--- /dev/null
+#include "EMGLLF.h"
+#include <gsl/gsl_linalg.h>
+
+// TODO: comment on EMGLLF purpose
+void EMGLLF(
+ // 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, // valeur de 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 associé à cet échantillon, pour les valeurs estimées des paramètres
+ Real* S,
+ // additional size parameters
+ mwSize n, // nombre d'echantillons
+ mwSize p, // nombre de covariables
+ mwSize m, // taille de Y (multivarié)
+ mwSize 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
+ Real* gam = (Real*)malloc(n*k*sizeof(Real));
+ copyArray(gamInit, gam, n*k);
+ Real* b = (Real*)malloc(k*sizeof(Real));
+ 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));
+ Real* gam2 = (Real*)malloc(k*sizeof(Real));
+ Real* pi2 = (Real*)malloc(k*sizeof(Real));
+ Real* Gram2 = (Real*)malloc(p*p*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* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
+ Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
+ Real* Gam = (Real*)malloc(n*k*sizeof(Real));
+ Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
+ Real* Y2 = (Real*)malloc(n*m*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));
+ Real dist = 0.0;
+ Real dist2 = 0.0;
+ Int ite = 0;
+ Real EPS = 1e-15;
+ Real* dotProducts = (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 associes a Y et X
+ for (mwSize r=0; r<k; r++)
+ {
+ for (mwSize mm=0; mm<m; mm++)
+ {
+ //Y2(:,mm,r)=sqrt(gam(:,r)).*transpose(Y(mm,:));
+ for (mwSize u=0; u<n; u++)
+ Y2[u*m*k+mm*k+r] = sqrt(gam[u*k+r]) * Y[u*m+mm];
+ }
+ for (mwSize i=0; i<n; i++)
+ {
+ //X2(i,:,r)=X(i,:).*sqrt(gam(i,r));
+ for (mwSize u=0; u<p; u++)
+ X2[i*p*k+u*k+r] = sqrt(gam[i*k+r]) * X[i*p+u];
+ }
+ for (mwSize mm=0; mm<m; mm++)
+ {
+ //ps2(:,mm,r)=transpose(X2(:,:,r))*Y2(:,mm,r);
+ for (mwSize u=0; u<p; u++)
+ {
+ Real dotProduct = 0.0;
+ for (mwSize v=0; v<n; v++)
+ dotProduct += X2[v*p*k+u*k+r] * Y2[v*m*k+mm*k+r];
+ ps2[u*m*k+mm*k+r] = dotProduct;
+ }
+ }
+ for (mwSize j=0; j<p; j++)
+ {
+ for (mwSize s=0; s<p; s++)
+ {
+ //Gram2(j,s,r)=transpose(X2(:,j,r))*(X2(:,s,r));
+ Real dotProduct = 0.0;
+ for (mwSize u=0; u<n; u++)
+ dotProduct += X2[u*p*k+j*k+r] * X2[u*p*k+s*k+r];
+ Gram2[j*p*k+s*k+r] = dotProduct;
+ }
+ }
+ }
+
+ /////////////
+ // Etape M //
+ /////////////
+
+ // Pour pi
+ for (mwSize r=0; r<k; r++)
+ {
+ //b(r) = sum(sum(abs(phi(:,:,r))));
+ Real sumAbsPhi = 0.0;
+ for (mwSize u=0; u<p; u++)
+ for (mwSize v=0; v<m; v++)
+ sumAbsPhi += fabs(phi[u*m*k+v*k+r]);
+ b[r] = sumAbsPhi;
+ }
+ //gam2 = sum(gam,1);
+ for (mwSize u=0; u<k; u++)
+ {
+ Real sumOnColumn = 0.0;
+ for (mwSize v=0; v<n; v++)
+ sumOnColumn += gam[v*k+u];
+ gam2[u] = sumOnColumn;
+ }
+ //a=sum(gam*transpose(log(pi)));
