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

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

// TODO: don't recompute indexes ai(...) and mi(...) when possible
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: same as in R
	Real* gam = (Real*)malloc(n*k*sizeof(Real));
	copyArray(gamInit, gam, n*k);
	Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
	Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
	Real* b = (Real*)malloc(k*sizeof(Real));
	Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
	Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
	Real dist = 0.;
	Real dist2 = 0.;
	int ite = 0;
	Real* pi2 = (Real*)malloc(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* Gam = (Real*)malloc(n*k*sizeof(Real));
	const Real EPS = 1e-15;
	// Additional (not at this place, in R file)
	Real* gam2 = (Real*)malloc(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));
	const Real gaussConstM = pow(2.*M_PI,m/2.);
	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));

	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,p,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;
				}
				//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(Y2[,mm,r])
				Real sumNy2 = 0.;
				for (int u=0; u<n; u++)
					sumNy2 += Y2[ai(u,mm,r,n,m,k)];
				nY2[mi(mm,r,m,k)] = sumNy2;
				//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[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
					Real dotPhiGram2 = 0.0;
					for (int u=0; u<p; u++)
					{
						if (u != j)
							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] + sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),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;
					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.;
		for (int i=0; i<n; i++)
		{
			for (int r=0; r<k; r++)
			{
				//compute Y[i,]%*%rho[,,r]
				for (int u=0; u<m; u++)
				{
					YiRhoR[u] = 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.;
					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.;
				for (int u=0; u<m; u++)
					sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
			}

			Real sumLLF1 = 0.;
			Real sumGamI = 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);
				Gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * 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.;
		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. + fabs(LLF[ite]));

		//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
		Real Dist1 = 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.+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.;
		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.+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.;
		for (int u=0; u<n; u++)
		{
			for (int v=0; v<k; v++)
			{
				Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+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++;
	}

	//TODO: affec = apply(gam, 1,which.max) à traduire, et retourner affec aussi.

	//free memory
	free(b);
	free(gam);
	free(Gam);
	free(Phi);
	free(Rho);
	free(Pi);
	free(ps);
	free(nY2);
	free(ps1);
	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
8e92c49c BA	1	#include "utils.h"
