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 ai(...) and mi(...) when possible
   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     int* affec,
  26     // additional size parameters
  27     int n, // nombre d'echantillons
  28     int p, // nombre de covariables
  29     int m, // taille de Y (multivarié)
  30     int k) // nombre de composantes dans le mélange
  31 {
  32     //Initialize outputs
  33     copyArray(phiInit, phi, p*m*k);
  34     copyArray(rhoInit, rho, m*m*k);
  35     copyArray(piInit, pi, k);
  36     zeroArray(LLF, maxi);
  37     //S is already allocated, and doesn't need to be 'zeroed'
  38
  39     //Other local variables: same as in R
  40     Real* gam = (Real*)malloc(n*k*sizeof(Real));
  41     copyArray(gamInit, gam, n*k);
  42     Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
  43     Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
  44     Real* b = (Real*)malloc(k*sizeof(Real));
  45     Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
  46     Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
  47     Real dist = 0.;
  48     Real dist2 = 0.;
  49     int ite = 0;
  50     Real* pi2 = (Real*)malloc(k*sizeof(Real));
  51     Real* ps = (Real*)malloc(m*k*sizeof(Real));
  52     Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
  53     Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
  54     Real* Gam = (Real*)malloc(n*k*sizeof(Real));
  55     const Real EPS = 1e-15;
  56     // Additional (not at this place, in R file)
  57     Real* gam2 = (Real*)malloc(k*sizeof(Real));
  58     Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
  59     gsl_matrix* matrix = gsl_matrix_alloc(m, m);
  60     gsl_permutation* permutation = gsl_permutation_alloc(m);
  61     Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
  62     Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
  63     const Real gaussConstM = pow(2.*M_PI,m/2.);
  64     Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
  65     Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
  66     Real* Pi = (Real*)malloc(k*sizeof(Real));
  67
  68     while (ite < mini || (ite < maxi && (dist >= tau || dist2 >= sqrt(tau))))
  69     {
  70         copyArray(phi, Phi, p*m*k);
  71         copyArray(rho, Rho, m*m*k);
  72         copyArray(pi, Pi, k);
  73
  74         // Calculs associés a Y et X
  75         for (int r=0; r<k; r++)
  76         {
  77             for (int mm=0; mm<m; mm++)
  78             {
  79                 //Y2[,mm,r] = sqrt(gam[,r]) * Y[,mm]
  80                 for (int u=0; u<n; u++)
  81                     Y2[ai(u,mm,r,n,m,k)] = sqrt(gam[mi(u,r,n,k)]) * Y[mi(u,mm,n,m)];
  82             }
  83             for (int i=0; i<n; i++)
  84             {
  85                 //X2[i,,r] = sqrt(gam[i,r]) * X[i,]
  86                 for (int u=0; u<p; u++)
  87                     X2[ai(i,u,r,n,p,k)] = sqrt(gam[mi(i,r,n,k)]) * X[mi(i,u,n,p)];
  88             }
  89             for (int mm=0; mm<m; mm++)
  90             {
  91                 //ps2[,mm,r] = crossprod(X2[,,r],Y2[,mm,r])
  92                 for (int u=0; u<p; u++)
  93                 {
  94                     Real dotProduct = 0.;
  95                     for (int v=0; v<n; v++)
  96                         dotProduct += X2[ai(v,u,r,n,p,k)] * Y2[ai(v,mm,r,n,m,k)];
  97                     ps2[ai(u,mm,r,p,m,k)] = dotProduct;
  98                 }
  99             }
 100             for (int j=0; j<p; j++)
 101             {
 102                 for (int s=0; s<p; s++)
 103                 {
 104                     //Gram2[j,s,r] = crossprod(X2[,j,r], X2[,s,r])
 105                     Real dotProduct = 0.;
 106                     for (int u=0; u<n; u++)
 107                         dotProduct += X2[ai(u,j,r,n,p,k)] * X2[ai(u,s,r,n,p,k)];
 108                     Gram2[ai(j,s,r,p,p,k)] = dotProduct;
 109                 }
 110             }
 111         }
 112
 113         /////////////
 114         // Etape M //
 115         /////////////
 116
 117         // Pour pi
 118         for (int r=0; r<k; r++)
 119         {
 120             //b[r] = sum(abs(phi[,,r]))
 121             Real sumAbsPhi = 0.;
 122             for (int u=0; u<p; u++)
 123                 for (int v=0; v<m; v++)
 124                     sumAbsPhi += fabs(phi[ai(u,v,r,p,m,k)]);
 125             b[r] = sumAbsPhi;
 126         }
 127         //gam2 = colSums(gam)
 128         for (int u=0; u<k; u++)
 129         {
 130             Real sumOnColumn = 0.;
 131             for (int v=0; v<n; v++)
 132                 sumOnColumn += gam[mi(v,u,n,k)];
 133             gam2[u] = sumOnColumn;
 134         }
 135         //a = sum(gam %*% log(pi))
 136         Real a = 0.;
 137         for (int u=0; u<n; u++)
 138         {
 139             Real dotProduct = 0.;
 140             for (int v=0; v<k; v++)
 141                 dotProduct += gam[mi(u,v,n,k)] * log(pi[v]);
 142             a += dotProduct;
 143         }
 144
 145         //tant que les proportions sont negatives
 146         int kk = 0;
 147         int pi2AllPositive = 0;
 148         Real invN = 1./n;
