pkg/src/sources/EMGLLF.c

   1 #include "utils.h"
   2 #include <stdlib.h>
   3 #include <gsl/gsl_linalg.h>
   4
   5 // TODO: don't recompute indexes every time......
   6 void EMGLLF_core(
   7     // IN parameters
   8     const Real* phiInit, // parametre initial de moyenne renormalisé
   9     const Real* rhoInit, // parametre initial de variance renormalisé
  10     const Real* piInit,  // parametre initial des proportions
  11     const Real* gamInit, // paramètre initial des probabilités a posteriori de chaque échantillon
  12     int mini, // nombre minimal d'itérations dans l'algorithme EM
  13     int maxi, // nombre maximal d'itérations dans l'algorithme EM
  14     Real gamma, // puissance des proportions dans la pénalisation pour un Lasso adaptatif
  15     Real lambda, // valeur du paramètre de régularisation du Lasso
  16     const Real* X, // régresseurs
  17     const Real* Y, // réponse
  18     Real tau, // seuil pour accepter la convergence
  19     // OUT parameters (all pointers, to be modified)
  20     Real* phi, // parametre de moyenne renormalisé, calculé par l'EM
  21     Real* rho, // parametre de variance renormalisé, calculé par l'EM
  22     Real* pi, // parametre des proportions renormalisé, calculé par l'EM
  23     Real* LLF, // log vraisemblance associée à cet échantillon, pour les valeurs estimées des paramètres
  24     Real* S,
  25     // additional size parameters
  26     int n, // nombre d'echantillons
  27     int p, // nombre de covariables
  28     int m, // taille de Y (multivarié)
  29     int k) // nombre de composantes dans le mélange
  30 {
  31     //Initialize outputs
  32     copyArray(phiInit, phi, p*m*k);
  33     copyArray(rhoInit, rho, m*m*k);
  34     copyArray(piInit, pi, k);
  35     zeroArray(LLF, maxi);
  36     //S is already allocated, and doesn't need to be 'zeroed'
  37
  38     //Other local variables
  39     Real* gam = (Real*)malloc(n*k*sizeof(Real));
  40     copyArray(gamInit, gam, n*k);
  41     Real* b = (Real*)malloc(k*sizeof(Real));
  42     Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
  43     Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
  44     Real* Pi = (Real*)malloc(k*sizeof(Real));
  45     Real* gam2 = (Real*)malloc(k*sizeof(Real));
  46     Real* pi2 = (Real*)malloc(k*sizeof(Real));
  47     Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
  48     Real* ps = (Real*)malloc(m*k*sizeof(Real));
  49     Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
  50     Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
  51     Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
  52     Real* nY21 = (Real*)malloc(n*m*k*sizeof(Real));
  53     Real* Gam = (Real*)malloc(n*k*sizeof(Real));
  54     Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
  55     Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
  56     Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
  57     gsl_matrix* matrix = gsl_matrix_alloc(m, m);
  58     gsl_permutation* permutation = gsl_permutation_alloc(m);
  59     Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
  60     Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
  61     Real dist = 0.;
  62     Real dist2 = 0.;
  63     int ite = 0;
  64     const Real EPS = 1e-15;
  65     const Real gaussConstM = pow(2.*M_PI,m/2.);
  66
  67     while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
  68     {
  69         copyArray(phi, Phi, p*m*k);
  70         copyArray(rho, Rho, m*m*k);
  71         copyArray(pi, Pi, k);
  72
  73         // Calculs associés a Y et X
  74         for (int r=0; r<k; r++)
  75         {
  76             for (int mm=0; mm<m; mm++)
  77             {
  78                 //Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
  79                 for (int u=0; u<n; u++)
  80                     Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,m,n)];
  81             }
  82             for (int i=0; i<n; i++)
  83             {
  84                 //X2[i,,r] = sqrt(gam[i,r]) * X[i,]
  85                 for (int u=0; u<p; u++)
  86                     X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
  87             }
  88             for (int mm=0; mm<m; mm++)
  89             {
  90                 //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
  91                 for (int u=0; u<p; u++)
  92                 {