8e92c49c BA	2	#include <stdlib.h>
1d3c1faa BA	3	#include <gsl/gsl_linalg.h>
1d3c1faa BA	4
b42f0f40	5	// TODO: don't recompute indexes ai(...) and mi(...) when possible
09ab3c16	6	void EMGLLF_core(
1d3c1faa	7	// IN parameters
9ff729fb BA	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
8e92c49c BA	12	int mini, // nombre minimal d'itérations dans l'algorithme EM
8e92c49c BA	13	int maxi, // nombre maximal d'itérations dans l'algorithme EM
9ff729fb BA	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
1d3c1faa	19	// OUT parameters (all pointers, to be modified)
9ff729fb BA	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,
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
b42f0f40	38	//Other local variables: same as in R
9ff729fb	39	Real* gam = (Real)malloc(nk*sizeof(Real));
1d3c1faa	40	copyArray(gamInit, gam, n*k);
b42f0f40 BA	41	Real* Gram2 = (Real)malloc(ppksizeof(Real));
b42f0f40 BA	42	Real* ps2 = (Real)malloc(pmksizeof(Real));
9ff729fb	43	Real* b = (Real)malloc(ksizeof(Real));
b42f0f40 BA	44	Real* X2 = (Real)malloc(npksizeof(Real));
	45	Real* Y2 = (Real)malloc(nmksizeof(Real));
	46	Real dist = 0.;
	47	Real dist2 = 0.;
	48	int ite = 0;
9ff729fb	49	Real* pi2 = (Real)malloc(ksizeof(Real));
9ff729fb BA	50	Real* ps = (Real)malloc(mk*sizeof(Real));
	51	Real* nY2 = (Real)malloc(mk*sizeof(Real));
	52	Real* ps1 = (Real)malloc(nmksizeof(Real));
9ff729fb	53	Real* Gam = (Real)malloc(nk*sizeof(Real));
b42f0f40 BA	54	const Real EPS = 1e-15;
	55	// Additional (not at this place, in R file)
	56	Real* gam2 = (Real)malloc(ksizeof(Real));
ef67d338	57	Real* sqNorm2 = (Real)malloc(ksizeof(Real));
1d3c1faa BA	58	gsl_matrix* matrix = gsl_matrix_alloc(m, m);
1d3c1faa BA	59	gsl_permutation* permutation = gsl_permutation_alloc(m);
9ff729fb BA	60	Real* YiRhoR = (Real)malloc(msizeof(Real));
9ff729fb BA	61	Real* XiPhiR = (Real)malloc(msizeof(Real));
ef67d338	62	const Real gaussConstM = pow(2.*M_PI,m/2.);
b42f0f40 BA	63	Real* Phi = (Real)malloc(pmksizeof(Real));
	64	Real* Rho = (Real)malloc(mmksizeof(Real));
	65	Real* Pi = (Real)malloc(ksizeof(Real));
4cab944a	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	77	{
ef67d338	78	//Y2[,mm,r] = sqrt(gam[,r]) * 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	83	{
ef67d338	84	//X2[i,,r] = sqrt(gam[i,r]) * X[i,]
4cab944a	85	for (int u=0; u<p; u++)
e39bc178	86	X2[ai(i,u,r,n,p,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	89	{
ef67d338	90	//ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
4cab944a	91	for (int u=0; u<p; u++)
1d3c1faa	92	{
9ff729fb	93	Real dotProduct = 0.;
4cab944a	94	for (int v=0; v<n; v++)
46a2e676	95	dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
e39bc178	96	ps2[ai(u,mm,r,p,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	102	{
ef67d338	103	//Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
9ff729fb	104	Real dotProduct = 0.;
4cab944a BA	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	118	{
ef67d338	119	//b[r] = sum(abs(phi[,,r]))
9ff729fb	120	Real sumAbsPhi = 0.;
4cab944a BA	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;
1d3c1faa BA	125	}
ef67d338	126	//gam2 = colSums(gam)
4cab944a	127	for (int u=0; u<k; u++)
