src/mr.cpp

   1 /*  Copyright (C) 2006-2008  Joris Mooij  [j dot mooij at science dot ru dot nl]
   2     Radboud University Nijmegen, The Netherlands
   3
   4     This file is part of libDAI.
   5
   6     libDAI is free software; you can redistribute it and/or modify
   7     it under the terms of the GNU General Public License as published by
   8     the Free Software Foundation; either version 2 of the License, or
   9     (at your option) any later version.
  10
  11     libDAI is distributed in the hope that it will be useful,
  12     but WITHOUT ANY WARRANTY; without even the implied warranty of
  13     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  14     GNU General Public License for more details.
  15
  16     You should have received a copy of the GNU General Public License
  17     along with libDAI; if not, write to the Free Software
  18     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  19 */
  20
  21
  22 #include <cstdio>
  23 #include <ctime>
  24 #include <cmath>
  25 #include <cstdlib>
  26 #include <dai/mr.h>
  27 #include <dai/bp.h>
  28 #include <dai/jtree.h>
  29 #include <dai/util.h>
  30 #include <dai/diffs.h>
  31
  32
  33 namespace dai {
  34
  35
  36 using namespace std;
  37
  38
  39 const char *MR::Name = "MR";
  40
  41
  42 void MR::setProperties( const PropertySet &opts ) {
  43     assert( opts.hasKey("tol") );
  44     assert( opts.hasKey("verbose") );
  45     assert( opts.hasKey("updates") );
  46     assert( opts.hasKey("inits") );
  47
  48     props.tol = opts.getStringAs<double>("tol");
  49     props.verbose = opts.getStringAs<size_t>("verbose");
  50     props.updates = opts.getStringAs<Properties::UpdateType>("updates");
  51     props.inits = opts.getStringAs<Properties::InitType>("inits");
  52 }
  53
  54
  55 PropertySet MR::getProperties() const {
  56     PropertySet opts;
  57     opts.Set( "tol", props.tol );
  58     opts.Set( "verbose", props.verbose );
  59     opts.Set( "updates", props.updates );
  60     opts.Set( "inits", props.inits );
  61     return opts;
  62 }
  63
  64
  65 // init N, con, nb, tJ, theta
  66 void MR::init(size_t Nin, double *_w, double *_th) {
  67     size_t i,j;
  68
  69     N = Nin;
  70
  71     con.resize(N);
  72     nb.resize(N);
  73     tJ.resize(N);
  74     for(i=0; i<N; i++ ) {
  75         nb[i].resize(kmax);
  76         tJ[i].resize(kmax);
  77         con[i]=0;
  78         for(j=0; j<N; j++ )
  79             if( _w[i*N+j] != 0.0 ) {
  80                 nb[i][con[i]] = j;
  81                 tJ[i][con[i]] = tanh(_w[i*N+j]);
  82                 con[i]++;
  83             }
  84     }
  85
  86     theta.resize(N);
  87     for(i=0; i<N; i++)
  88       theta[i] = _th[i];
  89 }
  90
  91
  92 // calculate cors
  93 double MR::init_cor_resp() {
  94     size_t j,k,l, runx,i2;
  95     double variab1, variab2;
  96     double md, maxdev;
  97     double thbJsite[kmax];
  98     double xinter;
  99     double rinter;
 100     double res[kmax];
 101     size_t s2;
 102     size_t flag;
 103     size_t concav;
 104     size_t runs = 3000;
 105     double eps = 0.2;
 106     size_t cavity;
 107
 108     vector<vector<double> > tJ_org;
 109     vector<vector<size_t> > nb_org;
 110     vector<size_t> con_org;
 111     vector<double> theta_org;
 112
 113     vector<double> xfield(N*kmax,0.0);
 114     vector<double> rfield(N*kmax,0.0);
 115     vector<double> Hfield(N,0.0);
 116     vector<double> devs(N*kmax,0.0);
 117     vector<double> devs2(N*kmax,0.0);
 118     vector<double> dev(N,0.0);
 119     vector<double> avmag(N,0.0);
 120
 121     // save original tJ, nb
 122     nb_org = nb;
 123     tJ_org = tJ;
 124     con_org = con;
 125     theta_org = theta;
 126
 127     maxdev = 0.0;
 128     for(cavity=0; cavity<N; cavity++){    // for each spin to be removed
