct = 0.;
 			for (int v=0; v<k; v++)
 				dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
 			a += dotProduct;
@@ -143,12 +144,14 @@ void EMGLLF(
 		//tant que les proportions sont negatives
 		int kk = 0;
 		int pi2AllPositive = 0;
-		double invN = 1./n;
+		Real invN = 1./n;
 		while (!pi2AllPositive)
 		{
-			//pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
+			//pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
+			Real pow_01_kk = pow(0.1,kk);
 			for (int r=0; r<k; r++)
-				pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
+				pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
+			//pi2AllPositive = all(pi2 >= 0)
 			pi2AllPositive = 1;
 			for (int r=0; r<k; r++)
 			{
@@ -161,24 +164,26 @@ void EMGLLF(
 			kk++;
 		}
 
-		//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
 		//(pi.^gamma)*b
-		double piPowGammaDotB = 0.;
+		Real piPowGammaDotB = 0.;
 		for (int v=0; v<k; v++)
 			piPowGammaDotB += pow(pi[v],gamma) * b[v];
 		//(pi2.^gamma)*b
-		double pi2PowGammaDotB = 0.;
+		Real pi2PowGammaDotB = 0.;
 		for (int v=0; v<k; v++)
 			pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 		//transpose(gam2)*log(pi2)
-		double prodGam2logPi2 = 0.;
+		Real prodGam2logPi2 = 0.;
 		for (int v=0; v<k; v++)
 			prodGam2logPi2 += gam2[v] * log(pi2[v]);
-		while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB && kk<1000)
+		//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
+		while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
+			&& kk<1000)
 		{
-			//pi2=pi+0.1^kk*(1/n*gam2-pi);
+			Real pow_01_kk = pow(0.1,kk);
+			//pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
 			for (int v=0; v<k; v++)
-				pi2[v] = pi[v] + pow(0.1,kk) * (invN*gam2[v] - pi[v]);
+				pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
 			//pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
 			pi2PowGammaDotB = 0.;
 			for (int v=0; v<k; v++)
@@ -188,12 +193,12 @@ void EMGLLF(
 				prodGam2logPi2 += gam2[v] * log(pi2[v]);
 			kk++;
 		}
-		double t = pow(0.1,kk);
-		//sum(pi+t*(pi2-pi))
-		double sumPiPlusTbyDiff = 0.;
+		Real t = pow(0.1,kk);
+		//sum(pi + t*(pi2-pi))
+		Real sumPiPlusTbyDiff = 0.;
 		for (int v=0; v<k; v++)
 			sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
-		//pi=(pi+t*(pi2-pi))/sum(pi+t*(pi2-pi));
+		//pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
 		for (int v=0; v<k; v++)
 			pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
 
@@ -205,26 +210,26 @@ void EMGLLF(
 				for (int i=0; i<n; i++)
 				{
 					//< X2(i,:,r) , phi(:,mm,r) >
-					double dotProduct = 0.0;
+					Real dotProduct = 0.;
 					for (int u=0; u<p; u++)
-						dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,n,m,k)];
-					//ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
+						dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
+					//ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
 					ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
 					nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
 				}
-				//ps(mm,r)=sum(ps1(:,mm,r));
-				double sumPs1 = 0.0;
+				//ps[mm,r] = sum(ps1[,mm,r])
+				Real sumPs1 = 0.;
 				for (int u=0; u<n; u++)
 					sumPs1 += ps1[ai(u,mm,r,n,m,k)];
 				ps[mi(mm,r,m,k)] = sumPs1;
-				//nY2(mm,r)=sum(nY21(:,mm,r));
-				double sumNy21 = 0.0;
+				//nY2[mm,r] = sum(nY21[,mm,r])
+				Real sumNy21 = 0.;
 				for (int u=0; u<n; u++)
 					sumNy21 += nY21[ai(u,mm,r,n,m,k)];
 				nY2[mi(mm,r,m,k)] = sumNy21;
-				//rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
-				rho[ai(mm,mm,k,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)] 
-					+ 4*nY2[mi(mm,r,m,k)] * (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
+				//rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r]))) / (2*nY2[mm,r])
+				rho[ai(mm,mm,r,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
+					+ 4*nY2[mi(mm,r,m,k)] * gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
 			}
 		}
 		for (int r=0; r<k; r++)
@@ -233,23 +238,30 @@ void EMGLLF(
 			{
 				for (int mm=0; mm<m; mm++)
 				{
-					//sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)))
-					double dotPhiGram2 = 0.0;
+					//sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r])
+					Real dotPhiGram2 = 0.0;
 					for (int u=0; u<j; u++)
 						dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
+					//sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r])
 					for (int u=j+1; u<p; u++)
 						dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
-					//S(j,r,mm)=-rho(mm,mm,r)*ps2(j,mm,r)+sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))
-					//    +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
+					//S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
+					//  (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
+					//  (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
 					S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)] + dotPhiGram2;
-					if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow(pi[r],gamma))
+					Real pow_pir_gamma = pow(pi[r],gamma);
+					if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow_pir_gamma)
 						phi[ai(j,mm,r,p,m,k)] = 0;
-					else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow(pi[r],gamma))
-						phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow(pi[r],gamma) - S[ai(j,mm,r,p,m,k)]) 
+					else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow_pir_gamma)
+					{
+						phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow_pir_gamma - S[ai(j,mm,r,p,m,k)])
 							/ Gram2[ai(j,j,r,p,p,k)];
+					}
 					else
-						phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)]) 
+					{
+						phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow_pir_gamma + S[ai(j,mm,r,p,m,k)])
 							/ Gram2[ai(j,j,r,p,p,k)];
+					}
 				}
 			}
 		}
@@ -259,26 +271,19 @@ void EMGLLF(
 		/////////////
 
