+#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 eps, // 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));
+ 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 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]);
+ }
+
+ // 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);
+}\f
projects / valse.git / commitdiff