[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 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, // 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
	// 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 associée à cet échantillon, pour les valeurs estimées des paramètres
	double* 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
	//NOTE: variables order is always [maxi],n,p,m,k
	double* gam = (double*)malloc(n*k*sizeof(double));
	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));
	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.;
	int ite = 0;
	double EPS = 1e-15;
	double* dotProducts = (double*)malloc(k*sizeof(double));

	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)).*transpose(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));
				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)];
			}
			for (int mm=0; mm<m; mm++)
			{
				//ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
				for (int u=0; u<p; u++)
				{
					double 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;
				}
			}
			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.;
					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(sum(abs(phi(:,:,r))));
			double 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);
		for (int u=0; u<k; u++)
		{
			double 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.;
		for (int u=0; u<n; u++)
		{
			double 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;
		double invN = 1./n;
		while (!pi2AllPositive)
		{
			//pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
			for (int r=0; r<k; r++)
				pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
			pi2AllPositive = 1;
			for (int r=0; r<k; r++)
			{
				if (pi2[r] < 0)
				{
					pi2AllPositive = 0;
					break;
				}
			}
			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.;
		for (int v=0; v<k; v++)
			piPowGammaDotB += pow(pi[v],gamma) * b[v];
		//(pi2.^gamma)*b
		double pi2PowGammaDotB = 0.;
		for (int v=0; v<k; v++)
			pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
		//transpose(gam2)*log(pi2)
		double 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)
		{
			//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 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++;
		}
		double t = pow(0.1,kk);
		//sum(pi+t*(pi2-pi))
		double 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) >
					double dotProduct = 0.0;
					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));
					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;
				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;
				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)]);
			}
		}
		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).*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;
					for (int u=0; u<j; u++)
						dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
					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[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))
						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)])
							/ 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)])
							/ Gram2[ai(j,j,r,p,p,k)];
				}
			}
		}

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

		int signum;
		double sumLogLLF2 = 0.0;
		for (int i=0; i<n; i++)
		{
			double sumLLF1 = 0.0;
			double sumGamI = 0.0;
			double minDotProduct = 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)
				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 dotProduct
				// < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
				dotProducts[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];