1d3c1faa	128	{
9ff729fb	129	Real sumOnColumn = 0.;
4cab944a BA	130	for (int v=0; v<n; v++)
4cab944a BA	131	sumOnColumn += gam[mi(v,u,n,k)];
1d3c1faa BA	132	gam2[u] = sumOnColumn;
1d3c1faa BA	133	}
ef67d338	134	//a = sum(gam %*% log(pi))
9ff729fb	135	Real a = 0.;
4cab944a	136	for (int u=0; u<n; u++)
1d3c1faa	137	{
9ff729fb	138	Real dotProduct = 0.;
4cab944a BA	139	for (int v=0; v<k; v++)
4cab944a BA	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;
9ff729fb	147	Real invN = 1./n;
1d3c1faa BA	148	while (!pi2AllPositive)
1d3c1faa BA	149	{
ef67d338 BA	150	//pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
ef67d338 BA	151	Real pow_01_kk = pow(0.1,kk);
4cab944a	152	for (int r=0; r<k; r++)
ef67d338 BA	153	pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
ef67d338 BA	154	//pi2AllPositive = all(pi2 >= 0)
1d3c1faa	155	pi2AllPositive = 1;
4cab944a	156	for (int r=0; r<k; r++)
1d3c1faa BA	157	{
	158	if (pi2[r] < 0)
	159	{
	160	pi2AllPositive = 0;
	161	break;
	162	}
	163	}
	164	kk++;
	165	}
4cab944a	166
1d3c1faa	167	//(pi.^gamma)*b
9ff729fb	168	Real piPowGammaDotB = 0.;
4cab944a	169	for (int v=0; v<k; v++)
1d3c1faa BA	170	piPowGammaDotB += pow(pi[v],gamma) * b[v];
1d3c1faa BA	171	//(pi2.^gamma)*b
9ff729fb	172	Real pi2PowGammaDotB = 0.;
4cab944a	173	for (int v=0; v<k; v++)
1d3c1faa BA	174	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
1d3c1faa BA	175	//transpose(gam2)*log(pi2)
9ff729fb	176	Real prodGam2logPi2 = 0.;
4cab944a	177	for (int v=0; v<k; v++)
1d3c1faa	178	prodGam2logPi2 += gam2[v] * log(pi2[v]);
ef67d338	179	//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
8e92c49c BA	180	while (-invNa + lambdapiPowGammaDotB < -invNprodGam2logPi2 + lambdapi2PowGammaDotB
8e92c49c BA	181	&& kk<1000)
1d3c1faa	182	{
ef67d338 BA	183	Real pow_01_kk = pow(0.1,kk);
ef67d338 BA	184	//pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
4cab944a	185	for (int v=0; v<k; v++)
ef67d338	186	pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
1d3c1faa	187	//pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
4cab944a BA	188	pi2PowGammaDotB = 0.;
4cab944a BA	189	for (int v=0; v<k; v++)
1d3c1faa	190	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
4cab944a BA	191	prodGam2logPi2 = 0.;
4cab944a BA	192	for (int v=0; v<k; v++)
1d3c1faa BA	193	prodGam2logPi2 += gam2[v] * log(pi2[v]);
	194	kk++;
	195	}
9ff729fb	196	Real t = pow(0.1,kk);
ef67d338	197	//sum(pi + t*(pi2-pi))
9ff729fb	198	Real sumPiPlusTbyDiff = 0.;
4cab944a	199	for (int v=0; v<k; v++)
1d3c1faa	200	sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
ef67d338	201	//pi = (pi + t(pi2-pi)) / sum(pi + t(pi2-pi))
4cab944a	202	for (int v=0; v<k; v++)
1d3c1faa	203	pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
4cab944a	204
1d3c1faa	205	//Pour phi et rho
4cab944a	206	for (int r=0; r<k; r++)
1d3c1faa	207	{
4cab944a	208	for (int mm=0; mm<m; mm++)
1d3c1faa	209	{
4cab944a	210	for (int i=0; i<n; i++)
1d3c1faa BA	211	{
1d3c1faa BA	212	//< X2(i,:,r) , phi(:,mm,r) >
ef67d338	213	Real dotProduct = 0.;
4cab944a	214	for (int u=0; u<p; u++)
a2d68d1d	215	dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
ef67d338	216	//ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