 129         con = con_org;
 130         concav=con[cavity];
 131
 132         nb = nb_org;
 133         tJ = tJ_org;
 134
 135         //  Adapt the graph variables nb[], tJ[] and con[]
 136         for(size_t i=0; i<con[cavity]; i++) {
 137             size_t ij = nb[cavity][i];
 138             flag=0;
 139             j=0;
 140             do{
 141                 if(nb[ij][j]==cavity){
 142                     while(j<(con[ij]-1)){
 143                         nb[ij][j]=nb[ij][j+1];
 144                         tJ[ij][j] = tJ[ij][j+1];
 145                         j++;
 146                     }
 147                 flag=1;
 148                 }
 149                 j++;
 150             } while(flag==0);
 151         }
 152         for(size_t i=0; i<con[cavity]; i++)
 153             con[nb[cavity][i]]--;
 154         con[cavity] = 0;
 155
 156
 157         // Do everything starting from the new graph********
 158
 159         makekindex();
 160         theta = theta_org;
 161
 162         for(size_t i=0; i<kmax*N; i++)
 163             xfield[i] = 3.0*(2*rnd_uniform()-1.);
 164
 165         for(i2=0; i2<concav; i2++){ // Subsequently apply a field to each cavity spin ****************
 166
 167             s2 = nb[cavity][i2];    // identify the index of the cavity spin
 168             for(size_t i=0; i<con[s2]; i++)
 169                 rfield[kmax*s2+i] = 1.;
 170
 171             runx=0;
 172             do {      // From here start the response and belief propagation
 173                 runx++;
 174                 md=0.0;
 175                 for(k=0; k<N; k++){
 176                     if(k!=cavity) {
 177                         for(size_t i=0; i<con[k]; i++)
 178                             thbJsite[i] = tJ[k][i];
 179                         for(l=0; l<con[k]; l++){
 180                             xinter = 1.;
 181                             rinter = 0.;
 182                             if(k==s2) rinter += 1.;
 183                             for(j=0; j<con[k]; j++)
 184                                 if(j!=l){
 185                                     variab2 = tanh(xfield[kmax*nb[k][j]+kindex[k][j]]);
 186                                     variab1 = thbJsite[j]*variab2;
 187                                     xinter *= (1.+variab1)/(1.-variab1);
 188
 189                                     rinter += thbJsite[j]*rfield[kmax*nb[k][j]+kindex[k][j]]*(1-variab2*variab2)/(1-variab1*variab1);
 190                                 }
 191
 192                             variab1 = 0.5*log(xinter);
 193                             xinter = variab1 + theta[k];
 194                             devs[kmax*k+l] = xinter-xfield[kmax*k+l];
 195                             xfield[kmax*k+l] = xfield[kmax*k+l]+devs[kmax*k+l]*eps;
 196                             if( fabs(devs[kmax*k+l]) > md )
 197                                 md = fabs(devs[kmax*k+l]);
 198
 199                             devs2[kmax*k+l] = rinter-rfield[kmax*k+l];
 200                             rfield[kmax*k+l] = rfield[kmax*k+l]+devs2[kmax*k+l]*eps;
 201                             if( fabs(devs2[kmax*k+l]) > md )
 202                                 md = fabs(devs2[kmax*k+l]);
 203                         }
 204                     }
 205                 }
 206             } while((md > props.tol)&&(runx<runs)); // Precision condition reached -> BP and RP finished
 207             if(runx==runs)
 208                 if( props.verbose >= 2 )
 209                     cout << "init_cor_resp: Convergence not reached (md=" << md << ")..." << endl;
 210             if(md > maxdev)
 211                 maxdev = md;
 212
 213             // compute the observables (i.e. magnetizations and responses)******
 214
 215             for(size_t i=0; i<concav; i++){
 216                 rinter = 0.;
 217                 xinter = 1.;