  93                     Real dotProduct = 0.;
  94                     for (int v=0; v<n; v++)
  95                         dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
  96                     ps2[ai(u,mm,r,p,m,k)] = dotProduct;
  97                 }
  98             }
  99             for (int j=0; j<p; j++)
 100             {
 101                 for (int s=0; s<p; s++)
 102                 {
 103                     //Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
 104                     Real dotProduct = 0.;
 105                     for (int u=0; u<n; u++)
 106                         dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
 107                     Gram2[ai(j,s,r,p,p,k)] = dotProduct;
 108                 }
 109             }
 110         }
 111
 112         /////////////
 113         // Etape M //
 114         /////////////
 115
 116         // Pour pi
 117         for (int r=0; r<k; r++)
 118         {
 119             //b[r] = sum(abs(phi[,,r]))
 120             Real sumAbsPhi = 0.;
 121             for (int u=0; u<p; u++)
 122                 for (int v=0; v<m; v++)
 123                     sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
 124             b[r] = sumAbsPhi;
 125         }
 126         //gam2 = colSums(gam)
 127         for (int u=0; u<k; u++)
 128         {
 129             Real sumOnColumn = 0.;
 130             for (int v=0; v<n; v++)
 131                 sumOnColumn += gam[mi(v,u,n,k)];
 132             gam2[u] = sumOnColumn;
 133         }
 134         //a = sum(gam %*% log(pi))
 135         Real a = 0.;
 136         for (int u=0; u<n; u++)
 137         {
 138             Real dotProduct = 0.;
 139             for (int v=0; v<k; v++)
 140                 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
 141             a += dotProduct;
 142         }
 143
 144         //tant que les proportions sont negatives
 145         int kk = 0;
 146         int pi2AllPositive = 0;
 147         Real invN = 1./n;
 148         while (!pi2AllPositive)
 149         {
 150             //pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
 151             Real pow_01_kk = pow(0.1,kk);
 152             for (int r=0; r<k; r++)
 153                 pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
 154             //pi2AllPositive = all(pi2 >= 0)
 155             pi2AllPositive = 1;
 156             for (int r=0; r<k; r++)
 157             {
 158                 if (pi2[r] < 0)
 159                 {
 160                     pi2AllPositive = 0;
 161                     break;
 162                 }
 163             }
 164             kk++;
 165         }
 166
 167         //(pi.^gamma)*b
 168         Real piPowGammaDotB = 0.;
 169         for (int v=0; v<k; v++)
 170             piPowGammaDotB += pow(pi[v],gamma) * b[v];
 171         //(pi2.^gamma)*b
 172         Real pi2PowGammaDotB = 0.;
 173         for (int v=0; v<k; v++)
 174             pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 175         //transpose(gam2)*log(pi2)
 176         Real prodGam2logPi2 = 0.;
 177         for (int v=0; v<k; v++)
 178             prodGam2logPi2 += gam2[v] * log(pi2[v]);
 179         //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
 180         while (-invN*a + lambda*piPowGammaDotB < -invN*prodGam2logPi2 + lambda*pi2PowGammaDotB
 181             && kk<1000)
 182         {
 183             Real pow_01_kk = pow(0.1,kk);
 184             //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
 185             for (int v=0; v<k; v++)
 186                 pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
 187             //pi2 was updated, so we recompute pi2PowGammaDotB and prodGam2logPi2
 188             pi2PowGammaDotB = 0.;
 189             for (int v=0; v<k; v++)
 190                 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 191             prodGam2logPi2 = 0.;
 192             for (int v=0; v<k; v++)
 193                 prodGam2logPi2 += gam2[v] * log(pi2[v]);
 194             kk++;
 195         }
 196         Real t = pow(0.1,kk);
 197         //sum(pi + t*(pi2-pi))
 198         Real sumPiPlusTbyDiff = 0.;
 199         for (int v=0; v<k; v++)
 200             sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
 201         //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
 202         for (int v=0; v<k; v++)