4cab944a	217	ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
1d3c1faa	218	}
ef67d338 BA	219	//ps[mm,r] = sum(ps1[,mm,r])
ef67d338 BA	220	Real sumPs1 = 0.;
4cab944a BA	221	for (int u=0; u<n; u++)
	222	sumPs1 += ps1[ai(u,mm,r,n,m,k)];
	223	ps[mi(mm,r,m,k)] = sumPs1;
5a190d9d	224	//nY2[mm,r] = sum(Y2[,mm,r])
37e11bb0	225	Real sumNy2 = 0.;
4cab944a	226	for (int u=0; u<n; u++)
5a190d9d	227	sumNy2 += Y2[ai(u,mm,r,n,m,k)];
37e11bb0	228	nY2[mi(mm,r,m,k)] = sumNy2;
ef67d338	229	//rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4nY2[mm,r](gam2[r]))) / (2*nY2[mm,r])
a2d68d1d	230	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)]
ef67d338	231	+ 4nY2[mi(mm,r,m,k)] gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
1d3c1faa BA	232	}
1d3c1faa BA	233	}
4cab944a	234	for (int r=0; r<k; r++)
1d3c1faa	235	{
4cab944a	236	for (int j=0; j<p; j++)
1d3c1faa	237	{
4cab944a	238	for (int mm=0; mm<m; mm++)
1d3c1faa	239	{
b42f0f40	240	//sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
9ff729fb	241	Real dotPhiGram2 = 0.0;
b42f0f40 BA	242	for (int u=0; u<p; u++)
	243	{
	244	if (u != j)
	245	dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
	246	}
	247	//S[j,mm,r] = -rho[mm,mm,r]ps2[j,mm,r] + sum(phi[-j,mm,r] Gram2[j, setdiff(1:p,j),r])
4cab944a	248	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;
ef67d338 BA	249	Real pow_pir_gamma = pow(pi[r],gamma);
ef67d338 BA	250	if (fabs(S[ai(j,mm,r,p,m,k)]) <= nlambdapow_pir_gamma)
4cab944a	251	phi[ai(j,mm,r,p,m,k)] = 0;
ef67d338 BA	252	else if (S[ai(j,mm,r,p,m,k)] > nlambdapow_pir_gamma)
	253	{
	254	phi[ai(j,mm,r,p,m,k)] = (nlambdapow_pir_gamma - S[ai(j,mm,r,p,m,k)])
4cab944a	255	/ Gram2[ai(j,j,r,p,p,k)];
ef67d338	256	}
1d3c1faa	257	else
ef67d338 BA	258	{
ef67d338 BA	259	phi[ai(j,mm,r,p,m,k)] = -(nlambdapow_pir_gamma + S[ai(j,mm,r,p,m,k)])
4cab944a	260	/ Gram2[ai(j,j,r,p,p,k)];
ef67d338	261	}
1d3c1faa BA	262	}
	263	}
	264	}
4cab944a	265
1d3c1faa BA	266	/////////////
	267	// Etape E //
	268	/////////////
4cab944a	269
1d3c1faa	270	int signum;
b42f0f40	271	Real sumLogLLF2 = 0.;
4cab944a	272	for (int i=0; i<n; i++)
1d3c1faa	273	{
4cab944a	274	for (int r=0; r<k; r++)
1d3c1faa	275	{
ef67d338	276	//compute Y[i,]%*%rho[,,r]
4cab944a	277	for (int u=0; u<m; u++)
1d3c1faa	278	{
b42f0f40	279	YiRhoR[u] = 0.;
4cab944a	280	for (int v=0; v<m; v++)
aa8df014	281	YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
1d3c1faa	282	}
4cab944a	283
1d3c1faa	284	//compute X(i,:)*phi(:,:,r)
4cab944a	285	for (int u=0; u<m; u++)
1d3c1faa	286	{
b42f0f40	287	XiPhiR[u] = 0.;
4cab944a BA	288	for (int v=0; v<p; v++)
4cab944a BA	289	XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
1d3c1faa	290	}
4cab944a	291
ef67d338	292	//compute sq norm \|\| Y(:,i)rho(:,:,r)-X(i,:)phi(:,:,r) \|\|_2^2
b42f0f40	293	sqNorm2[r] = 0.;
4cab944a	294	for (int u=0; u<m; u++)
ef67d338	295	sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
1d3c1faa	296	}
ef67d338	297
b42f0f40 BA	298	Real sumLLF1 = 0.;
b42f0f40 BA	299	Real sumGamI = 0.;
4cab944a	300	for (int r=0; r<k; r++)
1d3c1faa	301	{
ef67d338	302	//compute det(rho[,,r]) [TODO: avoid re-computations]
4cab944a	303	for (int u=0; u<m; u++)
