[valse.git] / src / sources / EMGLLF.c

#include "utils.h"
#include <stdlib.h>
#include <gsl/gsl_linalg.h>

// TODO: don't recompute indexes every time......
void EMGLLF_core(
	// IN parameters
	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)
	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
{
	//Initialize outputs
	copyArray(phiInit, phi, p*m*k);
	copyArray(rhoInit, rho, m*m*k);
	copyArray(piInit, pi, k);
	zeroArray(LLF, maxi);
	//S is already allocated, and doesn't need to be 'zeroed'

	//Other local variables
	Real* gam = (Real*)malloc(n*k*sizeof(Real));
	copyArray(gamInit, gam, n*k);
	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);
	Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
	Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
	Real dist = 0.;
	Real dist2 = 0.;
	int ite = 0;
	const Real EPS = 1e-15;
	const Real gaussConstM = pow(2.*M_PI,m/2.);

	while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
	{
		copyArray(phi, Phi, p*m*k);
		copyArray(rho, Rho, m*m*k);
		copyArray(pi, Pi, k);

		// Calculs associés a Y et X
		for (int r=0; r<k; r++)
		{
			for (int mm=0; mm<m; 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] = sqrt(gam[i,r]) * X[i,]
				for (int u=0; u<p; u++)
					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] = crossprod(X2[,,r],Y2[,mm,r])
				for (int u=0; u<p; u++)
				{
					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,p,m,k)] = dotProduct;
				}
			}
			for (int j=0; j<p; j++)
			{
				for (int s=0; s<p; s++)
				{
					//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;
				}
			}
		}

		/////////////
		// Etape M //
		/////////////

		// Pour pi
		for (int r=0; r<k; r++)
		{
			//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 = colSums(gam)
		for (int u=0; u<k; u++)
		{
			Real sumOnColumn = 0.;
			for (int v=0; v<n; v++)
				sumOnColumn += gam[mi(v,u,n,k)];
			gam2[u] = sumOnColumn;
		}
		//a = sum(gam %*% log(pi))
		Real a = 0.;
		for (int u=0; u<n; u++)
		{
			Real dotProduct = 0.;
			for (int v=0; v<k; v++)
				dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
			a += dotProduct;
		}

		//tant que les proportions sont negatives
		int kk = 0;
		int pi2AllPositive = 0;
		Real invN = 1./n;
		while (!pi2AllPositive)
		{
			//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_01_kk * (invN*gam2[r] - pi[r]);
			//pi2AllPositive = all(pi2 >= 0)
			pi2AllPositive = 1;
			for (int r=0; r<k; r++)
			{
				if (pi2[r] < 0)
				{
					pi2AllPositive = 0;
					break;
				}
			}
			kk++;
		}

		//(pi.^gamma)*b
		Real piPowGammaDotB = 0.;
		for (int v=0; v<k; v++)
			piPowGammaDotB += pow(pi[v],gamma) * b[v];
		//(pi2.^gamma)*b
		Real pi2PowGammaDotB = 0.;
		for (int v=0; v<k; v++)
			pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
		//transpose(gam2)*log(pi2)
		Real prodGam2logPi2 = 0.;
		for (int v=0; v<k; v++)
			prodGam2logPi2 += gam2[v] * log(pi2[v]);
		//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)
		{
			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_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++)
				pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
			prodGam2logPi2 = 0.;
			for (int v=0; v<k; v++)
				prodGam2logPi2 += gam2[v] * log(pi2[v]);
			kk++;
		}
		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))
		for (int v=0; v<k; v++)
			pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;

		//Pour phi et rho
		for (int r=0; r<k; r++)
		{
			for (int mm=0; mm<m; mm++)
			{
				for (int i=0; i<n; i++)
				{
					//< X2(i,:,r) , phi(:,mm,r) >
					Real dotProduct = 0.;
					for (int u=0; u<p; u++)
						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])
				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])
				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,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++)
		{
			for (int j=0; j<p; j++)
			{
				for (int mm=0; mm<m; mm++)
				{
					//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,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;
					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_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_pir_gamma + S[ai(j,mm,r,p,m,k)])
							/ Gram2[ai(j,j,r,p,p,k)];
					}
				}
			}
		}

		/////////////
		// Etape E //
		/////////////

		int signum;
		Real sumLogLLF2 = 0.0;
		for (int i=0; i<n; i++)
		{
			Real minSqNorm2 = INFINITY;

			for (int r=0; r<k; 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[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
				}