 218                 if(i!=i2)
 219                     for(j=0; j<con[nb[cavity][i]]; j++){
 220                         variab2 = tanh(xfield[kmax*nb[nb[cavity][i]][j]+kindex[nb[cavity][i]][j]]);
 221                         variab1 = tJ[nb[cavity][i]][j]*variab2;
 222                         rinter +=  tJ[nb[cavity][i]][j]*rfield[kmax*nb[nb[cavity][i]][j]+kindex[nb[cavity][i]][j]]*(1-variab2*variab2)/(1-variab1*variab1);
 223                         xinter *= (1.+variab1)/(1.-variab1);
 224                     }
 225                 xinter = tanh(0.5*log(xinter)+theta[nb[cavity][i]]);
 226                 res[i] = rinter*(1-xinter*xinter);
 227             }
 228
 229             // *******************
 230
 231             for(size_t i=0; i<concav; i++)
 232                 if(nb[cavity][i]!=s2)
 233             //      if(i!=i2)
 234                     cors[cavity][i2][i] = res[i];
 235                 else
 236                     cors[cavity][i2][i] = 0;
 237         } // close for i2 = 0...concav
 238     }
 239
 240     // restore nb, tJ, con
 241     tJ = tJ_org;
 242     nb = nb_org;
 243     con = con_org;
 244     theta = theta_org;
 245
 246     return maxdev;
 247 }
 248
 249
 250 double MR::T(size_t i, sub_nb A) {
 251     // i is a variable index
 252     // A is a subset of nb[i]
 253     //
 254     // calculate T{(i)}_A as defined in Rizzo&Montanari e-print (2.17)
 255
 256     sub_nb _nbi_min_A(con[i]);
 257     for( size_t __j = 0; __j < A.size(); __j++ )
 258         _nbi_min_A -= A[__j];
 259
 260     double res = theta[i];
 261     for( size_t __j = 0; __j < _nbi_min_A.size(); __j++ ) {
 262         size_t _j = _nbi_min_A[__j];
 263         res += atanh(tJ[i][_j] * M[i][_j]);
 264     }
 265     return tanh(res);
 266 }
 267
 268
 269 double MR::T(size_t i, size_t _j) {
 270     sub_nb j(con[i]);
 271     j.clear();
 272     j += _j;
 273     return T(i,j);
 274 }
 275
 276
 277 double MR::Omega(size_t i, size_t _j, size_t _l) {
 278     sub_nb jl(con[i]);
 279     jl.clear();
 280     jl += _j;
 281     jl += _l;
 282     double Tijl = T(i,jl);
 283     return Tijl / (1.0 + tJ[i][_l] * M[i][_l] * Tijl);
 284 }
 285
 286
 287 double MR::Gamma(size_t i, size_t _j, size_t _l1, size_t _l2) {
 288     sub_nb jll(con[i]);
 289     jll.clear();
 290     jll += _j;
 291     double Tij = T(i,jll);
 292     jll += _l1;
 293     jll += _l2;
 294     double Tijll = T(i,jll);
 295
 296     return (Tijll - Tij) / (1.0 + tJ[i][_l1] * tJ[i][_l2] * M[i][_l1] * M[i][_l2] + tJ[i][_l1] * M[i][_l1] * Tijll + tJ[i][_l2] * M[i][_l2] * Tijll);
 297 }
 298
 299
 300 double MR::Gamma(size_t i, size_t _l1, size_t _l2) {
 301     sub_nb ll(con[i]);
 302     ll.clear();
 303     double Ti = T(i,ll);
 304     ll += _l1;
 305     ll += _l2;
 306     double Till = T(i,ll);
 307
 308     return (Till - Ti) / (1.0 + tJ[i][_l1] * tJ[i][_l2] * M[i][_l1] * M[i][_l2] + tJ[i][_l1] * M[i][_l1] * Till + tJ[i][_l2] * M[i][_l2] * Till);
 309 }
 310
 311
 312 double MR::_tJ(size_t i, sub_nb A) {
 313     // i is a variable index
 314     // A is a subset of nb[i]
 315     //
 316     // calculate the product of all tJ[i][_j] for _j in A
 317
 318     size_t Asize = A.size();
 319     switch( Asize ) {
 320         case 0: return 1.0;
 321 //      case 1: return tJ[i][A[0]];
 322 //      case 2: return tJ[i][A[0]] * tJ[i][A[1]];
 323 //      case 3: return tJ[i][A[0]] * tJ[i][A[1]] * tJ[i][A[2]];
 324         default:
 325             size_t __j = Asize - 1;
 326             size_t _j = A[__j];
 327             sub_nb A_j = A - _j;
 328             return tJ[i][_j] * _tJ(i, A_j);
 329     }
 330
 331 }
 332
 333
 334 double MR::appM(size_t i, sub_nb A) {
 335     // i is a variable index
 336     // A is a subset of nb[i]
 337     //
 338     // calculate the moment of variables in A from M and cors, neglecting higher order cumulants,
