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

#include "utils.h"
#include <stdlib.h>
#include <math.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* llh, // (derniere) log vraisemblance associée à cet échantillon,
	           // pour les valeurs estimées des paramètres
	Real* S,
	int* affec,
	// 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);
	//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));
	*llh = -INFINITY;
	Real* pi2 = (Real*)malloc(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));
	Real* detRho = (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));

	for (int ite=1; ite<=maxi; ite++)
	{
		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,n,m)];
			}
			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,
			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++;
		}

		//sum(pi^gamma * b)
		Real piPowGammaDotB = 0.;
		for (int v=0; v<k; v++)
			piPowGammaDotB += pow(pi[v],gamma) * b[v];
		//sum(pi2^gamma * b)
		Real pi2PowGammaDotB = 0.;
		for (int v=0; v<k; v++)
			pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
		//sum(gam2 * log(pi2))
		Real gam2DotLogPi2 = 0.;
		for (int v=0; v<k; v++)
			gam2DotLogPi2 += 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*gam2DotLogPi2 + 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 gam2DotLogPi2
			pi2PowGammaDotB = 0.;
			for (int v=0; v<k; v++)
				pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
			gam2DotLogPi2 = 0.;
			for (int v=0; v<k; v++)
				gam2DotLogPi2 += 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++)
			{
				Real ps = 0.,
					nY2 = 0.;
				// Compute ps, and nY2 = sum(Y2[,mm,r]^2)
				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)];
					//ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
					ps += Y2[ai(i,mm,r,n,m,k)] * dotProduct;
					nY2 += Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
				}
				//rho[mm,mm,r] = (ps+sqrt(ps^2+4*nY2*gam2[r])) / (2*nY2)
				rho[ai(mm,mm,r,m,m,k)] = (ps + sqrt(ps*ps + 4*nY2 * gam2[r])) / (2*nY2);
			}
		}

		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,-j,r])
					Real phiDotGram2 = 0.;
					for (int u=0; u<p; u++)
					{
						if (u != j)
							phiDotGram2 += 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,-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)]
						+ phiDotGram2;
					Real pirPowGamma = pow(pi[r],gamma);
					if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
						phi[ai(j,mm,r,p,m,k)] = 0.;
					else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
					{
						phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - 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*pirPowGamma + S[ai(j,mm,r,p,m,k)])
							/ Gram2[ai(j,j,r,p,p,k)];
					}
				}
			}
		}

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

		// Precompute det(rho[,,r]) for r in 1...k
		int signum;
		for (int r=0; r<k; r++)
		{
			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);
			detRho[r] = gsl_linalg_LU_det(matrix, signum);
		}

		Real sumLogLLH = 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 sumGamI = 0.;
			for (int r=0; r<k; r++)
			{
				gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRho[r];
				sumGamI += gam[mi(i,r,n,k)];
			}

			sumLogLLH += log(sumGamI) - log(gaussConstM);
			if (sumGamI > EPS) //else: gam[i,] is already ~=0
			{
				for (int r=0; r<k; r++)
					gam[mi(i,r,n,k)] /= sumGamI;
			}
		}

		//sumPen = sum(pi^gamma * b)
		Real sumPen = 0.;
		for (int r=0; r<k; r++)
			sumPen += pow(pi[r],gamma) * b[r];
		Real last_llh = *llh;
		//llh = -sumLogLLH/n + lambda*sumPen
		*llh = -invN * sumLogLLH + lambda * sumPen;
		Real dist = ite==1 ? *llh : (*llh - last_llh) / (1. + fabs(*llh));

		//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)]);
		Real dist2 = Dist1;
		if (Dist2 > dist2)
			dist2 = Dist2;
		if (Dist3 > dist2)
			dist2 = Dist3;

		if (ite >= mini && (dist >= tau || dist2 >= sqrt(tau)))
			break;
	}

	//affec = apply(gam, 1, which.max)
	for (int i=0; i<n; i++)
	{
		Real rowMax = 0.;
		affec[i] = 0;
		for (int j=0; j<k; j++)
		{
			if (gam[mi(i,j,n,k)] > rowMax)
			{
				affec[i] = j+1; //R indices start at 1
				rowMax = gam[mi(i,j,n,k)];
			}
		}
	}