 203             pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
 204
 205         //Pour phi et rho
 206         for (int r=0; r<k; r++)
 207         {
 208             for (int mm=0; mm<m; mm++)
 209             {
 210                 for (int i=0; i<n; i++)
 211                 {
 212                     //< X2(i,:,r) , phi(:,mm,r) >
 213                     Real dotProduct = 0.;
 214                     for (int u=0; u<p; u++)
 215                         dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
 216                     //ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
 217                     ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
 218                     nY21[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * Y2[ai(i,mm,r,n,m,k)];
 219                 }
 220                 //ps[mm,r] = sum(ps1[,mm,r])
 221                 Real sumPs1 = 0.;
 222                 for (int u=0; u<n; u++)
 223                     sumPs1 += ps1[ai(u,mm,r,n,m,k)];
 224                 ps[mi(mm,r,m,k)] = sumPs1;
 225                 //nY2[mm,r] = sum(nY21[,mm,r])
 226                 Real sumNy21 = 0.;
 227                 for (int u=0; u<n; u++)
 228                     sumNy21 += nY21[ai(u,mm,r,n,m,k)];
 229                 nY2[mi(mm,r,m,k)] = sumNy21;
 230                 //rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r]))) / (2*nY2[mm,r])
 231                 rho[ai(mm,mm,r,m,m,k)] = ( ps[mi(mm,r,m,k)] + sqrt( ps[mi(mm,r,m,k)]*ps[mi(mm,r,m,k)]
 232                     + 4*nY2[mi(mm,r,m,k)] * gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
 233             }
 234         }
 235         for (int r=0; r<k; r++)
 236         {
 237             for (int j=0; j<p; j++)
 238             {
 239                 for (int mm=0; mm<m; mm++)
 240                 {
 241                     //sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r])
 242                     Real dotPhiGram2 = 0.0;
 243                     for (int u=0; u<j; u++)
 244                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 245                     //sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r])
 246                     for (int u=j+1; u<p; u++)
 247                         dotPhiGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 248                     //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] +
 249                     //  (if(j>1) sum(phi[1:(j-1),mm,r] * Gram2[j,1:(j-1),r]) else 0) +
 250                     //  (if(j<p) sum(phi[(j+1):p,mm,r] * Gram2[j,(j+1):p,r]) else 0)
 251                     S[ai(j,mm,r,p,m,k)] = -rho[ai(mm,mm,r,m,m,k)] * ps2[ai(j,mm,r,p,m,k)] + dotPhiGram2;
 252                     Real pow_pir_gamma = pow(pi[r],gamma);
 253                     if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pow_pir_gamma)
 254                         phi[ai(j,mm,r,p,m,k)] = 0;
 255                     else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pow_pir_gamma)
 256                     {
 257                         phi[ai(j,mm,r,p,m,k)] = (n*lambda*pow_pir_gamma - S[ai(j,mm,r,p,m,k)])
 258                             / Gram2[ai(j,j,r,p,p,k)];
 259                     }
 260                     else
 261                     {
 262                         phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pow_pir_gamma + S[ai(j,mm,r,p,m,k)])
 263                             / Gram2[ai(j,j,r,p,p,k)];
 264                     }
 265                 }
 266             }
 267         }
 268
 269         /////////////
 270         // Etape E //
 271         /////////////
 272
 273         int signum;
 274         Real sumLogLLF2 = 0.0;
 275         for (int i=0; i<n; i++)
 276         {
 277             Real minSqNorm2 = INFINITY;
 278
 279             for (int r=0; r<k; r++)
 280             {
 281                 //compute Y[i,]%*%rho[,,r]
 282                 for (int u=0; u<m; u++)
 283                 {
 284                     YiRhoR[u] = 0.0;
 285                     for (int v=0; v<m; v++)
 286                         YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 287                 }
 288
 289                 //compute X(i,:)*phi(:,:,r)
 290                 for (int u=0; u<m; u++)
 291                 {
 292                     XiPhiR[u] = 0.0;
 293                     for (int v=0; v<p; v++)