 339     // defined as the sum over all partitions of A into subsets of cardinality two at most of the
 340     // product of the cumulants (either first order, i.e. M, or second order, i.e. cors) of the
 341     // entries of the partitions
 342
 343     size_t Asize = A.size();
 344     switch( Asize ) {
 345         case 0: return 1.0;
 346 //      case 1: return M[i][A[0]];
 347 //      case 2: return M[i][A[0]] * M[i][A[1]] + cors[i][A[0]][A[1]];
 348 //      case 3: return M[i][A[0]] * M[i][A[1]] * M[i][A[2]] + M[i][A[0]] * cors[i][A[1]][A[2]] + M[i][A[1]] * cors[i][A[0]][A[2]] + M[i][A[2]] * cors[i][A[0]][A[1]];
 349         default:
 350             size_t __j = Asize - 1;
 351             size_t _j = A[__j];
 352             sub_nb A_j = A - _j;
 353
 354             double result = M[i][_j] * appM(i, A_j);
 355             for( size_t __k = 0; __k < __j; __k++ ) {
 356                 size_t _k = A[__k];
 357                 result += cors[i][_j][_k] * appM(i,A_j - _k);
 358             }
 359
 360             return result;
 361     }
 362 }
 363
 364
 365 void MR::sum_subs(size_t j, sub_nb A, double *sum_even, double *sum_odd) {
 366     // j is a variable index
 367     // A is a subset of nb[j]
 368
 369     // calculate sum over all even/odd subsets B of A of _tJ(j,B) appM(j,B)
 370
 371     *sum_even = 0.0;
 372     *sum_odd = 0.0;
 373
 374     sub_nb S(A.size());
 375     S.clear();
 376     do { // for all subsets of A
 377
 378         // construct subset B of A corresponding to S
 379         sub_nb B = A;
 380         B.clear();
 381         size_t Ssize = S.size();
 382         for( size_t bit = 0; bit < Ssize; bit++ )
 383             B += A[S[bit]];
 384
 385         if( S.size() % 2 )
 386             *sum_odd += _tJ(j,B) * appM(j,B);
 387         else
 388             *sum_even += _tJ(j,B) * appM(j,B);
 389
 390         ++S;
 391     } while( !S.empty() );
 392 }
 393
 394
 395 void MR::solvemcav() {
 396     double sum_even, sum_odd;
 397     double maxdev;
 398     size_t maxruns = 1000;
 399
 400     makekindex();
 401     for(size_t i=0; i<N; i++)
 402         for(size_t _j=0; _j<con[i]; _j++)
 403             M[i][_j]=0.1;
 404
 405     size_t run=0;
 406     do {
 407         maxdev=0.0;
 408         run++;
 409         for(size_t i=0; i<N; i++){ // for all i
 410             for(size_t _j=0; _j<con[i]; _j++){ // for all j in N_i
 411                 size_t _i = kindex[i][_j];
 412                 size_t j = nb[i][_j];
 413                 assert( nb[j][_i] == i );
 414
 415                 double newM = 0.0;
 416                 if( props.updates == Properties::UpdateType::FULL ) {
 417                     // find indices in nb[j] that do not correspond with i
 418                     sub_nb _nbj_min_i(con[j]);
 419                     _nbj_min_i -= kindex[i][_j];
 420
 421                     // find indices in nb[i] that do not correspond with j
 422                     sub_nb _nbi_min_j(con[i]);
 423                     _nbi_min_j -= _j;
 424
 425                     sum_subs(j, _nbj_min_i, &sum_even, &sum_odd);
 426                     newM = (tanh(theta[j]) * sum_even + sum_odd) / (sum_even + tanh(theta[j]) * sum_odd);
 427
 428                     sum_subs(i, _nbi_min_j, &sum_even, &sum_odd);
 429                     double denom = sum_even + tanh(theta[i]) * sum_odd;
 430                     double numer = 0.0;
 431                     for(size_t _k=0; _k<con[i]; _k++) if(_k != _j) {
 432                         sum_subs(i, _nbi_min_j - _k, &sum_even, &sum_odd);
 433                         numer += tJ[i][_k] * cors[i][_j][_k] * (tanh(theta[i]) * sum_even + sum_odd);
 434                     }
 435                     newM -= numer / denom;
 436                 } else if( props.updates == Properties::UpdateType::LINEAR ) {
