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     // 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: same as in R
  39     Real* gam = (Real*)malloc(n*k*sizeof(Real));
  40     copyArray(gamInit, gam, n*k);
  41     Real* Gram2 = (Real*)malloc(p*p*k*sizeof(Real));
  42     Real* ps2 = (Real*)malloc(p*m*k*sizeof(Real));
  43     Real* b = (Real*)malloc(k*sizeof(Real));
  44     Real* X2 = (Real*)malloc(n*p*k*sizeof(Real));
  45     Real* Y2 = (Real*)malloc(n*m*k*sizeof(Real));
  46     Real dist = 0.;
  47     Real dist2 = 0.;
  48     int ite = 0;
  49     Real* pi2 = (Real*)malloc(k*sizeof(Real));
  50     Real* ps = (Real*)malloc(m*k*sizeof(Real));
  51     Real* nY2 = (Real*)malloc(m*k*sizeof(Real));
  52     Real* ps1 = (Real*)malloc(n*m*k*sizeof(Real));
  53     Real* Gam = (Real*)malloc(n*k*sizeof(Real));
  54     const Real EPS = 1e-15;
  55     // Additional (not at this place, in R file)
  56     Real* gam2 = (Real*)malloc(k*sizeof(Real));
  57     Real* sqNorm2 = (Real*)malloc(k*sizeof(Real));
  58     gsl_matrix* matrix = gsl_matrix_alloc(m, m);
  59     gsl_permutation* permutation = gsl_permutation_alloc(m);
  60     Real* YiRhoR = (Real*)malloc(m*sizeof(Real));
  61     Real* XiPhiR = (Real*)malloc(m*sizeof(Real));
  62     const Real gaussConstM = pow(2.*M_PI,m/2.);
  63     Real* Phi = (Real*)malloc(p*m*k*sizeof(Real));
  64     Real* Rho = (Real*)malloc(m*m*k*sizeof(Real));
  65     Real* Pi = (Real*)malloc(k*sizeof(Real));
  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,n,m)];
  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         //sum(pi^gamma * b)
 168         Real piPowGammaDotB = 0.;
 169         for (int v=0; v<k; v++)
 170             piPowGammaDotB += pow(pi[v],gamma) * b[v];
 171         //sum(pi2^gamma * b)
 172         Real pi2PowGammaDotB = 0.;
 173         for (int v=0; v<k; v++)
 174             pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 175         //sum(gam2 * log(pi2))
 176         Real gam2DotLogPi2 = 0.;
 177         for (int v=0; v<k; v++)
 178             gam2DotLogPi2 += gam2[v] * log(pi2[v]);
 179
 180         //t(m) la plus grande valeur dans la grille O.1^k tel que ce soit décroissante ou constante
 181         while (-invN*a + lambda*piPowGammaDotB < -invN*gam2DotLogPi2 + lambda*pi2PowGammaDotB
 182             && kk<1000)
 183         {
 184             Real pow_01_kk = pow(0.1,kk);
 185             //pi2 = pi + 0.1^kk * (1/n*gam2 - pi)
 186             for (int v=0; v<k; v++)
 187                 pi2[v] = pi[v] + pow_01_kk * (invN*gam2[v] - pi[v]);
 188             //pi2 was updated, so we recompute pi2PowGammaDotB and gam2DotLogPi2
 189             pi2PowGammaDotB = 0.;
 190             for (int v=0; v<k; v++)
 191                 pi2PowGammaDotB += pow(pi2[v],gamma) * b[v];
 192             gam2DotLogPi2 = 0.;
 193             for (int v=0; v<k; v++)
 194                 gam2DotLogPi2 += gam2[v] * log(pi2[v]);
 195             kk++;
 196         }
 197         Real t = pow(0.1,kk);
 198         //sum(pi + t*(pi2-pi))
 199         Real sumPiPlusTbyDiff = 0.;
 200         for (int v=0; v<k; v++)
 201             sumPiPlusTbyDiff += (pi[v] + t*(pi2[v] - pi[v]));
 202         //pi = (pi + t*(pi2-pi)) / sum(pi + t*(pi2-pi))
 203         for (int v=0; v<k; v++)
 204             pi[v] = (pi[v] + t*(pi2[v] - pi[v])) / sumPiPlusTbyDiff;
 205
 206         //Pour phi et rho
 207         for (int r=0; r<k; r++)
 208         {
 209             for (int mm=0; mm<m; mm++)
 210             {
 211                 for (int i=0; i<n; i++)
 212                 {