				//compute X(i,:)*phi(:,:,r)
				for (int u=0; u<m; u++)
				{
					XiPhiR[u] = 0.0;
					for (int v=0; v<p; v++)
						XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
				}

				//compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
				sqNorm2[r] = 0.0;
				for (int u=0; u<m; u++)
					sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
				if (sqNorm2[r] < minSqNorm2)
					minSqNorm2 = sqNorm2[r];
			}
			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]
				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);
				Real detRhoR = gsl_linalg_LU_det(matrix, signum);

				//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,] = Gam[i,] / sumGamI
				gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 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] = -sumLogLLF2/n + lambda*sumPen
		LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
		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++)
				{
					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( (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++)
				{
					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( (abs(pi-Pi)) / (1+abs(Pi)))
		Real Dist3 = 0.0;
		for (int u=0; u<n; u++)
		{
			for (int v=0; v<k; v++)
			{
				Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
				if (tmpDist > Dist3)
					Dist3 = tmpDist;
			}
		}
		//dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
		dist2 = Dist1;
		if (Dist2 > dist2)
			dist2 = Dist2;
		if (Dist3 > dist2)
			dist2 = Dist3;

		ite++;
	}

	//free memory
	free(b);
	free(gam);
	free(Gam);
	free(Phi);
	free(Rho);
	free(Pi);
	free(ps);
	free(nY2);
	free(ps1);
	free(nY21);
	free(Gram2);
	free(ps2);
	gsl_matrix_free(matrix);
	gsl_permutation_free(permutation);
	free(XiPhiR);
	free(YiRhoR);
	free(gam2);
	free(pi2);
	free(X2);
	free(Y2);
	free(sqNorm2);
}
Commit	Line	Data
	1	#include "utils.h"
	2	#include <stdlib.h>
	3	#include <gsl/gsl_linalg.h>
	4
	5	// TODO: don't recompute indexes every time......
	6	void EMGLLF_core(
	7	// IN parameters
	8	const Real* phiInit, // parametre initial de moyenne renormalisé
	9	const Real* rhoInit, // parametre initial de variance renormalisé
	10	const Real* piInit, // parametre initial des proportions
	11	const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
	12	int mini, // nombre minimal d'itérations dans l'algorithme EM
	13	int maxi, // nombre maximal d'itérations dans l'algorithme EM
	14	Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
	15	Real lambda, // valeur du paramètre de régularisation du Lasso
	16	const Real* X, // régresseurs
	17	const Real* Y, // réponse
	18	Real tau, // seuil pour accepter la convergence
	19	// OUT parameters (all pointers, to be modified)
	20	Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
	21	Real* rho, // parametre de variance renormalisé, calculé par l'EM
	22	Real* pi, // parametre des proportions renormalisé, calculé par l'EM
	23	Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
	24	Real* S,
	25	// additional size parameters
	26	int n, // nombre d'echantillons
	27	int p, // nombre de covariables
	28	int m, // taille de Y (multivarié)
	29	int k) // nombre de composantes dans le mélange
	30	{
	31	//Initialize outputs
	32	copyArray(phiInit, phi, pmk);
	33	copyArray(rhoInit, rho, mmk);
	34	copyArray(piInit, pi, k);
	35	zeroArray(LLF, maxi);
	36	//S is already allocated, and doesn't need to be 'zeroed'
	37
	38	//Other local variables
	39	Real* gam = (Real)malloc(nk*sizeof(Real));
	40	copyArray(gamInit, gam, n*k);
	41	Real* b = (Real)malloc(ksizeof(Real));
	42	Real* Phi = (Real)malloc(pmksizeof(Real));