 437                     newM = T(j,_i);
 438                     for(size_t _l=0; _l<con[i]; _l++) if( _l != _j )
 439                         newM -= Omega(i,_j,_l) * tJ[i][_l] * cors[i][_j][_l];
 440                     for(size_t _l1=0; _l1<con[j]; _l1++) if( _l1 != _i )
 441                         for( size_t _l2=_l1+1; _l2<con[j]; _l2++) if( _l2 != _i)
 442                             newM += Gamma(j,_i,_l1,_l2) * tJ[j][_l1] * tJ[j][_l2] * cors[j][_l1][_l2];
 443                 }
 444
 445                 double dev = newM - M[i][_j];
 446 //              dev *= 0.02;
 447                 if( fabs(dev) >= maxdev )
 448                     maxdev = fabs(dev);
 449
 450                 newM = M[i][_j] + dev;
 451                 if( fabs(newM) > 1.0 )
 452                     newM = sign(newM);
 453                 M[i][_j] = newM;
 454             }
 455         }
 456     } while((maxdev>props.tol)&&(run<maxruns));
 457
 458     if( maxdev > maxdiff )
 459         maxdiff = maxdev;
 460
 461     if(run==maxruns){
 462         if( props.verbose >= 1 )
 463             cout << "solve_mcav: Convergence not reached (maxdev=" << maxdev << ")..." << endl;
 464     }
 465 }
 466
 467
 468 void MR::solveM() {
 469     for(size_t i=0; i<N; i++) {
 470         if( props.updates == Properties::UpdateType::FULL ) {
 471             // find indices in nb[i]
 472             sub_nb _nbi(con[i]);
 473
 474             // calc numerator1 and denominator1
 475             double sum_even, sum_odd;
 476             sum_subs(i, _nbi, &sum_even, &sum_odd);
 477
 478             Mag[i] = (tanh(theta[i]) * sum_even + sum_odd) / (sum_even + tanh(theta[i]) * sum_odd);
 479
 480         } else if( props.updates == Properties::UpdateType::LINEAR ) {
 481             sub_nb empty(con[i]);
 482             empty.clear();
 483             Mag[i] = T(i,empty);
 484
 485             for(size_t _l1=0; _l1<con[i]; _l1++)
 486                 for( size_t _l2=_l1+1; _l2<con[i]; _l2++)
 487                     Mag[i] += Gamma(i,_l1,_l2) * tJ[i][_l1] * tJ[i][_l2] * cors[i][_l1][_l2];
 488         }
 489         if(fabs(Mag[i])>1.)
 490             Mag[i] = sign(Mag[i]);
 491     }
 492 }
 493
 494
 495 void MR::init_cor() {
 496     for( size_t i = 0; i < nrVars(); i++ ) {
 497         vector<Factor> pairq;
 498         if( props.inits == Properties::InitType::CLAMPING ) {
 499             BP bpcav(*this, PropertySet()("updates", string("SEQMAX"))("tol", string("1e-9"))("maxiter", string("1000UL"))("verbose", string("0UL"))("logdomain", string("0")));
 500             bpcav.makeCavity( i );
 501             pairq = calcPairBeliefs( bpcav, delta(i), false );
 502         } else if( props.inits == Properties::InitType::EXACT ) {
 503             JTree jtcav(*this, PropertySet()("updates", string("HUGIN"))("verbose", string("0UL")) );
 504             jtcav.makeCavity( i );
 505             pairq = calcPairBeliefs( jtcav, delta(i), false );
 506         }
 507         for( size_t jk = 0; jk < pairq.size(); jk++ ) {
 508             VarSet::const_iterator kit = pairq[jk].vars().begin();
 509             size_t j = findVar( *(kit) );
 510             size_t k = findVar( *(++kit) );
 511             pairq[jk].normalize(Prob::NORMPROB);
 512             double cor = (pairq[jk][3] - pairq[jk][2] - pairq[jk][1] + pairq[jk][0]) - (pairq[jk][3] + pairq[jk][2] - pairq[jk][1] - pairq[jk][0]) * (pairq[jk][3] - pairq[jk][2] + pairq[jk][1] - pairq[jk][0]);
 513             for( size_t _j = 0; _j < con[i]; _j++ ) if( nb[i][_j] == j )
 514                 for( size_t _k = 0; _k < con[i]; _k++ ) if( nb[i][_k] == k ) {
 515                     cors[i][_j][_k] = cor;
 516                     cors[i][_k][_j] = cor;
 517                 }
 518         }
 519     }
 520 }
 521
 522
 523 string MR::identify() const {
 524     stringstream result (stringstream::out);