	//free memory
	free(b);
	free(gam);
	free(Phi);
	free(Rho);
	free(Pi);
	free(Gram2);
	free(ps2);
	free(detRho);
	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>
d6d71630	3	#include <math.h>
1d3c1faa BA	4	#include <gsl/gsl_linalg.h>
1d3c1faa BA	5
b42f0f40	6	// TODO: don't recompute indexes ai(...) and mi(...) when possible
2e813ad2	7	void EMGLLF_core(
1d3c1faa	8	// IN parameters
9ff729fb BA	9	const Real* phiInit, // parametre initial de moyenne renormalisé
	10	const Real* rhoInit, // parametre initial de variance renormalisé
	11	const Real* piInit, // parametre initial des proportions
	12	const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
8e92c49c BA	13	int mini, // nombre minimal d'itérations dans l'algorithme EM
8e92c49c BA	14	int maxi, // nombre maximal d'itérations dans l'algorithme EM
9ff729fb BA	15	Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
	16	Real lambda, // valeur du paramètre de régularisation du Lasso
	17	const Real* X, // régresseurs
	18	const Real* Y, // réponse
	19	Real tau, // seuil pour accepter la convergence
1d3c1faa	20	// OUT parameters (all pointers, to be modified)
9ff729fb BA	21	Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
	22	Real* rho, // parametre de variance renormalisé, calculé par l'EM
	23	Real* pi, // parametre des proportions renormalisé, calculé par l'EM
d6d71630 BA	24	Real* llh, // (derniere) log vraisemblance associée à cet échantillon,
d6d71630 BA	25	// pour les valeurs estimées des paramètres
9ff729fb	26	Real* S,
8be79c46	27	int* affec,
1d3c1faa	28	// additional size parameters
8e92c49c BA	29	int n, // nombre d'echantillons
	30	int p, // nombre de covariables
	31	int m, // taille de Y (multivarié)
	32	int k) // nombre de composantes dans le mélange
1d3c1faa BA	33	{
	34	//Initialize outputs
	35	copyArray(phiInit, phi, pmk);
	36	copyArray(rhoInit, rho, mmk);
	37	copyArray(piInit, pi, k);
1d3c1faa	38	//S is already allocated, and doesn't need to be 'zeroed'
4cab944a	39
b42f0f40	40	//Other local variables: same as in R
9ff729fb	41	Real* gam = (Real)malloc(nk*sizeof(Real));
1d3c1faa	42	copyArray(gamInit, gam, n*k);
b42f0f40 BA	43	Real* Gram2 = (Real)malloc(ppksizeof(Real));
b42f0f40 BA	44	Real* ps2 = (Real)malloc(pmksizeof(Real));
9ff729fb	45	Real* b = (Real)malloc(ksizeof(Real));
b42f0f40 BA	46	Real* X2 = (Real)malloc(npksizeof(Real));
b42f0f40 BA	47	Real* Y2 = (Real)malloc(nmksizeof(Real));
d6d71630	48	*llh = -INFINITY;
9ff729fb	49	Real* pi2 = (Real)malloc(ksizeof(Real));
b42f0f40 BA	50	const Real EPS = 1e-15;
	51	// Additional (not at this place, in R file)
	52	Real* gam2 = (Real)malloc(ksizeof(Real));
ef67d338	53	Real* sqNorm2 = (Real)malloc(ksizeof(Real));
d6d71630	54	Real* detRho = (Real)malloc(ksizeof(Real));
1d3c1faa BA	55	gsl_matrix* matrix = gsl_matrix_alloc(m, m);
1d3c1faa BA	56	gsl_permutation* permutation = gsl_permutation_alloc(m);
9ff729fb BA	57	Real* YiRhoR = (Real)malloc(msizeof(Real));