+ Real a = 0.0;
+ for (mwSize u=0; u<n; u++)
+ {
+ Real dotProduct = 0.0;
+ for (mwSize v=0; v<k; v++)
+ dotProduct += gam[u*k+v] * log(pi[v]);
+ a += dotProduct;
+ }
+
+ //tant que les proportions sont negatives
+ mwSize kk = 0;
+ int pi2AllPositive = 0;
+ Real invN = 1.0/n;
+ while (!pi2AllPositive)
+ {
+ //pi2(:)=pi(:)+0.1^kk*(1/n*gam2(:)-pi(:));
+ for (mwSize r=0; r<k; r++)
+ pi2[r] = pi[r] + pow(0.1,kk) * (invN*gam2[r] - pi[r]);
+ pi2AllPositive = 1;
+ for (mwSize 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
+ Real piPowGammaDotB = 0.0;
+ for (mwSize v=0; v<k; v++)
+ piPowGammaDotB += pow(pi[v],gamma) * b[v];
+ //(pi2.^gamma)*b
+ Real pi2PowGammaDotB = 0.0;
+ for (mwSize v=0; v<k; v++)
+ pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
+ //transpose(gam2)*log(pi2)
+ Real prodGam2logPi2 = 0.0;
+ for (mwSize 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 (mwSize 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 = 0.0;
+ for (mwSize v=0; v<k; v++)
+ pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
+ prodGam2logPi2 = 0.0;
+ for (mwSize 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 = 0.0;
+ for (mwSize v=0; v<k; v++)
+ sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
+ //pi=(pi+t*(pi2-pi))/sum(pi+t*(pi2-pi));
+ for (mwSize v=0; v<k; v++)
+ pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
+
+ //Pour phi et rho
+ for (mwSize r=0; r<k; r++)
+ {
+ for (mwSize mm=0; mm<m; mm++)
+ {
+ for (mwSize i=0; i<n; i++)
+ {
+ //< X2(i,:,r) , phi(:,mm,r) >
+ Real dotProduct = 0.0;
+ for (mwSize u=0; u<p; u++)
+ dotProduct += X2[i*p*k+u*k+r] * phi[u*m*k+mm*k+r];
+ //ps1(i,mm,r)=Y2(i,mm,r)*dot(X2(i,:,r),phi(:,mm,r));
+ ps1[i*m*k+mm*k+r] = Y2[i*m*k+mm*k+r] * dotProduct;
+ nY21[i*m*k+mm*k+r] = Y2[i*m*k+mm*k+r] * Y2[i*m*k+mm*k+r];
+ }
+ //ps(mm,r)=sum(ps1(:,mm,r));
+ Real sumPs1 = 0.0;
+ for (mwSize u=0; u<n; u++)
+ sumPs1 += ps1[u*m*k+mm*k+r];
+ ps[mm*k+r] = sumPs1;
+ //nY2(mm,r)=sum(nY21(:,mm,r));
+ Real sumNy21 = 0.0;
+ for (mwSize u=0; u<n; u++)
+ sumNy21 += nY21[u*m*k+mm*k+r];
+ nY2[mm*k+r] = sumNy21;
+ //rho(mm,mm,r)=((ps(mm,r)+sqrt(ps(mm,r)^2+4*nY2(mm,r)*(gam2(r))))/(2*nY2(mm,r)));
+ rho[mm*m*k+mm*k+r] = ( ps[mm*k+r] + sqrt( ps[mm*k+r]*ps[mm*k+r]
+ + 4*nY2[mm*k+r] * (gam2[r]) ) ) / (2*nY2[mm*k+r]);
+ }
+ }
+ for (mwSize r=0; r<k; r++)
+ {
+ for (mwSize j=0; j<p; j++)
+ {
+ for (mwSize 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)))
+ Real dotPhiGram2 = 0.0;
+ for (mwSize u=0; u<j; u++)
+ dotPhiGram2 += phi[u*m*k+mm*k+r] * Gram2[j*p*k+u*k+r];
+ for (mwSize u=j+1; u<p; u++)
+ dotPhiGram2 += phi[u*m*k+mm*k+r] * Gram2[j*p*k+u*k+r];
+ //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[j*m*k+mm*k+r] = -rho[mm*m*k+mm*k+r] * ps2[j*m*k+mm*k+r] + dotPhiGram2;
