X-Git-Url: https://git.auder.net/?a=blobdiff_plain;f=pkg%2Fsrc%2FEMGLLF.c;fp=pkg%2Fsrc%2FEMGLLF.c;h=978f2530936e47235d22e8d124a55d488d8f1268;hb=1196a43d961a95abc18d3c8e777e9a4e8233e562;hp=0000000000000000000000000000000000000000;hpb=859c30ec72871f923da0498c14a94e67b0219875;p=valse.git

diff --git a/pkg/src/EMGLLF.c b/pkg/src/EMGLLF.c
new file mode 100644
index 0000000..978f253
--- /dev/null
+++ b/pkg/src/EMGLLF.c
@@ -0,0 +1,420 @@
+#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 renormalise
+	const Real* rhoInit, // parametre initial de variance renormalise
+	const Real* piInit,	 // parametre initial des proportions
+	const Real* gamInit, // parametre initial des probabilites a posteriori de chaque echantillon
+	int mini, // nombre minimal d'iterations dans l'algorithme EM
+	int maxi, // nombre maximal d'iterations dans l'algorithme EM
+	Real gamma, // puissance des proportions dans la penalisation pour un Lasso adaptatif
+	Real lambda, // valeur du parametre de regularisation du Lasso
+	const Real* X, // regresseurs
+	const Real* Y, // reponse
+	Real eps, // seuil pour accepter la convergence
+	// OUT parameters (all pointers, to be modified)
+	Real* phi, // parametre de moyenne renormalise, calcule par l'EM
+	Real* rho, // parametre de variance renormalise, calcule par l'EM
+	Real* pi, // parametre des proportions renormalise, calcule par l'EM
+	Real* llh, // (derniere) log vraisemblance associee a cet echantillon,
+	           // pour les valeurs estimees des parametres
+	Real* S,
+	int* affec,
+	// additional size parameters
+	int n, // nombre d'echantillons
+	int p, // nombre de covariables
+	int m, // taille de Y (multivarie)
+	int k) // nombre de composantes dans le melange
+{
+	//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));
+	Real* logGam = (Real*)malloc(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));
+	// 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 associes 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 decroissante 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]);
+			}
+
+			// Update gam[,]; use log to avoid numerical problems
+			Real maxLogGam = -INFINITY;
+			for (int r=0; r<k; r++)
+			{
+				logGam[r] = log(pi[r]) - .5 * sqNorm2[r] + log(detRho[r]);
+				if (maxLogGam < logGam[r])
+					maxLogGam = logGam[r];
+			}
+			Real norm_fact = 0.;
+			for (int r=0; r<k; r++)
+			{
+				logGam[r] = logGam[r] - maxLogGam; //adjust without changing proportions
+				gam[mi(i,r,n,k)] = exp(logGam[r]); //gam[i, ] <- exp(logGam)
+				norm_fact += gam[mi(i,r,n,k)]; //norm_fact <- sum(gam[i, ])
+			}
+			// gam[i, ] <- gam[i, ] / norm_fact
+			for (int r=0; r<k; r++)
+				gam[mi(i,r,n,k)] /= norm_fact;
+
+			sumLogLLH += log(norm_fact) - log(gaussConstM);
+		}
+
+		//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 >= eps || dist2 >= sqrt(eps)))
+			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(logGam);
+	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);
+}