9ff729fb BA	58	Real* XiPhiR = (Real)malloc(msizeof(Real));
ef67d338	59	const Real gaussConstM = pow(2.*M_PI,m/2.);
b42f0f40 BA	60	Real* Phi = (Real)malloc(pmksizeof(Real));
	61	Real* Rho = (Real)malloc(mmksizeof(Real));
	62	Real* Pi = (Real)malloc(ksizeof(Real));
4cab944a	63
9a73b966	64	for (int ite=1; ite<=maxi; ite++)
1d3c1faa BA	65	{
	66	copyArray(phi, Phi, pmk);
	67	copyArray(rho, Rho, mmk);
	68	copyArray(pi, Pi, k);
4cab944a BA	69
	70	// Calculs associés a Y et X
	71	for (int r=0; r<k; r++)
1d3c1faa	72	{
4cab944a	73	for (int mm=0; mm<m; mm++)
1d3c1faa	74	{
ef67d338	75	//Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
4cab944a	76	for (int u=0; u<n; u++)
435cb841	77	Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,n,m)];
1d3c1faa	78	}
4cab944a	79	for (int i=0; i<n; i++)
1d3c1faa	80	{
ef67d338	81	//X2[i,,r] = sqrt(gam[i,r]) * X[i,]
4cab944a	82	for (int u=0; u<p; u++)
e39bc178	83	X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
1d3c1faa	84	}
4cab944a	85	for (int mm=0; mm<m; mm++)
1d3c1faa	86	{
ef67d338	87	//ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
4cab944a	88	for (int u=0; u<p; u++)
1d3c1faa	89	{
9ff729fb	90	Real dotProduct = 0.;
4cab944a	91	for (int v=0; v<n; v++)
46a2e676	92	dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
e39bc178	93	ps2[ai(u,mm,r,p,m,k)] = dotProduct;
1d3c1faa BA	94	}
1d3c1faa BA	95	}
4cab944a	96	for (int j=0; j<p; j++)
1d3c1faa	97	{
4cab944a	98	for (int s=0; s<p; s++)
1d3c1faa	99	{
ef67d338	100	//Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
9ff729fb	101	Real dotProduct = 0.;
4cab944a BA	102	for (int u=0; u<n; u++)
	103	dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
	104	Gram2[ai(j,s,r,p,p,k)] = dotProduct;
1d3c1faa BA	105	}
	106	}
	107	}
	108
	109	/////////////
	110	// Etape M //
	111	/////////////
4cab944a	112
1d3c1faa	113	// Pour pi
4cab944a	114	for (int r=0; r<k; r++)
1d3c1faa	115	{
ef67d338	116	//b[r] = sum(abs(phi[,,r]))
9ff729fb	117	Real sumAbsPhi = 0.;
4cab944a BA	118	for (int u=0; u<p; u++)
	119	for (int v=0; v<m; v++)
	120	sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
1d3c1faa BA	121	b[r] = sumAbsPhi;
1d3c1faa BA	122	}
ef67d338	123	//gam2 = colSums(gam)
4cab944a	124	for (int u=0; u<k; u++)
1d3c1faa	125	{
9ff729fb	126	Real sumOnColumn = 0.;
4cab944a BA	127	for (int v=0; v<n; v++)
4cab944a BA	128	sumOnColumn += gam[mi(v,u,n,k)];
1d3c1faa BA	129	gam2[u] = sumOnColumn;
1d3c1faa BA	130	}
ef67d338	131	//a = sum(gam %*% log(pi))
9ff729fb	132	Real a = 0.;
4cab944a	133	for (int u=0; u<n; u++)
1d3c1faa	134	{
9ff729fb	135	Real dotProduct = 0.;
4cab944a BA	136	for (int v=0; v<k; v++)
4cab944a BA	137	dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
1d3c1faa BA	138	a += dotProduct;
1d3c1faa BA	139	}
4cab944a	140
1d3c1faa	141	//tant que les proportions sont negatives
d6d71630 BA	142	int kk = 0,
d6d71630 BA	143	pi2AllPositive = 0;
9ff729fb	144	Real invN = 1./n;
1d3c1faa BA	145	while (!pi2AllPositive)
1d3c1faa BA	146	{