			}
			double shift = 0.5*minDotProduct;
			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);
				double 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);
				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;
			}
		}
		
		//sum(pen(ite,:))
		double 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] = -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;
		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)]) 
						/ (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;
		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)]) 
						/ (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;
		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]));
				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(dotProducts);
}
Commit	Line	Data
8e92c49c BA	1	#include "utils.h"
8e92c49c BA	2	#include <stdlib.h>
1d3c1faa BA	3	#include <gsl/gsl_linalg.h>
1d3c1faa BA	4
4cab944a	5	// TODO: don't recompute indexes every time......
09ab3c16	6	void EMGLLF_core(
1d3c1faa	7	// IN parameters
8e92c49c BA	8	const double* phiInit, // parametre initial de moyenne renormalisé
	9	const double* rhoInit, // parametre initial de variance renormalisé
	10	const double* piInit, // parametre initial des proportions
	11	const double* 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	double gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
4cab944a	15	double lambda, // valeur du paramètre de régularisation du Lasso
8e92c49c BA	16	const double* X, // régresseurs
	17	const double* Y, // réponse
	18	double tau, // seuil pour accepter la convergence
1d3c1faa	19	// OUT parameters (all pointers, to be modified)
8e92c49c BA	20	double* phi, // parametre de moyenne renormalisé, calculé par l'EM
	21	double* rho, // parametre de variance renormalisé, calculé par l'EM
	22	double* pi, // parametre des proportions renormalisé, calculé par l'EM
	23	double* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
	24	double* S,
1d3c1faa	25	// additional size parameters
8e92c49c BA	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
1d3c1faa BA	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'
4cab944a	37
1d3c1faa BA	38	//Other local variables
1d3c1faa BA	39	//NOTE: variables order is always [maxi],n,p,m,k
4cab944a	40	double* gam = (double)malloc(nk*sizeof(double));
1d3c1faa	41	copyArray(gamInit, gam, n*k);
4cab944a BA	42	double* b = (double)malloc(ksizeof(double));
	43	double* Phi = (double)malloc(pmksizeof(double));
	44	double* Rho = (double)malloc(mmksizeof(double));
	45	double* Pi = (double)malloc(ksizeof(double));
	46	double* gam2 = (double)malloc(ksizeof(double));
	47	double* pi2 = (double)malloc(ksizeof(double));
	48	double* Gram2 = (double)malloc(ppksizeof(double));
	49	double* ps = (double)malloc(mk*sizeof(double));
	50	double* nY2 = (double)malloc(mk*sizeof(double));
	51	double* ps1 = (double)malloc(nmksizeof(double));
	52	double* ps2 = (double)malloc(pmksizeof(double));
	53	double* nY21 = (double)malloc(nmksizeof(double));
	54	double* Gam = (double)malloc(nk*sizeof(double));
	55	double* X2 = (double)malloc(npksizeof(double));
	56	double* Y2 = (double)malloc(nmksizeof(double));
1d3c1faa BA	57	gsl_matrix* matrix = gsl_matrix_alloc(m, m);
1d3c1faa BA	58	gsl_permutation* permutation = gsl_permutation_alloc(m);
4cab944a BA	59	double* YiRhoR = (double)malloc(msizeof(double));
	60	double* XiPhiR = (double)malloc(msizeof(double));
	61	double dist = 0.;
	62	double dist2 = 0.;
	63	int ite = 0;
	64	double EPS = 1e-15;
	65	double* dotProducts = (double)malloc(ksizeof(double));
	66
1d3c1faa BA	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);