+ if (fabs(S[j*m*k+mm*k+r]) <= n*lambda*pow(pi[r],gamma))
+ phi[j*m*k+mm*k+r] = 0;
+ else if (S[j*m*k+mm*k+r] > n*lambda*pow(pi[r],gamma))
+ phi[j*m*k+mm*k+r] = (n*lambda*pow(pi[r],gamma) - S[j*m*k+mm*k+r])
+ / Gram2[j*p*k+j*k+r];
+ else
+ phi[j*m*k+mm*k+r] = -(n*lambda*pow(pi[r],gamma) + S[j*m*k+mm*k+r])
+ / Gram2[j*p*k+j*k+r];
+ }
+ }
+ }
+
+ /////////////
+ // Etape E //
+ /////////////
+
+ int signum;
+ Real sumLogLLF2 = 0.0;
+ for (mwSize i=0; i<n; i++)
+ {
+ Real sumLLF1 = 0.0;
+ Real sumGamI = 0.0;
+ Real minDotProduct = INFINITY;
+
+ for (mwSize 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 (mwSize u=0; u<m; u++)
+ {
+ YiRhoR[u] = 0.0;
+ for (mwSize v=0; v<m; v++)
+ YiRhoR[u] += Y[i*m+v] * rho[v*m*k+u*k+r];
+ }
+
+ //compute X(i,:)*phi(:,:,r)
+ for (mwSize u=0; u<m; u++)
+ {
+ XiPhiR[u] = 0.0;
+ for (mwSize v=0; v<p; v++)
+ XiPhiR[u] += X[i*p+v] * phi[v*m*k+u*k+r];
+ }
+
+ // compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
+ dotProducts[r] = 0.0;
+ for (mwSize u=0; u<m; u++)
+ dotProducts[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
+ if (dotProducts[r] < minDotProduct)
+ minDotProduct = dotProducts[r];
+ }
+ Real shift = 0.5*minDotProduct;
+ for (mwSize r=0; r<k; r++)
+ {
+ //compute det(rho(:,:,r)) [TODO: avoid re-computations]
+ for (mwSize u=0; u<m; u++)
+ {
+ for (mwSize v=0; v<m; v++)
+ matrix->data[u*m+v] = rho[u*m*k+v*k+r];
+ }
+ gsl_linalg_LU_decomp(matrix, permutation, &signum);
+ Real detRhoR = gsl_linalg_LU_det(matrix, signum);
+
+ Gam[i*k+r] = pi[r] * detRhoR * exp(-0.5*dotProducts[r] + shift);
+ sumLLF1 += Gam[i*k+r] / pow(2*M_PI,m/2.0);
+ sumGamI += Gam[i*k+r];
+ }
+ sumLogLLF2 += log(sumLLF1);
+ for (mwSize r=0; r<k; r++)
+ {
+ //gam(i,r)=Gam(i,r)/sum(Gam(i,:));
+ gam[i*k+r] = sumGamI > EPS
+ ? Gam[i*k+r] / sumGamI
+ : 0.0;
+ }
+ }
+
+ //sum(pen(ite,:))
+ Real sumPen = 0.0;
+ for (mwSize 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))));
+ Real Dist1 = 0.0;
+ for (mwSize u=0; u<p; u++)
+ {
+ for (mwSize v=0; v<m; v++)
+ {
+ for (mwSize w=0; w<k; w++)
+ {
+ Real tmpDist = fabs(phi[u*m*k+v*k+w]-Phi[u*m*k+v*k+w])
+ / (1.0+fabs(phi[u*m*k+v*k+w]));
+ if (tmpDist > Dist1)
+ Dist1 = tmpDist;
+ }
+ }
+ }
+ //Dist2=max(max((abs(rho-Rho))./(1+abs(rho))));
+ Real Dist2 = 0.0;
+ for (mwSize u=0; u<m; u++)
+ {
+ for (mwSize v=0; v<m; v++)
+ {
+ for (mwSize w=0; w<k; w++)
+ {
+ Real tmpDist = fabs(rho[u*m*k+v*k+w]-Rho[u*m*k+v*k+w])
+ / (1.0+fabs(rho[u*m*k+v*k+w]));
+ if (tmpDist > Dist2)
+ Dist2 = tmpDist;
+ }
+ }
+ }
+ //Dist3=max(max((abs(pi-Pi))./(1+abs(Pi))));
+ Real Dist3 = 0.0;
+ for (mwSize u=0; u<n; u++)
+ {
+ for (mwSize v=0; v<k; v++)
+ {
+ Real 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);
+}
projects / valse.git / blobdiff