ef67d338 BA	147	//pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
ef67d338 BA	148	Real pow_01_kk = pow(0.1,kk);
4cab944a	149	for (int r=0; r<k; r++)
ef67d338 BA	150	pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
ef67d338 BA	151	//pi2AllPositive = all(pi2 >= 0)
1d3c1faa	152	pi2AllPositive = 1;
4cab944a	153	for (int r=0; r<k; r++)
1d3c1faa BA	154	{
	155	if (pi2[r] < 0)
	156	{
	157	pi2AllPositive = 0;
	158	break;
	159	}
	160	}
	161	kk++;
	162	}
4cab944a	163
435cb841	164	//sum(pi^gamma * b)
9ff729fb	165	Real piPowGammaDotB = 0.;
4cab944a	166	for (int v=0; v<k; v++)
1d3c1faa	167	piPowGammaDotB += pow(pi[v],gamma) * b[v];
435cb841	168	//sum(pi2^gamma * b)
9ff729fb	169	Real pi2PowGammaDotB = 0.;
4cab944a	170	for (int v=0; v<k; v++)
1d3c1faa	171	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
435cb841 BA	172	//sum(gam2 * log(pi2))
435cb841 BA	173	Real gam2DotLogPi2 = 0.;
4cab944a	174	for (int v=0; v<k; v++)
435cb841 BA	175	gam2DotLogPi2 += gam2[v] * log(pi2[v]);
435cb841 BA	176
ef67d338	177	//t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
435cb841	178	while (-invNa + lambdapiPowGammaDotB < -invNgam2DotLogPi2 + lambdapi2PowGammaDotB
8e92c49c	179	&& kk<1000)
1d3c1faa	180	{
ef67d338 BA	181	Real pow_01_kk = pow(0.1,kk);
ef67d338 BA	182	//pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
4cab944a	183	for (int v=0; v<k; v++)
ef67d338	184	pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
435cb841	185	//pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
4cab944a BA	186	pi2PowGammaDotB = 0.;
4cab944a BA	187	for (int v=0; v<k; v++)
1d3c1faa	188	pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
435cb841	189	gam2DotLogPi2 = 0.;
4cab944a	190	for (int v=0; v<k; v++)
435cb841	191	gam2DotLogPi2 += gam2[v] * log(pi2[v]);
1d3c1faa BA	192	kk++;
1d3c1faa BA	193	}
9ff729fb	194	Real t = pow(0.1,kk);
ef67d338	195	//sum(pi + t*(pi2-pi))
9ff729fb	196	Real sumPiPlusTbyDiff = 0.;
4cab944a	197	for (int v=0; v<k; v++)
1d3c1faa	198	sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
ef67d338	199	//pi = (pi + t(pi2-pi)) / sum(pi + t(pi2-pi))
4cab944a	200	for (int v=0; v<k; v++)
1d3c1faa	201	pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
4cab944a	202
1d3c1faa	203	//Pour phi et rho
4cab944a	204	for (int r=0; r<k; r++)
1d3c1faa	205	{
4cab944a	206	for (int mm=0; mm<m; mm++)
1d3c1faa	207	{
d6d71630 BA	208	Real ps = 0.,
	209	nY2 = 0.;
	210	// Compute ps, and nY2 = sum(Y2[,mm,r]^2)
4cab944a	211	for (int i=0; i<n; i++)
1d3c1faa	212	{
435cb841	213	//< X2[i,,r] , phi[,mm,r] >
ef67d338	214	Real dotProduct = 0.;
4cab944a	215	for (int u=0; u<p; u++)
a2d68d1d	216	dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
d6d71630 BA	217	//ps = ps + Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
	218	ps += Y2[ai(i,mm,r,n,m,k)] * dotProduct;
	219	nY2 += Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
1d3c1faa	220	}
d6d71630 BA	221	//rho[mm,mm,r] = (ps+sqrt(ps^2+4nY2gam2[r])) / (2*nY2)