4cab944a BA	72
	73	// Calculs associés a Y et X
	74	for (int r=0; r<k; r++)
1d3c1faa	75	{
4cab944a	76	for (int mm=0; mm<m; mm++)
1d3c1faa BA	77	{
1d3c1faa BA	78	//Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
4cab944a BA	79	for (int u=0; u<n; u++)
4cab944a BA	80	Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
1d3c1faa	81	}
4cab944a	82	for (int i=0; i<n; i++)
1d3c1faa BA	83	{
1d3c1faa BA	84	//X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
4cab944a BA	85	for (int u=0; u<p; u++)
4cab944a BA	86	X2[ai(i,u,r,n,m,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
1d3c1faa	87	}
4cab944a	88	for (int mm=0; mm<m; mm++)
1d3c1faa BA	89	{
1d3c1faa BA	90	//ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
4cab944a	91	for (int u=0; u<p; u++)
1d3c1faa	92	{
4cab944a BA	93	double 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,n,m,k)] = dotProduct;
1d3c1faa BA	97	}
1d3c1faa BA	98	}
4cab944a	99	for (int j=0; j<p; j++)
1d3c1faa	100	{
4cab944a	101	for (int s=0; s<p; s++)
1d3c1faa BA	102	{
1d3c1faa BA	103	//Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
4cab944a BA	104	double 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;
1d3c1faa BA	108	}
	109	}
	110	}
	111
	112	/////////////
	113	// Etape M //
	114	/////////////
4cab944a	115
1d3c1faa	116	// Pour pi
4cab944a	117	for (int r=0; r<k; r++)
1d3c1faa BA	118	{
1d3c1faa BA	119	//b(r) = sum(sum(abs(phi(:,:,r))));
4cab944a BA	120	double 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)]);
1d3c1faa BA	124	b[r] = sumAbsPhi;
	125	}
	126	//gam2 = sum(gam,1);
4cab944a	127	for (int u=0; u<k; u++)
1d3c1faa	128	{
4cab944a BA	129	double sumOnColumn = 0.;
	130	for (int v=0; v<n; v++)
	131	sumOnColumn += gam[mi(v,u,n,k)];
1d3c1faa BA	132	gam2[u] = sumOnColumn;
	133	}
	134	//a=sum(gam*transpose(log(pi)));
4cab944a BA	135	double a = 0.;
4cab944a BA	136	for (int u=0; u<n; u++)
1d3c1faa	137	{
4cab944a BA	138	double dotProduct = 0.;
	139	for (int v=0; v<k; v++)
	140	dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
1d3c1faa BA	141	a += dotProduct;
1d3c1faa BA	142	}
4cab944a	143
1d3c1faa	144	//tant que les proportions sont negatives
4cab944a	145	int kk = 0;
1d3c1faa	146	int pi2AllPositive = 0;
4cab944a	147	double invN = 1./n;
1d3c1faa BA	148	while (!pi2AllPositive)
	149	{
	150	//pi2(:)=pi(:)+0.1^kk(1/ngam2(:)-pi(:));
4cab944a	151	for (int r=0; r<k; r++)
1d3c1faa BA	152	pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
1d3c1faa BA	153	pi2AllPositive = 1;
4cab944a	154	for (int r=0; r<k; r++)
1d3c1faa BA	155	{
	156	if (pi2[r] < 0)
	157	{
	158	pi2AllPositive = 0;
	159	break;
	160	}
	161	}
	162	kk++;
	163	}
4cab944a	164
1d3c1faa BA	165	//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
1d3c1faa BA	166	//(pi.^gamma)*b
4cab944a BA	167	double piPowGammaDotB = 0.;
4cab944a BA	168	for (int v=0; v<k; v++)
1d3c1faa BA	169	piPowGammaDotB += pow(pi[v],gamma) * b[v];
1d3c1faa BA	170	//(pi2.^gamma)*b
4cab944a BA	171	double pi2PowGammaDotB = 0.;
4cab944a BA	172	for (int v=0; v<k; v++)
1d3c1faa BA	173	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
1d3c1faa BA	174	//transpose(gam2)*log(pi2)
4cab944a BA	175	double prodGam2logPi2 = 0.;
4cab944a BA	176	for (int v=0; v<k; v++)
1d3c1faa	177	prodGam2logPi2 += gam2[v] * log(pi2[v]);
8e92c49c BA	178	while (-invNa + lambdapiPowGammaDotB < -invNprodGam2logPi2 + lambdapi2PowGammaDotB
8e92c49c BA	179	&& kk<1000)
1d3c1faa BA	180	{
1d3c1faa BA	181	//pi2=pi+0.1^kk(1/ngam2-pi);
4cab944a	182	for (int v=0; v<k; v++)
1d3c1faa BA	183	pi2[v] = pi[v] + pow(0.1,kk) * (invN*gam2[v] - pi[v]);
1d3c1faa BA	184	//pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