 294                         XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 295                 }
 296
 297                 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
 298                 sqNorm2[r] = 0.0;
 299                 for (int u=0; u<m; u++)
 300                     sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
 301                 if (sqNorm2[r] < minSqNorm2)
 302                     minSqNorm2 = sqNorm2[r];
 303             }
 304             Real shift = 0.5*minSqNorm2;
 305
 306             Real sumLLF1 = 0.0;
 307             Real sumGamI = 0.0;
 308             for (int r=0; r<k; r++)
 309             {
 310                 //compute det(rho[,,r]) [TODO: avoid re-computations]
 311                 for (int u=0; u<m; u++)
 312                 {
 313                     for (int v=0; v<m; v++)
 314                         matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 315                 }
 316                 gsl_linalg_LU_decomp(matrix, permutation, &signum);
 317                 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
 318
 319                 //FIXME: det(rho[,,r]) too small(?!). See EMGLLF.R
 320                 Gam[mi(i,r,n,k)] = pi[r] * exp(-0.5*sqNorm2[r] + shift) ; //* detRhoR;
 321                 sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
 322                 sumGamI += Gam[mi(i,r,n,k)];
 323             }
 324             sumLogLLF2 += log(sumLLF1);
 325             for (int r=0; r<k; r++)
 326             {
 327                 //gam[i,] = Gam[i,] / sumGamI
 328                 gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
 329             }
 330         }
 331
 332         //sumPen = sum(pi^gamma * b)
 333         Real sumPen = 0.0;
 334         for (int r=0; r<k; r++)
 335             sumPen += pow(pi[r],gamma) * b[r];
 336         //LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 337         LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
 338         dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1.0 + fabs(LLF[ite]));
 339
 340         //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
 341         Real Dist1 = 0.0;
 342         for (int u=0; u<p; u++)
 343         {
 344             for (int v=0; v<m; v++)
 345             {
 346                 for (int w=0; w<k; w++)
 347                 {
 348                     Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
 349                         / (1.0+fabs(phi[ai(u,v,w,p,m,k)]));
 350                     if (tmpDist > Dist1)
 351                         Dist1 = tmpDist;
 352                 }
 353             }
 354         }
 355         //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
 356         Real Dist2 = 0.0;
 357         for (int u=0; u<m; u++)
 358         {
 359             for (int v=0; v<m; v++)
 360             {
 361                 for (int w=0; w<k; w++)
 362                 {
 363                     Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
 364                         / (1.0+fabs(rho[ai(u,v,w,m,m,k)]));
 365                     if (tmpDist > Dist2)
 366                         Dist2 = tmpDist;
 367                 }
 368             }
 369         }
 370         //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
 371         Real Dist3 = 0.0;
 372         for (int u=0; u<n; u++)
 373         {
 374             for (int v=0; v<k; v++)
 375             {
 376                 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.0+fabs(pi[v]));
 377                 if (tmpDist > Dist3)
 378                     Dist3 = tmpDist;
 379             }
 380         }
 381         //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
 382         dist2 = Dist1;
 383         if (Dist2 > dist2)
 384             dist2 = Dist2;
 385         if (Dist3 > dist2)
 386             dist2 = Dist3;
 387
 388         ite++;
 389     }
 390
 391     //free memory
 392     free(b);
 393     free(gam);
 394     free(Gam);
 395     free(Phi);
 396     free(Rho);
 397     free(Pi);
 398     free(ps);
 399     free(nY2);
 400     free(ps1);
 401     free(nY21);
 402     free(Gram2);
 403     free(ps2);
 404     gsl_matrix_free(matrix);
 405     gsl_permutation_free(permutation);
 406     free(XiPhiR);
 407     free(YiRhoR);
 408     free(gam2);
 409     free(pi2);
 410     free(X2);
 411     free(Y2);
 412     free(sqNorm2);
 413 }