d6d71630 BA	222	rho[ai(mm,mm,r,m,m,k)] = (ps + sqrt(psps + 4nY2 * gam2[r])) / (2*nY2);
1d3c1faa BA	223	}
1d3c1faa BA	224	}
435cb841	225
4cab944a	226	for (int r=0; r<k; r++)
1d3c1faa	227	{
4cab944a	228	for (int j=0; j<p; j++)
1d3c1faa	229	{
4cab944a	230	for (int mm=0; mm<m; mm++)
1d3c1faa	231	{
d6d71630	232	//sum(phi[-j,mm,r] * Gram2[j,-j,r])
435cb841	233	Real phiDotGram2 = 0.;
b42f0f40 BA	234	for (int u=0; u<p; u++)
	235	{
	236	if (u != j)
435cb841	237	phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
b42f0f40	238	}
435cb841	239	//S[j,mm,r] = -rho[mm,mm,r]ps2[j,mm,r] + sum(phi[-j,mm,r] Gram2[j,-j,r])
d6d71630 BA	240	S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)]
d6d71630 BA	241	+ phiDotGram2;
435cb841 BA	242	Real pirPowGamma = pow(pi[r],gamma);
	243	if (fabs(S[ai(j,mm,r,p,m,k)]) <= nlambdapirPowGamma)
	244	phi[ai(j,mm,r,p,m,k)] = 0.;
	245	else if (S[ai(j,mm,r,p,m,k)] > nlambdapirPowGamma)
ef67d338	246	{
435cb841	247	phi[ai(j,mm,r,p,m,k)] = (nlambdapirPowGamma - S[ai(j,mm,r,p,m,k)])
4cab944a	248	/ Gram2[ai(j,j,r,p,p,k)];
ef67d338	249	}
1d3c1faa	250	else
ef67d338	251	{
435cb841	252	phi[ai(j,mm,r,p,m,k)] = -(nlambdapirPowGamma + S[ai(j,mm,r,p,m,k)])
4cab944a	253	/ Gram2[ai(j,j,r,p,p,k)];
ef67d338	254	}
1d3c1faa BA	255	}
	256	}
	257	}
4cab944a	258
1d3c1faa BA	259	/////////////
	260	// Etape E //
	261	/////////////
4cab944a	262
d6d71630	263	// Precompute det(rho[,,r]) for r in 1...k
2e813ad2	264	int signum;
d6d71630 BA	265	for (int r=0; r<k; r++)
	266	{
	267	for (int u=0; u<m; u++)
	268	{
	269	for (int v=0; v<m; v++)
	270	matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
	271	}
	272	gsl_linalg_LU_decomp(matrix, permutation, &signum);
	273	detRho[r] = gsl_linalg_LU_det(matrix, signum);
	274	}
	275
d6d71630	276	Real sumLogLLH = 0.;
4cab944a	277	for (int i=0; i<n; i++)
1d3c1faa	278	{
4cab944a	279	for (int r=0; r<k; r++)
1d3c1faa	280	{
ef67d338	281	//compute Y[i,]%*%rho[,,r]
4cab944a	282	for (int u=0; u<m; u++)
1d3c1faa	283	{
b42f0f40	284	YiRhoR[u] = 0.;
4cab944a	285	for (int v=0; v<m; v++)
aa8df014	286	YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
1d3c1faa	287	}
4cab944a	288
435cb841	289	//compute X[i,]%*%phi[,,r]
4cab944a	290	for (int u=0; u<m; u++)
1d3c1faa	291	{
b42f0f40	292	XiPhiR[u] = 0.;
4cab944a BA	293	for (int v=0; v<p; v++)
4cab944a BA	294	XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
1d3c1faa	295	}
4cab944a	296
ef67d338	297	//compute sq norm \|\| Y(:,i)rho(:,:,r)-X(i,:)phi(:,:,r) \|\|_2^2
b42f0f40	298	sqNorm2[r] = 0.;
4cab944a	299	for (int u=0; u<m; u++)
ef67d338	300	sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
1d3c1faa	301	}
ef67d338	302
b42f0f40	303	Real sumGamI = 0.;
4cab944a	304	for (int r=0; r<k; r++)
1d3c1faa	305	{
d6d71630 BA	306	gam[mi(i,r,n,k)] = pi[r] * exp(-.5sqNorm2[r]) detRho[r];
d6d71630 BA	307	sumGamI += gam[mi(i,r,n,k)];
1d3c1faa	308	}
435cb841	309
d6d71630 BA	310	sumLogLLH += log(sumGamI) - log(gaussConstM);