4cab944a BA	185	pi2PowGammaDotB = 0.;
4cab944a BA	186	for (int v=0; v<k; v++)
1d3c1faa	187	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
4cab944a BA	188	prodGam2logPi2 = 0.;
4cab944a BA	189	for (int v=0; v<k; v++)
1d3c1faa BA	190	prodGam2logPi2 += gam2[v] * log(pi2[v]);
	191	kk++;
	192	}
4cab944a	193	double t = pow(0.1,kk);
1d3c1faa	194	//sum(pi+t*(pi2-pi))
4cab944a BA	195	double sumPiPlusTbyDiff = 0.;
4cab944a BA	196	for (int v=0; v<k; v++)
1d3c1faa BA	197	sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
1d3c1faa BA	198	//pi=(pi+t(pi2-pi))/sum(pi+t(pi2-pi));
4cab944a	199	for (int v=0; v<k; v++)
1d3c1faa	200	pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
4cab944a	201
1d3c1faa	202	//Pour phi et rho
4cab944a	203	for (int r=0; r<k; r++)
1d3c1faa	204	{
4cab944a	205	for (int mm=0; mm<m; mm++)
1d3c1faa	206	{
4cab944a	207	for (int i=0; i<n; i++)
1d3c1faa BA	208	{
1d3c1faa BA	209	//< X2(i,:,r) , phi(:,mm,r) >
4cab944a BA	210	double dotProduct = 0.0;
	211	for (int u=0; u<p; u++)
	212	dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,n,m,k)];
1d3c1faa	213	//ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
4cab944a BA	214	ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
4cab944a BA	215	nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
1d3c1faa BA	216	}
1d3c1faa BA	217	//ps(mm,r)=sum(ps1(:,mm,r));
4cab944a BA	218	double sumPs1 = 0.0;
	219	for (int u=0; u<n; u++)
	220	sumPs1 += ps1[ai(u,mm,r,n,m,k)];
	221	ps[mi(mm,r,m,k)] = sumPs1;
1d3c1faa	222	//nY2(mm,r)=sum(nY21(:,mm,r));
4cab944a BA	223	double sumNy21 = 0.0;
	224	for (int u=0; u<n; u++)
	225	sumNy21 += nY21[ai(u,mm,r,n,m,k)];
	226	nY2[mi(mm,r,m,k)] = sumNy21;
1d3c1faa	227	//rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4nY2(mm,r)(gam2(r))))/(2*nY2(mm,r)));
8e92c49c	228	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)]
4cab944a	229	+ 4nY2[mi(mm,r,m,k)] (gam2[r]) ) ) / (2*nY2[mi(mm,r,m,k)]);
1d3c1faa BA	230	}
1d3c1faa BA	231	}
4cab944a	232	for (int r=0; r<k; r++)
1d3c1faa	233	{
4cab944a	234	for (int j=0; j<p; j++)
1d3c1faa	235	{
4cab944a	236	for (int mm=0; mm<m; mm++)
1d3c1faa	237	{
8e92c49c BA	238	//sum(phi(1:j-1,mm,r).*transpose(Gram2(j,1:j-1,r)))+sum(phi(j+1:p,mm,r)
8e92c49c BA	239	// .*transpose(Gram2(j,j+1:p,r)))
4cab944a BA	240	double dotPhiGram2 = 0.0;
	241	for (int u=0; u<j; u++)
	242	dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
	243	for (int u=j+1; u<p; u++)
	244	dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
1d3c1faa	245	//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)))
8e92c49c	246	// +sum(phi(j+1:p,mm,r).*transpose(Gram2(j,j+1:p,r)));
4cab944a BA	247	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;
	248	if (fabs(S[ai(j,mm,r,p,m,k)]) <= nlambdapow(pi[r],gamma))
	249	phi[ai(j,mm,r,p,m,k)] = 0;
	250	else if (S[ai(j,mm,r,p,m,k)] > nlambdapow(pi[r],gamma))
8e92c49c	251	phi[ai(j,mm,r,p,m,k)] = (nlambdapow(pi[r],gamma) - S[ai(j,mm,r,p,m,k)])
4cab944a	252	/ Gram2[ai(j,j,r,p,p,k)];
1d3c1faa	253	else
8e92c49c	254	phi[ai(j,mm,r,p,m,k)] = -(nlambdapow(pi[r],gamma) + S[ai(j,mm,r,p,m,k)])
4cab944a	255	/ Gram2[ai(j,j,r,p,p,k)];
1d3c1faa BA	256	}
	257	}
	258	}
4cab944a	259
1d3c1faa BA	260	/////////////
	261	// Etape E //
	262	/////////////
4cab944a	263
1d3c1faa	264	int signum;
4cab944a BA	265	double sumLogLLF2 = 0.0;
4cab944a BA	266	for (int i=0; i<n; i++)
1d3c1faa	267	{
4cab944a BA	268	double sumLLF1 = 0.0;
	269	double sumGamI = 0.0;
	270	double minDotProduct = INFINITY;
	271
	272	for (int r=0; r<k; r++)
1d3c1faa BA	273	{
	274	//Compute
	275	//Gam(i,r) = Pi(r) * det(Rho(:,:,r)) * exp( -1/2 * (Y(i,:)*Rho(:,:,r) - X(i,:)...