	43	Real* Rho = (Real)malloc(mmksizeof(Real));
	44	Real* Pi = (Real)malloc(ksizeof(Real));
	45	Real* gam2 = (Real)malloc(ksizeof(Real));
	46	Real* pi2 = (Real)malloc(ksizeof(Real));
	47	Real* Gram2 = (Real)malloc(ppksizeof(Real));
	48	Real* ps = (Real)malloc(mk*sizeof(Real));
	49	Real* nY2 = (Real)malloc(mk*sizeof(Real));
	50	Real* ps1 = (Real)malloc(nmksizeof(Real));
	51	Real* ps2 = (Real)malloc(pmksizeof(Real));
	52	Real* nY21 = (Real)malloc(nmksizeof(Real));
	53	Real* Gam = (Real)malloc(nk*sizeof(Real));
	54	Real* X2 = (Real)malloc(npksizeof(Real));
	55	Real* Y2 = (Real)malloc(nmksizeof(Real));
	56	Real* sqNorm2 = (Real)malloc(ksizeof(Real));
	57	gsl_matrix* matrix = gsl_matrix_alloc(m, m);
	58	gsl_permutation* permutation = gsl_permutation_alloc(m);
	59	Real* YiRhoR = (Real)malloc(msizeof(Real));
	60	Real* XiPhiR = (Real)malloc(msizeof(Real));
	61	Real dist = 0.;
	62	Real dist2 = 0.;
	63	int ite = 0;
	64	const Real EPS = 1e-15;
	65	const Real gaussConstM = pow(2.*M_PI,m/2.);
	66
	67	while (ite < mini \|\| (ite < maxi && (dist >= tau \|\| dist2 >= sqrt(tau))))
	68	{
	69	copyArray(phi, Phi, pmk);
	70	copyArray(rho, Rho, mmk);
	71	copyArray(pi, Pi, k);
	72
	73	// Calculs associés a Y et X
	74	for (int r=0; r<k; r++)
	75	{
	76	for (int mm=0; mm<m; mm++)
	77	{
	78	//Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
	79	for (int u=0; u<n; u++)
	80	Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
	81	}
	82	for (int i=0; i<n; i++)
	83	{
	84	//X2[i,,r] = sqrt(gam[i,r]) * X[i,]
	85	for (int u=0; u<p; u++)
	86	X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
	87	}
	88	for (int mm=0; mm<m; mm++)
	89	{
	90	//ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
	91	for (int u=0; u<p; u++)
	92	{
	93	Real dotProduct = 0.;
	94	for (int v=0; v<n; v++)
	95	dotProduct += X2[ai(v,u,r,n,m,k)] * Y2[ai(v,mm,r,n,m,k)];
	96	ps2[ai(u,mm,r,p,m,k)] = dotProduct;
	97	}
	98	}
	99	for (int j=0; j<p; j++)
	100	{
	101	for (int s=0; s<p; s++)
	102	{
	103	//Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
	104	Real dotProduct = 0.;
	105	for (int u=0; u<n; u++)
	106	dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
	107	Gram2[ai(j,s,r,p,p,k)] = dotProduct;
	108	}
	109	}
	110	}
	111
	112	/////////////
	113	// Etape M //
	114	/////////////
	115
	116	// Pour pi
	117	for (int r=0; r<k; r++)
	118	{
	119	//b[r] = sum(abs(phi[,,r]))
	120	Real sumAbsPhi = 0.;
	121	for (int u=0; u<p; u++)
	122	for (int v=0; v<m; v++)
	123	sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
	124	b[r] = sumAbsPhi;
	125	}
	126	//gam2 = colSums(gam)
	127	for (int u=0; u<k; u++)
	128	{
	129	Real sumOnColumn = 0.;
	130	for (int v=0; v<n; v++)
	131	sumOnColumn += gam[mi(v,u,n,k)];
	132	gam2[u] = sumOnColumn;
	133	}
	134	//a = sum(gam %*% log(pi))
	135	Real a = 0.;
	136	for (int u=0; u<n; u++)
	137	{
	138	Real dotProduct = 0.;
	139	for (int v=0; v<k; v++)
	140	dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
	141	a += dotProduct;
	142	}
	143
	144	//tant que les proportions sont negatives
	145	int kk = 0;
	146	int pi2AllPositive = 0;
	147	Real invN = 1./n;
	148	while (!pi2AllPositive)
	149	{
	150	//pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
	151	Real pow_01_kk = pow(0.1,kk);
	152	for (int r=0; r<k; r++)
	153	pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
	154	//pi2AllPositive = all(pi2 >= 0)
	155	pi2AllPositive = 1;
	156	for (int r=0; r<k; r++)
	157	{
	158	if (pi2[r] < 0)
	159	{
	160	pi2AllPositive = 0;
	161	break;
	162	}
	163	}
	164	kk++;
	165	}
	166
	167	//(pi.^gamma)*b
	168	Real piPowGammaDotB = 0.;
	169	for (int v=0; v<k; v++)