 213                     //< X2[i,,r] , phi[,mm,r] >
 214                     Real dotProduct = 0.;
 215                     for (int u=0; u<p; u++)
 216                         dotProduct += X2[ai(i,u,r,n,p,k)] * phi[ai(u,mm,r,p,m,k)];
 217                     //ps1[i,mm,r] = Y2[i,mm,r] * sum(X2[i,,r] * phi[,mm,r])
 218                     ps1[ai(i,mm,r,n,m,k)] = Y2[ai(i,mm,r,n,m,k)] * dotProduct;
 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(Y2[,mm,r]^2)
 226                 Real sumY2 = 0.;
 227                 for (int u=0; u<n; u++)
 228                     sumY2 += Y2[ai(u,mm,r,n,m,k)] * Y2[ai(u,mm,r,n,m,k)];
 229                 nY2[mi(mm,r,m,k)] = sumY2;
 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
 236         for (int r=0; r<k; r++)
 237         {
 238             for (int j=0; j<p; j++)
 239             {
 240                 for (int mm=0; mm<m; mm++)
 241                 {
 242                     //sum(phi[-j,mm,r] * Gram2[j, setdiff(1:p,j),r])
 243                     Real phiDotGram2 = 0.;
 244                     for (int u=0; u<p; u++)
 245                     {
 246                         if (u != j)
 247                             phiDotGram2 += phi[ai(u,mm,r,p,m,k)] * Gram2[ai(j,u,r,p,p,k)];
 248                     }
 249                     //S[j,mm,r] = -rho[mm,mm,r]*ps2[j,mm,r] + sum(phi[-j,mm,r] * Gram2[j,-j,r])
 250                     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;
 251                     Real pirPowGamma = pow(pi[r],gamma);
 252                     if (fabs(S[ai(j,mm,r,p,m,k)]) <= n*lambda*pirPowGamma)
 253                         phi[ai(j,mm,r,p,m,k)] = 0.;
 254                     else if (S[ai(j,mm,r,p,m,k)] > n*lambda*pirPowGamma)
 255                     {
 256                         phi[ai(j,mm,r,p,m,k)] = (n*lambda*pirPowGamma - S[ai(j,mm,r,p,m,k)])
 257                             / Gram2[ai(j,j,r,p,p,k)];
 258                     }
 259                     else
 260                     {
 261                         phi[ai(j,mm,r,p,m,k)] = -(n*lambda*pirPowGamma + S[ai(j,mm,r,p,m,k)])
 262                             / Gram2[ai(j,j,r,p,p,k)];
 263                     }
 264                 }
 265             }
 266         }
 267
 268         /////////////
 269         // Etape E //
 270         /////////////
 271
 272         int signum;
 273         Real sumLogLLF2 = 0.;
 274         for (int i=0; i<n; i++)
 275         {
 276             for (int r=0; r<k; r++)
 277             {
 278                 //compute Y[i,]%*%rho[,,r]
 279                 for (int u=0; u<m; u++)
 280                 {
 281                     YiRhoR[u] = 0.;
 282                     for (int v=0; v<m; v++)
 283                         YiRhoR[u] += Y[mi(i,v,n,m)] * rho[ai(v,u,r,m,m,k)];
 284                 }
 285
 286                 //compute X[i,]%*%phi[,,r]
 287                 for (int u=0; u<m; u++)
 288                 {
 289                     XiPhiR[u] = 0.;
 290                     for (int v=0; v<p; v++)
 291                         XiPhiR[u] += X[mi(i,v,n,p)] * phi[ai(v,u,r,p,m,k)];
 292                 }
 293
 294                 //compute sq norm || Y(:,i)*rho(:,:,r)-X(i,:)*phi(:,:,r) ||_2^2
 295                 sqNorm2[r] = 0.;
 296                 for (int u=0; u<m; u++)
 297                     sqNorm2[r] += (YiRhoR[u]-XiPhiR[u]) * (YiRhoR[u]-XiPhiR[u]);
 298             }
 299
 300             Real sumLLF1 = 0.;
 301             Real sumGamI = 0.;
 302             for (int r=0; r<k; r++)
 303             {
 304                 //compute det(rho[,,r]) [TODO: avoid re-computations]