8e92c49c	276	// phi(:,:,r)) transpose( Y(i,:)Rho(:,:,r) - X(i,:)phi(:,:,r) ) );
1d3c1faa BA	277	//split in several sub-steps
	278
	279	//compute Y(i,:)*rho(:,:,r)
4cab944a	280	for (int u=0; u<m; u++)
1d3c1faa BA	281	{
1d3c1faa BA	282	YiRhoR[u] = 0.0;
4cab944a	283	for (int v=0; v<m; v++)
aa8df014	284	YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
1d3c1faa	285	}
4cab944a	286
1d3c1faa	287	//compute X(i,:)*phi(:,:,r)
4cab944a	288	for (int u=0; u<m; u++)
1d3c1faa BA	289	{
1d3c1faa BA	290	XiPhiR[u] = 0.0;
4cab944a BA	291	for (int v=0; v<p; v++)
4cab944a BA	292	XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
1d3c1faa	293	}
4cab944a	294
8e92c49c BA	295	//compute dotProduct
8e92c49c BA	296	// < Y(:,i)rho(:,:,r)-X(i,:)phi(:,:,r) . Y(:,i)rho(:,:,r)-X(i,:)phi(:,:,r) >
1d3c1faa	297	dotProducts[r] = 0.0;
4cab944a	298	for (int u=0; u<m; u++)
1d3c1faa BA	299	dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
	300	if (dotProducts[r] < minDotProduct)
	301	minDotProduct = dotProducts[r];
	302	}
4cab944a BA	303	double shift = 0.5*minDotProduct;
4cab944a BA	304	for (int r=0; r<k; r++)
1d3c1faa BA	305	{
1d3c1faa BA	306	//compute det(rho(:,:,r)) [TODO: avoid re-computations]
4cab944a	307	for (int u=0; u<m; u++)
1d3c1faa	308	{
4cab944a BA	309	for (int v=0; v<m; v++)
4cab944a BA	310	matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
1d3c1faa BA	311	}
1d3c1faa BA	312	gsl_linalg_LU_decomp(matrix, permutation, &signum);
4cab944a BA	313	double detRhoR = gsl_linalg_LU_det(matrix, signum);
	314
	315	Gam[mi(i,r,n,k)] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
	316	sumLLF1 += Gam[mi(i,r,n,k)] / pow(2*M_PI,m/2.0);
	317	sumGamI += Gam[mi(i,r,n,k)];
1d3c1faa BA	318	}
1d3c1faa BA	319	sumLogLLF2 += log(sumLLF1);
4cab944a	320	for (int r=0; r<k; r++)
1d3c1faa BA	321	{
1d3c1faa BA	322	//gam(i,r)=Gam(i,r)/sum(Gam(i,:));
4cab944a BA	323	gam[mi(i,r,n,k)] = sumGamI > EPS
4cab944a BA	324	? Gam[mi(i,r,n,k)] / sumGamI
1d3c1faa BA	325	: 0.0;
	326	}
	327	}
	328
	329	//sum(pen(ite,:))
4cab944a BA	330	double sumPen = 0.0;
4cab944a BA	331	for (int r=0; r<k; r++)
1d3c1faa BA	332	sumPen += pow(pi[r],gamma) * b[r];
	333	//LLF(ite)=-1/nsum(log(LLF2(ite,:)))+lambdasum(pen(ite,:));
	334	LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
	335	if (ite == 0)
	336	dist = LLF[ite];
	337	else
	338	dist = (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
	339
	340	//Dist1=max(max((abs(phi-Phi))./(1+abs(phi))));
4cab944a BA	341	double Dist1 = 0.0;
4cab944a BA	342	for (int u=0; u<p; u++)
1d3c1faa	343	{
4cab944a	344	for (int v=0; v<m; v++)
1d3c1faa	345	{
4cab944a	346	for (int w=0; w<k; w++)
1d3c1faa	347	{
4cab944a BA	348	double tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
4cab944a BA	349	/ (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
1d3c1faa BA	350	if (tmpDist > Dist1)
	351	Dist1 = tmpDist;
	352	}
	353	}
	354	}
	355	//Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
4cab944a BA	356	double Dist2 = 0.0;
4cab944a BA	357	for (int u=0; u<m; u++)
1d3c1faa	358	{
4cab944a	359	for (int v=0; v<m; v++)
1d3c1faa	360	{
4cab944a	361	for (int w=0; w<k; w++)
1d3c1faa	362	{
4cab944a BA	363	double tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
4cab944a BA	364	/ (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
1d3c1faa BA	365	if (tmpDist > Dist2)
	366	Dist2 = tmpDist;
	367	}
	368	}
	369	}
	370	//Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
4cab944a BA	371	double Dist3 = 0.0;
4cab944a BA	372	for (int u=0; u<n; u++)
1d3c1faa	373	{
4cab944a	374	for (int v=0; v<k; v++)
1d3c1faa	375	{
4cab944a	376	double tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
1d3c1faa BA	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(dotProducts);
	413	}