 149         while (!pi2AllPositive)
 150         {
 151             //pi2 = pi + 0.1^kk * ((1/n)*gam2 - pi)
 152             Real pow_01_kk = pow(0.1,kk);
 153             for (int r=0; r<k; r++)
 154                 pi2[r] = pi[r] + pow_01_kk * (invN*gam2[r] - pi[r]);
 155             //pi2AllPositive = all(pi2 >= 0)
 156             pi2AllPositive = 1;
 157             for (int r=0; r<k; r++)
 158             {
 159                 if (pi2[r] < 0)
 160                 {
 161                     pi2AllPositive = 0;
 162                     break;
 163                 }
 164             }
 165             kk++;
 166         }
 167
 168         //sum(pi^gamma * b)
 169         Real piPowGammaDotB = 0.;
 170         for (int v=0; v<k; v++)
 171             piPowGammaDotB += pow(pi[v],gamma) * b[v];
 172         //sum(pi2^gamma * b)
 173         Real pi2PowGammaDotB = 0.;
 174         for (int v=0; v<k; v++)
 175             pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 176         //sum(gam2 * log(pi2))
 177         Real gam2DotLogPi2 = 0.;
 178         for (int v=0; v<k; v++)
 179             gam2DotLogPi2 += gam2[v] * log(pi2[v]);
 180
 181         //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
 182         while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
 183             && kk<1000)
 184         {
 185             Real pow_01_kk = pow(0.1,kk);
 186             //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
 187             for (int v=0; v<k; v++)
 188                 pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
 189             //pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
 190             pi2PowGammaDotB = 0.;
 191             for (int v=0; v<k; v++)
 192                 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 193             gam2DotLogPi2 = 0.;
 194             for (int v=0; v<k; v++)
 195                 gam2DotLogPi2 += gam2[v] * log(pi2[v]);
 196             kk++;
 197         }
 198         Real t = pow(0.1,kk);
 199         //sum(pi + t*(pi2-pi))
 200         Real sumPiPlusTbyDiff = 0.;
 201         for (int v=0; v<k; v++)
 202             sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
 203         //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
 204         for (int v=0; v<k; v++)
 205             pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
 206
 207         //Pour phi et rho
 208         for (int r=0; r<k; r++)
 209         {
 210             for (int mm=0; mm<m; mm++)
 211             {
 212                 for (int i=0; i<n; i++)
 213                 {
 214                     //< X2[i,,r] , phi[,mm,r] >
 215                     Real dotProduct = 0.;
 216                     for (int u=0; u<p; u++)
 217                         dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
 218                     //ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
 219                     ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
 220                 }
 221                 //ps[mm,r] = sum(ps1[,mm,r])
 222                 Real sumPs1 = 0.;
 223                 for (int u=0; u<n; u++)
 224                     sumPs1 += ps1[ai(u,mm,r,n,m,k)];
 225                 ps[mi(mm,r,m,k)] = sumPs1;
 226                 //nY2[mm,r] = sum(Y2[,mm,r]^2)
 227                 Real sumY2 = 0.;
 228                 for (int u=0; u<n; u++)
 229                     sumY2 += Y2[ai(u,mm,r,n,m,k)] * Y2[ai(u,mm,r,n,m,k)];
 230                 nY2[mi(mm,r,m,k)] = sumY2;
 231                 //rho[mm,mm,r] = (ps[mm,r]+sqrt(ps[mm,r]^2+4*nY2[mm,r]*(gam2[r]))) / (2*nY2[mm,r])
 232                 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)]
 233                     + 4*nY2[mi(mm,r,m,k)] * gam2[r] ) ) / (2*nY2[mi(mm,r,m,k)]);
 234             }
 235         }
 236
 237         for (int r=0; r<k; r++)
 238         {
 239             for (int j=0; j<p; j++)
 240             {
 241                 for (int mm=0; mm<m; mm++)
 242                 {
 243                     //sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
 244                     Real phiDotGram2 = 0.;
 245                     for (int u=0; u<p; u++)
 246                     {
 247                         if (u != j)
 248                             phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 249                     }
 250                     //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
 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)] + phiDotGram2;
 252                     Real pirPowGamma = pow(pi[r],gamma);
 253                     if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
 254                         phi[ai(j,mm,r,p,m,k)] = 0.;
 255                     else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
 256                     {
 257                         phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - 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*pirPowGamma + 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.;
 275         for (int i=0; i<n; i++)
 276         {
 277             for (int r=0; r<k; r++)
