+++ /dev/null
-#include <stdlib.h>
-#include <gsl/gsl_linalg.h>
-#include "utils.h"
-
-// Compute pseudo-inverse of a square matrix
-static Real* pinv(const Real* matrix, int dim)
-{
- gsl_matrix* U = gsl_matrix_alloc(dim,dim);
- gsl_matrix* V = gsl_matrix_alloc(dim,dim);
- gsl_vector* S = gsl_vector_alloc(dim);
- gsl_vector* work = gsl_vector_alloc(dim);
- Real EPS = 1e-10; //threshold for singular value "== 0"
-
- //copy matrix into U
- copyArray(matrix, U->data, dim*dim);
-
- //U,S,V = SVD of matrix
- gsl_linalg_SV_decomp(U, V, S, work);
- gsl_vector_free(work);
-
- // Obtain pseudo-inverse by V*S^{-1}*t(U)
- Real* inverse = (Real*)malloc(dim*dim*sizeof(Real));
- for (int i=0; i<dim; i++)
- {
- for (int ii=0; ii<dim; ii++)
- {
- Real dotProduct = 0.0;
- for (int j=0; j<dim; j++)
- dotProduct += V->data[i*dim+j] * (S->data[j] > EPS ? 1.0/S->data[j] : 0.0) * U->data[ii*dim+j];
- inverse[i*dim+ii] = dotProduct;
- }
- }
-
- gsl_matrix_free(U);
- gsl_matrix_free(V);
- gsl_vector_free(S);
- return inverse;
-}
-
-// TODO: comment EMGrank purpose
-void EMGrank_core(
- // IN parameters
- const Real* Pi, // parametre de proportion
- const Real* Rho, // parametre initial de variance renormalisé
- int mini, // nombre minimal d'itérations dans l'algorithme EM
- int maxi, // nombre maximal d'itérations dans l'algorithme EM
- const Real* X, // régresseurs
- const Real* Y, // réponse
- Real tau, // seuil pour accepter la convergence
- const int* rank, // vecteur des rangs possibles
- // OUT parameters
- Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
- Real* LLF, // log vraisemblance associé à cet échantillon, pour les valeurs estimées des paramètres
- // additional size parameters
- int n, // taille de l'echantillon
- int p, // nombre de covariables
- int m, // taille de Y (multivarié)
- int k) // nombre de composantes
-{
- // Allocations, initializations
- Real* Phi = (Real*)calloc(p*m*k,sizeof(Real));
- Real* hatBetaR = (Real*)malloc(p*m*sizeof(Real));
- int signum;
- Real invN = 1.0/n;
- int deltaPhiBufferSize = 20;
- Real* deltaPhi = (Real*)malloc(deltaPhiBufferSize*sizeof(Real));
- int ite = 0;
- Real sumDeltaPhi = 0.0;
- Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
- Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
- Real* Xr = (Real*)malloc(n*p*sizeof(Real));
- Real* Yr = (Real*)malloc(n*m*sizeof(Real));
- Real* tXrXr = (Real*)malloc(p*p*sizeof(Real));
- Real* tXrYr = (Real*)malloc(p*m*sizeof(Real));
- gsl_matrix* matrixM = gsl_matrix_alloc(p, m);
- gsl_matrix* matrixE = gsl_matrix_alloc(m, m);
- gsl_permutation* permutation = gsl_permutation_alloc(m);
- gsl_matrix* V = gsl_matrix_alloc(m,m);
- gsl_vector* S = gsl_vector_alloc(m);
- gsl_vector* work = gsl_vector_alloc(m);
-
- //Initialize class memberships (all elements in class 0; TODO: randomize ?)
- int* Z = (int*)calloc(n, sizeof(int));
-
- //Initialize phi to zero, because some M loops might exit before phi affectation
- zeroArray(phi, p*m*k);
-
- while (ite<mini || (ite<maxi && sumDeltaPhi>tau))
- {
- /////////////
- // Etape M //
- /////////////
-
- //M step: Mise à jour de Beta (et donc phi)
- for (int r=0; r<k; r++)
- {
- //Compute Xr = X(Z==r,:) and Yr = Y(Z==r,:)
- int cardClustR=0;
- for (int i=0; i<n; i++)
- {
- if (Z[i] == r)
- {
- for (int j=0; j<p; j++)
- Xr[mi(cardClustR,j,n,p)] = X[mi(i,j,n,p)];
- for (int j=0; j<m; j++)
- Yr[mi(cardClustR,j,n,m)] = Y[mi(i,j,n,m)];
- cardClustR++;
- }
- }
- if (cardClustR == 0)
- continue;
-
- //Compute tXrXr = t(Xr) * Xr
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<p; jj++)
- {
- Real dotProduct = 0.0;
- for (int u=0; u<cardClustR; u++)
- dotProduct += Xr[mi(u,j,n,p)] * Xr[mi(u,jj,n,p)];
- tXrXr[mi(j,jj,p,p)] = dotProduct;
- }
- }
-
- //Get pseudo inverse = (t(Xr)*Xr)^{-1}
- Real* invTXrXr = pinv(tXrXr, p);
-
- // Compute tXrYr = t(Xr) * Yr
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<m; jj++)
- {
- Real dotProduct = 0.0;
- for (int u=0; u<cardClustR; u++)
