+++ /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