 305                 for (int u=0; u<m; u++)
 306                 {
 307                     for (int v=0; v<m; v++)
 308                         matrix->data[u*m+v] = rho[ai(u,v,r,m,m,k)];
 309                 }
 310                 gsl_linalg_LU_decomp(matrix, permutation, &signum);
 311                 Real detRhoR = gsl_linalg_LU_det(matrix, signum);
 312                 Gam[mi(i,r,n,k)] = pi[r] * exp(-.5*sqNorm2[r]) * detRhoR;
 313                 sumLLF1 += Gam[mi(i,r,n,k)] / gaussConstM;
 314                 sumGamI += Gam[mi(i,r,n,k)];
 315             }
 316
 317             sumLogLLF2 += log(sumLLF1);
 318             for (int r=0; r<k; r++)
 319             {
 320                 //gam[i,] = Gam[i,] / sumGamI
 321                 gam[mi(i,r,n,k)] = sumGamI > EPS ? Gam[mi(i,r,n,k)] / sumGamI : 0.;
 322             }
 323         }
 324
 325         //sumPen = sum(pi^gamma * b)
 326         Real sumPen = 0.;
 327         for (int r=0; r<k; r++)
 328             sumPen += pow(pi[r],gamma) * b[r];
 329         //LLF[ite] = -sumLogLLF2/n + lambda*sumPen
 330         LLF[ite] = -invN * sumLogLLF2 + lambda * sumPen;
 331         dist = ite==0 ? LLF[ite] : (LLF[ite] - LLF[ite-1]) / (1. + fabs(LLF[ite]));
 332
 333         //Dist1 = max( abs(phi-Phi) / (1+abs(phi)) )
 334         Real Dist1 = 0.;
 335         for (int u=0; u<p; u++)
 336         {
 337             for (int v=0; v<m; v++)
 338             {
 339                 for (int w=0; w<k; w++)
 340                 {
 341                     Real tmpDist = fabs(phi[ai(u,v,w,p,m,k)]-Phi[ai(u,v,w,p,m,k)])
 342                         / (1.+fabs(phi[ai(u,v,w,p,m,k)]));
 343                     if (tmpDist > Dist1)
 344                         Dist1 = tmpDist;
 345                 }
 346             }
 347         }
 348         //Dist2 = max( (abs(rho-Rho)) / (1+abs(rho)) )
 349         Real Dist2 = 0.;
 350         for (int u=0; u<m; u++)
 351         {
 352             for (int v=0; v<m; v++)
 353             {
 354                 for (int w=0; w<k; w++)
 355                 {
 356                     Real tmpDist = fabs(rho[ai(u,v,w,m,m,k)]-Rho[ai(u,v,w,m,m,k)])
 357                         / (1.+fabs(rho[ai(u,v,w,m,m,k)]));
 358                     if (tmpDist > Dist2)
 359                         Dist2 = tmpDist;
 360                 }
 361             }
 362         }
 363         //Dist3 = max( (abs(pi-Pi)) / (1+abs(Pi)))
 364         Real Dist3 = 0.;
 365         for (int u=0; u<n; u++)
 366         {
 367             for (int v=0; v<k; v++)
 368             {
 369                 Real tmpDist = fabs(pi[v]-Pi[v]) / (1.+fabs(pi[v]));
 370                 if (tmpDist > Dist3)
 371                     Dist3 = tmpDist;
 372             }
 373         }
 374         //dist2=max([max(Dist1),max(Dist2),max(Dist3)]);
 375         dist2 = Dist1;
 376         if (Dist2 > dist2)
 377             dist2 = Dist2;
 378         if (Dist3 > dist2)
 379             dist2 = Dist3;
 380
 381         ite++;
 382     }
 383
 384     //TODO: affec = apply(gam, 1,which.max) à traduire, et retourner affec aussi.
 385
 386     //free memory
 387     free(b);
 388     free(gam);
 389     free(Gam);
 390     free(Phi);
 391     free(Rho);
 392     free(Pi);
 393     free(ps);
 394     free(nY2);
 395     free(ps1);
 396     free(Gram2);
 397     free(ps2);
 398     gsl_matrix_free(matrix);
 399     gsl_permutation_free(permutation);
 400     free(XiPhiR);
 401     free(YiRhoR);
 402     free(gam2);
 403     free(pi2);
 404     free(X2);
 405     free(Y2);
 406     free(sqNorm2);
 407 }