	170	piPowGammaDotB += pow(pi[v],gamma) * b[v];
	171	//(pi2.^gamma)*b
	172	Real pi2PowGammaDotB = 0.;
	173	for (int v=0; v<k; v++)
	174	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
	175	//transpose(gam2)*log(pi2)
	176	Real prodGam2logPi2 = 0.;
	177	for (int v=0; v<k; v++)
	178	prodGam2logPi2 += gam2[v] * log(pi2[v]);
	179	//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
	180	while (-invNa + lambdapiPowGammaDotB < -invNprodGam2logPi2 + lambdapi2PowGammaDotB
	181	&& kk<1000)
	182	{
	183	Real pow_01_kk = pow(0.1,kk);
	184	//pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
	185	for (int v=0; v<k; v++)
	186	pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
	187	//pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
	188	pi2PowGammaDotB = 0.;
	189	for (int v=0; v<k; v++)
	190	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
	191	prodGam2logPi2 = 0.;
	192	for (int v=0; v<k; v++)
	193	prodGam2logPi2 += gam2[v] * log(pi2[v]);
	194	kk++;
	195	}
	196	Real t = pow(0.1,kk);
	197	//sum(pi + t*(pi2-pi))
	198	Real sumPiPlusTbyDiff = 0.;
	199	for (int v=0; v<k; v++)
	200	sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
	201	//pi = (pi + t(pi2-pi)) / sum(pi + t(pi2-pi))
	202	for (int v=0; v<k; v++)
	203	pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
	204
	205	//Pour phi et rho
	206	for (int r=0; r<k; r++)
	207	{
	208	for (int mm=0; mm<m; mm++)
	209	{
	210	for (int i=0; i<n; i++)
	211	{
	212	//< X2(i,:,r) , phi(:,mm,r) >
	213	Real dotProduct = 0.;
	214	for (int u=0; u<p; u++)
	215	dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
	216	//ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
	217	ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
	218	nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
	219	}
	220	//ps[mm,r] = sum(ps1[,mm,r])
	221	Real sumPs1 = 0.;
	222	for (int u=0; u<n; u++)
	223	sumPs1 += ps1[ai(u,mm,r,n,m,k)];
	224	ps[mi(mm,r,m,k)] = sumPs1;
	225	//nY2[mm,r] = sum(nY21[,mm,r])
	226	Real sumNy21 = 0.;
	227	for (int u=0; u<n; u++)
	228	sumNy21 += nY21[ai(u,mm,r,n,m,k)];
	229	nY2[mi(mm,r,m,k)] = sumNy21;
	230	//rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4nY2[mm,r](gam2[r]))) / (2*nY2[mm,r])
	231	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)]
	232	+ 4nY2[mi(mm,r,m,k)] gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
	233	}
	234	}
	235	for (int r=0; r<k; r++)
	236	{
	237	for (int j=0; j<p; j++)
	238	{
	239	for (int mm=0; mm<m; mm++)
	240	{
	241	//sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r])
	242	Real dotPhiGram2 = 0.0;
	243	for (int u=0; u<j; u++)
	244	dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
	245	//sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r])
	246	for (int u=j+1; u<p; u++)
	247	dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
	248	//S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
	249	// (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
	250	// (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
	251	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;
	252	Real pow_pir_gamma = pow(pi[r],gamma);
	253	if (fabs(S[ai(j,mm,r,p,m,k)]) <= nlambdapow_pir_gamma)
	254	phi[ai(j,mm,r,p,m,k)] = 0;
	255	else if (S[ai(j,mm,r,p,m,k)] > nlambdapow_pir_gamma)
	256	{
	257	phi[ai(j,mm,r,p,m,k)] = (nlambdapow_pir_gamma - S[ai(j,mm,r,p,m,k)])
	258	/ Gram2[ai(j,j,r,p,p,k)];
	259	}
	260	else
	261	{
	262	phi[ai(j,mm,r,p,m,k)] = -(nlambdapow_pir_gamma + S[ai(j,mm,r,p,m,k)])
	263	/ Gram2[ai(j,j,r,p,p,k)];
	264	}
	265	}
	266	}
	267	}
	268
	269	/////////////
	270	// Etape E //
	271	/////////////