1d3c1faa	304	{
4cab944a BA	305	for (int v=0; v<m; v++)
4cab944a BA	306	matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
1d3c1faa BA	307	}
1d3c1faa BA	308	gsl_linalg_LU_decomp(matrix, permutation, &signum);
9ff729fb	309	Real detRhoR = gsl_linalg_LU_det(matrix, signum);
b42f0f40	310	Gam[mi(i,r,n,k)] = pi[r] * exp(-.5sqNorm2[r]) detRhoR;
ef67d338	311	sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
4cab944a	312	sumGamI += Gam[mi(i,r,n,k)];
1d3c1faa BA	313	}
1d3c1faa BA	314	sumLogLLF2 += log(sumLLF1);
4cab944a	315	for (int r=0; r<k; r++)
1d3c1faa	316	{
ef67d338 BA	317	//gam[i,] = Gam[i,] / sumGamI
ef67d338 BA	318	gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
1d3c1faa BA	319	}
1d3c1faa BA	320	}
ef67d338 BA	321
ef67d338 BA	322	//sumPen = sum(pi^gamma * b)
b42f0f40	323	Real sumPen = 0.;
4cab944a	324	for (int r=0; r<k; r++)
1d3c1faa	325	sumPen += pow(pi[r],gamma) * b[r];
ef67d338	326	//LLF[ite] = -sumLogLLF2/n + lambda*sumPen
1d3c1faa	327	LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
b42f0f40	328	dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1. + fabs(LLF[ite]));
ef67d338 BA	329
ef67d338 BA	330	//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
b42f0f40	331	Real Dist1 = 0.;
4cab944a	332	for (int u=0; u<p; u++)
1d3c1faa	333	{
4cab944a	334	for (int v=0; v<m; v++)
1d3c1faa	335	{
4cab944a	336	for (int w=0; w<k; w++)
1d3c1faa	337	{
b42f0f40 BA	338	Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
b42f0f40 BA	339	/ (1.+fabs(phi[ai(u,v,w,p,m,k)]));
1d3c1faa BA	340	if (tmpDist > Dist1)
	341	Dist1 = tmpDist;
	342	}
	343	}
	344	}
ef67d338	345	//Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
b42f0f40	346	Real Dist2 = 0.;
4cab944a	347	for (int u=0; u<m; u++)
1d3c1faa	348	{
4cab944a	349	for (int v=0; v<m; v++)
1d3c1faa	350	{
4cab944a	351	for (int w=0; w<k; w++)
1d3c1faa	352	{
b42f0f40 BA	353	Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
b42f0f40 BA	354	/ (1.+fabs(rho[ai(u,v,w,m,m,k)]));
1d3c1faa BA	355	if (tmpDist > Dist2)
	356	Dist2 = tmpDist;
	357	}
	358	}
	359	}
ef67d338	360	//Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
b42f0f40	361	Real Dist3 = 0.;
4cab944a	362	for (int u=0; u<n; u++)
1d3c1faa	363	{
4cab944a	364	for (int v=0; v<k; v++)
1d3c1faa	365	{
b42f0f40	366	Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
1d3c1faa BA	367	if (tmpDist > Dist3)
	368	Dist3 = tmpDist;
	369	}
	370	}
	371	//dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
	372	dist2 = Dist1;
	373	if (Dist2 > dist2)
	374	dist2 = Dist2;
	375	if (Dist3 > dist2)
	376	dist2 = Dist3;
ef67d338	377
1d3c1faa BA	378	ite++;
1d3c1faa BA	379	}
ef67d338	380
37e11bb0 BA	381	//TODO: affec = apply(gam, 1,which.max) à traduire, et retourner affec aussi.
37e11bb0 BA	382
1d3c1faa BA	383	//free memory
	384	free(b);
	385	free(gam);
	386	free(Gam);
	387	free(Phi);
	388	free(Rho);
	389	free(Pi);
	390	free(ps);
	391	free(nY2);
	392	free(ps1);
1d3c1faa BA	393	free(Gram2);
	394	free(ps2);
	395	gsl_matrix_free(matrix);
	396	gsl_permutation_free(permutation);
	397	free(XiPhiR);
	398	free(YiRhoR);
	399	free(gam2);
	400	free(pi2);
	401	free(X2);
	402	free(Y2);
ef67d338	403	free(sqNorm2);
1d3c1faa	404	}