 278             {
 279                 //compute Y[i,]%*%rho[,,r]
 280                 for (int u=0; u<m; u++)
 281                 {
 282                     YiRhoR[u] = 0.;
 283                     for (int v=0; v<m; v++)
 284                         YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 285                 }
 286
 287                 //compute X[i,]%*%phi[,,r]
 288                 for (int u=0; u<m; u++)
 289                 {
 290                     XiPhiR[u] = 0.;
 291                     for (int v=0; v<p; v++)
 292                         XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 293                 }
 294
 295                 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
 296                 sqNorm2[r] = 0.;
 297                 for (int u=0; u<m; u++)
 298                     sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
 299             }
 300
 301             Real sumLLF1 = 0.;
 302             Real sumGamI = 0.;
 303             for (int r=0; r<k; r++)
 304             {
 305                 //compute det(rho[,,r]) [TODO: avoid re-computations]
 306                 for (int u=0; u<m; u++)
 307                 {
 308                     for (int v=0; v<m; v++)
 309                         matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 310                 }
 311                 gsl_linalg_LU_decomp(matrix, permutation, &signum);
 312                 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
 313                 Gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRhoR;
 314                 sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
 315                 sumGamI += Gam[mi(i,r,n,k)];
 316             }
 317
 318             sumLogLLF2 += log(sumLLF1);
 319             for (int r=0; r<k; r++)
 320             {
 321                 //gam[i,] = Gam[i,] / sumGamI
 322                 gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
 323             }
 324         }
 325
 326         //sumPen = sum(pi^gamma * b)
 327         Real sumPen = 0.;
 328         for (int r=0; r<k; r++)
 329             sumPen += pow(pi[r],gamma) * b[r];
 330         //LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 331         LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
 332         dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1. + fabs(LLF[ite]));
 333
 334         //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
 335         Real Dist1 = 0.;
 336         for (int u=0; u<p; u++)
 337         {
 338             for (int v=0; v<m; v++)
 339             {
 340                 for (int w=0; w<k; w++)
 341                 {
 342                     Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
 343                         / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
 344                     if (tmpDist > Dist1)
 345                         Dist1 = tmpDist;
 346                 }
 347             }
 348         }
 349         //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
 350         Real Dist2 = 0.;
 351         for (int u=0; u<m; u++)
 352         {
 353             for (int v=0; v<m; v++)
 354             {
 355                 for (int w=0; w<k; w++)
 356                 {
 357                     Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
 358                         / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
 359                     if (tmpDist > Dist2)
 360                         Dist2 = tmpDist;
 361                 }
 362             }
 363         }
 364         //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
 365         Real Dist3 = 0.;
 366         for (int u=0; u<n; u++)
 367         {
 368             for (int v=0; v<k; v++)
 369             {
 370                 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
 371                 if (tmpDist > Dist3)
 372                     Dist3 = tmpDist;
 373             }
 374         }
 375         //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
 376         dist2 = Dist1;
 377         if (Dist2 > dist2)
 378             dist2 = Dist2;
 379         if (Dist3 > dist2)
 380             dist2 = Dist3;
 381
 382         ite++;
 383     }
 384
 385     //affec = apply(gam, 1, which.max)
 386     for (int i=0; i<n; i++)
 387     {
 388         Real rowMax = 0.;
 389         affec[i] = 0;
 390         for (int j=0; j<k; j++)
 391         {
 392             if (gam[mi(i,j,n,k)] > rowMax)
 393             {
 394                 affec[i] = j+1; //R indices start at 1
 395                 rowMax = gam[mi(i,j,n,k)];
 396             }
 397         }
 398     }
 399
 400     //free memory
 401     free(b);
 402     free(gam);
 403     free(Gam);
 404     free(Phi);
 405     free(Rho);
 406     free(Pi);
 407     free(ps);
 408     free(nY2);
 409     free(ps1);
 410     free(Gram2);
 411     free(ps2);
 412     gsl_matrix_free(matrix);
 413     gsl_permutation_free(permutation);
 414     free(XiPhiR);
 415     free(YiRhoR);
 416     free(gam2);
 417     free(pi2);
 418     free(X2);
 419     free(Y2);
 420     free(sqNorm2);
 421 }