+++ /dev/null
-#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);
-}
projects / valse.git / blobdiff