- dotProduct += Xr[mi(u,j,n,p)] * Yr[mi(u,jj,n,m)];
- tXrYr[mi(j,jj,p,m)] = dotProduct;
- }
- }
-
- //Fill matrixM with inverse * tXrYr = (t(Xr)*Xr)^{-1} * t(Xr) * Yr
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<m; jj++)
- {
- Real dotProduct = 0.0;
- for (int u=0; u<p; u++)
- dotProduct += invTXrXr[mi(j,u,p,p)] * tXrYr[mi(u,jj,p,m)];
- matrixM->data[j*m+jj] = dotProduct;
- }
- }
- free(invTXrXr);
-
- //U,S,V = SVD of (t(Xr)Xr)^{-1} * t(Xr) * Yr
- gsl_linalg_SV_decomp(matrixM, V, S, work);
-
- //Set m-rank(r) singular values to zero, and recompose
- //best rank(r) approximation of the initial product
- for (int j=rank[r]; j<m; j++)
- S->data[j] = 0.0;
-
- //[intermediate step] Compute hatBetaR = U * S * t(V)
- double* U = matrixM->data; //GSL require double precision
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<m; jj++)
- {
- Real dotProduct = 0.0;
- for (int u=0; u<m; u++)
- dotProduct += U[j*m+u] * S->data[u] * V->data[jj*m+u];
- hatBetaR[mi(j,jj,p,m)] = dotProduct;
- }
- }
-
- //Compute phi(:,:,r) = hatBetaR * Rho(:,:,r)
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<m; jj++)
- {
- Real dotProduct=0.0;
- for (int u=0; u<m; u++)
- dotProduct += hatBetaR[mi(j,u,p,m)] * Rho[ai(u,jj,r,m,m,k)];
- phi[ai(j,jj,r,p,m,k)] = dotProduct;
- }
- }
- }
-
- /////////////
- // Etape E //
- /////////////
-
- Real sumLogLLF2 = 0.0;
- for (int i=0; i<n; i++)
- {
- Real sumLLF1 = 0.0;
- Real maxLogGamIR = -INFINITY;
- for (int 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 det(Rho(:,:,r)) [TODO: avoid re-computations]
- for (int j=0; j<m; j++)
- {
- for (int jj=0; jj<m; jj++)
- matrixE->data[j*m+jj] = Rho[ai(j,jj,r,m,m,k)];
- }
- gsl_linalg_LU_decomp(matrixE, permutation, &signum);
- Real detRhoR = gsl_linalg_LU_det(matrixE, signum);
-
- //compute Y(i,:)*Rho(:,:,r)
- for (int j=0; j<m; j++)
- {
- YiRhoR[j] = 0.0;
- for (int u=0; u<m; u++)
- YiRhoR[j] += Y[mi(i,u,n,m)] * Rho[ai(u,j,r,m,m,k)];
- }
-
- //compute X(i,:)*phi(:,:,r)
- for (int j=0; j<m; j++)
- {
- XiPhiR[j] = 0.0;
- for (int u=0; u<p; u++)
- XiPhiR[j] += X[mi(i,u,n,p)] * phi[ai(u,j,r,p,m,k)];
- }
-
- //compute dotProduct < Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) . Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) >
- Real dotProduct = 0.0;
- for (int u=0; u<m; u++)
- dotProduct += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
- Real logGamIR = log(Pi[r]) + log(detRhoR) - 0.5*dotProduct;
-
- //Z(i) = index of max (gam(i,:))
- if (logGamIR > maxLogGamIR)
- {
- Z[i] = r;
- maxLogGamIR = logGamIR;
- }
- sumLLF1 += exp(logGamIR) / pow(2*M_PI,m/2.0);
- }
-
- sumLogLLF2 += log(sumLLF1);
- }
-
- // Assign output variable LLF
- *LLF = -invN * sumLogLLF2;
-
- //newDeltaPhi = max(max((abs(phi-Phi))./(1+abs(phi))));
- Real newDeltaPhi = 0.0;
- for (int j=0; j<p; j++)
- {
- for (int jj=0; jj<m; jj++)
- {
- for (int r=0; r<k; r++)
- {
- Real tmpDist = fabs(phi[ai(j,jj,r,p,m,k)]-Phi[ai(j,jj,r,p,m,k)])
- / (1.0+fabs(phi[ai(j,jj,r,p,m,k)]));
- if (tmpDist > newDeltaPhi)
- newDeltaPhi = tmpDist;
- }
- }
- }
-
- //update distance parameter to check algorithm convergence (delta(phi, Phi))
- //TODO: deltaPhi should be a linked list for perf.
- if (ite < deltaPhiBufferSize)
- deltaPhi[ite] = newDeltaPhi;
- else
- {
- sumDeltaPhi -= deltaPhi[0];
- for (int u=0; u<deltaPhiBufferSize-1; u++)
- deltaPhi[u] = deltaPhi[u+1];
- deltaPhi[deltaPhiBufferSize-1] = newDeltaPhi;
- }
- sumDeltaPhi += newDeltaPhi;
-
- // update other local variables
- for (int j=0; j<m; j++)
- {
- for (int jj=0; jj<p; jj++)
- {
- for (int r=0; r<k; r++)
- Phi[ai(jj,j,r,p,m,k)] = phi[ai(jj,j,r,p,m,k)];
- }
- }
- ite++;
- }
-
- //free memory
- free(hatBetaR);
- free(deltaPhi);
- free(Phi);
- gsl_matrix_free(matrixE);
- gsl_matrix_free(matrixM);
- gsl_permutation_free(permutation);
- gsl_vector_free(work);
- gsl_matrix_free(V);
- gsl_vector_free(S);
- free(XiPhiR);
- free(YiRhoR);
- free(Xr);
- free(Yr);
- free(tXrXr);
- free(tXrYr);
- free(Z);
-}
projects / valse.git / blobdiff