 		int signum;
-		double sumLogLLF2 = 0.0;
+		Real sumLogLLF2 = 0.0;
 		for (int i=0; i<n; i++)
 		{
-			double sumLLF1 = 0.0;
-			double sumGamI = 0.0;
-			double minDotProduct = INFINITY;
+			Real minSqNorm2 = 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 Y(i,:)*rho(:,:,r)
+				//compute Y[i,]%*%rho[,,r]
 				for (int u=0; u<m; u++)
 				{
 					YiRhoR[u] = 0.0;
 					for (int v=0; v<m; v++)
-						YiRhoR[u] += Y[imi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
+						YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 				}
 
 				//compute X(i,:)*phi(:,:,r)
@@ -289,87 +294,86 @@ void EMGLLF(
 						XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 				}
 
-				// compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
-				dotProducts[r] = 0.0;
+				//compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
+				sqNorm2[r] = 0.0;
 				for (int u=0; u<m; u++)
-					dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
-				if (dotProducts[r] < minDotProduct)
-					minDotProduct = dotProducts[r];
+					sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+				if (sqNorm2[r] < minSqNorm2)
+					minSqNorm2 = sqNorm2[r];
 			}
-			double shift = 0.5*minDotProduct;
+			Real shift = 0.5*minSqNorm2;
+
+			Real sumLLF1 = 0.0;
+			Real sumGamI = 0.0;
 			for (int r=0; r<k; r++)
 			{
-				//compute det(rho(:,:,r)) [TODO: avoid re-computations]
+				//compute det(rho[,,r]) [TODO: avoid re-computations]
 				for (int u=0; u<m; u++)
 				{
 					for (int v=0; v<m; v++)
 						matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 				}
 				gsl_linalg_LU_decomp(matrix, permutation, &signum);
-				double detRhoR = gsl_linalg_LU_det(matrix, signum);
+				Real detRhoR = gsl_linalg_LU_det(matrix, signum);
 
-				Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
-				sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
+				//FIXME: det(rho[,,r]) too small(?!). See EMGLLF.R
+				Gam[mi(i,r,n,k)] = pi[r] * exp(-0.5*sqNorm2[r] + shift) * detRhoR;
+				sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
 				sumGamI += Gam[mi(i,r,n,k)];
 			}
 			sumLogLLF2 += log(sumLLF1);
 			for (int r=0; r<k; r++)
 			{
-				//gam(i,r)=Gam(i,r)/sum(Gam(i,:));
-				gam[mi(i,r,n,k)] = sumGamI > EPS
-					? Gam[mi(i,r,n,k)] / sumGamI
-					: 0.0;
+				//gam[i,] = Gam[i,] / sumGamI
+				gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
 			}
 		}
-		
-		//sum(pen(ite,:))
-		double sumPen = 0.0;
+
+		//sumPen = sum(pi^gamma * b)
+		Real sumPen = 0.0;
 		for (int r=0; r<k; r++)
 			sumPen += pow(pi[r],gamma) * b[r];
-		//LLF(ite)=-1/n*sum(log(LLF2(ite,:)))+lambda*sum(pen(ite,:));
+		//LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 		LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
-		if (ite == 0)
-			dist = LLF[ite];
-		else 
-			dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
-		
-		//Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
-		double Dist1 = 0.0;
+		dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
+
+		//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
+		Real Dist1 = 0.0;
 		for (int u=0; u<p; u++)
 		{
 			for (int v=0; v<m; v++)
 			{
 				for (int w=0; w<k; w++)
 				{
-					double tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)]) 
+					Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)]) 
 						/ (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
 					if (tmpDist > Dist1)
 						Dist1 = tmpDist;
 				}
 			}
 		}
-		//Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
-		double Dist2 = 0.0;
+		//Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
+		Real Dist2 = 0.0;
 		for (int u=0; u<m; u++)
 		{
 			for (int v=0; v<m; v++)
 			{
 				for (int w=0; w<k; w++)
 				{
-					double tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)]) 
+					Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)]) 
 						/ (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
 					if (tmpDist > Dist2)
 						Dist2 = tmpDist;
 				}
 			}
 		}
-		//Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
-		double Dist3 = 0.0;
+		//Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
+		Real Dist3 = 0.0;
 		for (int u=0; u<n; u++)
 		{
 			for (int v=0; v<k; v++)
 			{
-				double tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
+				Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
 				if (tmpDist > Dist3)
 					Dist3 = tmpDist;
 			}
@@ -380,10 +384,10 @@ void EMGLLF(
 			dist2 = Dist2;
 		if (Dist3 > dist2)
 			dist2 = Dist3;
-		
+
 		ite++;
 	}
-	
+
 	//free memory
 	free(b);
 	free(gam);
@@ -405,5 +409,5 @@ void EMGLLF(
 	free(pi2);
 	free(X2);
 	free(Y2);
-	free(dotProducts);
+	free(sqNorm2);
 }