	272
	273	int signum;
	274	Real sumLogLLF2 = 0.0;
	275	for (int i=0; i<n; i++)
	276	{
	277	Real minSqNorm2 = INFINITY;
	278
	279	for (int r=0; r<k; r++)
	280	{
	281	//compute Y[i,]%*%rho[,,r]
	282	for (int u=0; u<m; u++)
	283	{
	284	YiRhoR[u] = 0.0;
	285	for (int v=0; v<m; v++)
	286	YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
	287	}
	288
	289	//compute X(i,:)*phi(:,:,r)
	290	for (int u=0; u<m; u++)
	291	{
	292	XiPhiR[u] = 0.0;
	293	for (int v=0; v<p; v++)
	294	XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
	295	}
	296
	297	//compute sq norm \|\| Y(:,i)rho(:,:,r)-X(i,:)phi(:,:,r) \|\|_2^2
	298	sqNorm2[r] = 0.0;
	299	for (int u=0; u<m; u++)
	300	sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
	301	if (sqNorm2[r] < minSqNorm2)
	302	minSqNorm2 = sqNorm2[r];
	303	}
	304	Real shift = 0.5*minSqNorm2;
	305
	306	Real sumLLF1 = 0.0;
	307	Real sumGamI = 0.0;
	308	for (int r=0; r<k; r++)
	309	{
	310	//compute det(rho[,,r]) [TODO: avoid re-computations]
	311	for (int u=0; u<m; u++)
	312	{
	313	for (int v=0; v<m; v++)
	314	matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
	315	}
	316	gsl_linalg_LU_decomp(matrix, permutation, &signum);
	317	Real detRhoR = gsl_linalg_LU_det(matrix, signum);
	318
	319	//FIXME: det(rho[,,r]) too small(?!). See EMGLLF.R
	320	Gam[mi(i,r,n,k)] = pi[r] * exp(-0.5sqNorm2[r] + shift) detRhoR;
	321	sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
	322	sumGamI += Gam[mi(i,r,n,k)];
	323	}
	324	sumLogLLF2 += log(sumLLF1);
	325	for (int r=0; r<k; r++)
	326	{
	327	//gam[i,] = Gam[i,] / sumGamI
	328	gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
	329	}
	330	}
	331
	332	//sumPen = sum(pi^gamma * b)
	333	Real sumPen = 0.0;
	334	for (int r=0; r<k; r++)
	335	sumPen += pow(pi[r],gamma) * b[r];
	336	//LLF[ite] = -sumLogLLF2/n + lambda*sumPen
	337	LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
	338	dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
	339
	340	//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
	341	Real Dist1 = 0.0;
	342	for (int u=0; u<p; u++)
	343	{
	344	for (int v=0; v<m; v++)
	345	{
	346	for (int w=0; w<k; w++)
	347	{
	348	Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
	349	/ (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
	350	if (tmpDist > Dist1)
	351	Dist1 = tmpDist;
	352	}
	353	}
	354	}
	355	//Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
	356	Real Dist2 = 0.0;
	357	for (int u=0; u<m; u++)
	358	{
	359	for (int v=0; v<m; v++)
	360	{
	361	for (int w=0; w<k; w++)
	362	{
	363	Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
	364	/ (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
	365	if (tmpDist > Dist2)
	366	Dist2 = tmpDist;
	367	}
	368	}
	369	}
	370	//Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
	371	Real Dist3 = 0.0;
	372	for (int u=0; u<n; u++)
	373	{
	374	for (int v=0; v<k; v++)
	375	{
	376	Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
	377	if (tmpDist > Dist3)
	378	Dist3 = tmpDist;
	379	}
	380	}
	381	//dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
	382	dist2 = Dist1;
	383	if (Dist2 > dist2)
	384	dist2 = Dist2;
	385	if (Dist3 > dist2)
	386	dist2 = Dist3;
	387
	388	ite++;
	389	}
	390
	391	//free memory
	392	free(b);
	393	free(gam);
	394	free(Gam);
	395	free(Phi);
	396	free(Rho);
	397	free(Pi);
	398	free(ps);
	399	free(nY2);
	400	free(ps1);
	401	free(nY21);
	402	free(Gram2);
	403	free(ps2);
	404	gsl_matrix_free(matrix);
	405	gsl_permutation_free(permutation);
	406	free(XiPhiR);
	407	free(YiRhoR);
	408	free(gam2);
	409	free(pi2);
	410	free(X2);
	411	free(Y2);
	412	free(sqNorm2);
	413	}