d6d71630 BA	311	if (sumGamI > EPS) //else: gam[i,] is already ~=0
1d3c1faa	312	{
d6d71630 BA	313	for (int r=0; r<k; r++)
d6d71630 BA	314	gam[mi(i,r,n,k)] /= sumGamI;
1d3c1faa BA	315	}
1d3c1faa BA	316	}
ef67d338 BA	317
ef67d338 BA	318	//sumPen = sum(pi^gamma * b)
b42f0f40	319	Real sumPen = 0.;
4cab944a	320	for (int r=0; r<k; r++)
1d3c1faa	321	sumPen += pow(pi[r],gamma) * b[r];
d6d71630 BA	322	Real last_llh = *llh;
	323	//llh = -sumLogLLH/n + lambda*sumPen
	324	llh = -invN sumLogLLH + lambda * sumPen;
9a73b966	325	Real dist = ite==1 ? llh : (llh - last_llh) / (1. + fabs(*llh));
ef67d338 BA	326
ef67d338 BA	327	//Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
b42f0f40	328	Real Dist1 = 0.;
4cab944a	329	for (int u=0; u<p; u++)
1d3c1faa	330	{
4cab944a	331	for (int v=0; v<m; v++)
1d3c1faa	332	{
4cab944a	333	for (int w=0; w<k; w++)
1d3c1faa	334	{
b42f0f40 BA	335	Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
b42f0f40 BA	336	/ (1.+fabs(phi[ai(u,v,w,p,m,k)]));
1d3c1faa BA	337	if (tmpDist > Dist1)
	338	Dist1 = tmpDist;
	339	}
	340	}
	341	}
ef67d338	342	//Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
b42f0f40	343	Real Dist2 = 0.;
4cab944a	344	for (int u=0; u<m; u++)
1d3c1faa	345	{
4cab944a	346	for (int v=0; v<m; v++)
1d3c1faa	347	{
4cab944a	348	for (int w=0; w<k; w++)
1d3c1faa	349	{
b42f0f40 BA	350	Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
b42f0f40 BA	351	/ (1.+fabs(rho[ai(u,v,w,m,m,k)]));
1d3c1faa BA	352	if (tmpDist > Dist2)
	353	Dist2 = tmpDist;
	354	}
	355	}
	356	}
ef67d338	357	//Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
b42f0f40	358	Real Dist3 = 0.;
4cab944a	359	for (int u=0; u<n; u++)
1d3c1faa	360	{
4cab944a	361	for (int v=0; v<k; v++)
1d3c1faa	362	{
b42f0f40	363	Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
1d3c1faa BA	364	if (tmpDist > Dist3)
	365	Dist3 = tmpDist;
	366	}
	367	}
	368	//dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
d6d71630	369	Real dist2 = Dist1;
1d3c1faa BA	370	if (Dist2 > dist2)
	371	dist2 = Dist2;
	372	if (Dist3 > dist2)
	373	dist2 = Dist3;
ef67d338	374
d6d71630 BA	375	if (ite >= mini && (dist >= tau \|\| dist2 >= sqrt(tau)))
d6d71630 BA	376	break;
1d3c1faa	377	}
ef67d338	378
8be79c46 BA	379	//affec = apply(gam, 1, which.max)
	380	for (int i=0; i<n; i++)
	381	{
	382	Real rowMax = 0.;
	383	affec[i] = 0;
	384	for (int j=0; j<k; j++)
	385	{
	386	if (gam[mi(i,j,n,k)] > rowMax)
	387	{
	388	affec[i] = j+1; //R indices start at 1
	389	rowMax = gam[mi(i,j,n,k)];
	390	}
	391	}
	392	}
37e11bb0	393
1d3c1faa BA	394	//free memory
	395	free(b);
	396	free(gam);
1d3c1faa BA	397	free(Phi);
	398	free(Rho);
	399	free(Pi);
1d3c1faa BA	400	free(Gram2);
1d3c1faa BA	401	free(ps2);
9a73b966	402	free(detRho);
1d3c1faa BA	403	gsl_matrix_free(matrix);
	404	gsl_permutation_free(permutation);
	405	free(XiPhiR);
	406	free(YiRhoR);
	407	free(gam2);
	408	free(pi2);
	409	free(X2);
	410	free(Y2);
ef67d338	411	free(sqNorm2);
1d3c1faa	412	}