 525     result << Name << getProperties();
 526     return result.str();
 527 }
 528
 529
 530 double MR::run() {
 531     if( supported ) {
 532         if( props.verbose >= 1 )
 533             cout << "Starting " << identify() << "...";
 534
 535         double tic = toc();
 536 //        Diffs diffs(nrVars(), 1.0);
 537
 538         M.resize(N);
 539         for(size_t i=0; i<N; i++)
 540           M[i].resize(kmax);
 541
 542         cors.resize(N);
 543         for(size_t i=0; i<N; i++)
 544           cors[i].resize(kmax);
 545         for(size_t i=0; i<N; i++)
 546           for(size_t j=0; j<kmax; j++)
 547             cors[i][j].resize(kmax);
 548
 549         kindex.resize(N);
 550         for(size_t i=0; i<N; i++)
 551           kindex[i].resize(kmax);
 552
 553         if( props.inits == Properties::InitType::RESPPROP ) {
 554             double md = init_cor_resp();
 555             if( md > maxdiff )
 556                 maxdiff = md;
 557         } else if( props.inits == Properties::InitType::EXACT )
 558             init_cor(); // FIXME no MaxDiff() calculation
 559         else if( props.inits == Properties::InitType::CLAMPING )
 560             init_cor(); // FIXME no MaxDiff() calculation
 561
 562         solvemcav();
 563
 564         Mag.resize(N);
 565         solveM();
 566
 567         if( props.verbose >= 1 )
 568             cout << "MR needed " << toc() - tic << " clocks." << endl;
 569
 570         return 0.0;
 571     } else
 572         return -1.0;
 573 }
 574
 575
 576 void MR::makekindex() {
 577     for(size_t i=0; i<N; i++)
 578         for(size_t j=0; j<con[i]; j++) {
 579             size_t ij = nb[i][j];       // ij is the j'th neighbour of spin i
 580             size_t k=0;
 581             while( nb[ij][k] != i )
 582                 k++;
 583             kindex[i][j] = k;   // the j'th neighbour of spin i has spin i as its k'th neighbour
 584         }
 585 }
 586
 587
 588 Factor MR::belief( const Var &n ) const {
 589     if( supported ) {
 590         size_t i = findVar( n );
 591
 592         Real x[2];
 593         x[0] = 0.5 - Mag[i] / 2.0;
 594         x[1] = 0.5 + Mag[i] / 2.0;
 595
 596         return Factor( n, x );
 597     } else
 598         return Factor();
 599 }
 600
 601
 602 vector<Factor> MR::beliefs() const {
 603     vector<Factor> result;
 604     for( size_t i = 0; i < nrVars(); i++ )
 605         result.push_back( belief( var(i) ) );
 606     return result;
 607 }
 608
 609
 610
 611 MR::MR( const FactorGraph &fg, const PropertySet &opts ) : DAIAlgFG(fg), supported(true), maxdiff(0.0) {
 612     setProperties( opts );
 613
 614     // check whether all vars in fg are binary
 615     // check whether connectivity is <= kmax
 616     for( size_t i = 0; i < fg.nrVars(); i++ )
 617         if( (fg.var(i).states() > 2) || (fg.delta(i).size() > kmax) ) {
 618             supported = false;
 619             break;
 620         }
 621
 622     if( !supported )
 623         return;
 624
 625     // check whether all interactions are pairwise or single
 626     for( size_t I = 0; I < fg.nrFactors(); I++ )
 627         if( fg.factor(I).vars().size() > 2 ) {
 628             supported = false;
 629             break;
 630         }
 631
 632     if( !supported )
 633         return;
 634
 635     // create w and th
 636     size_t Nin = fg.nrVars();
 637
 638     double *w = new double[Nin*Nin];
 639     double *th = new double[Nin];
 640
 641     for( size_t i = 0; i < Nin; i++ ) {
 642         th[i] = 0.0;
 643         for( size_t j = 0; j < Nin; j++ )
 644             w[i*Nin+j] = 0.0;
 645     }
 646
 647     for( size_t I = 0; I < fg.nrFactors(); I++ ) {
 648         const Factor &psi = fg.factor(I);
 649         if( psi.vars().size() == 1 ) {
 650             size_t i = fg.findVar( *(psi.vars().begin()) );
 651             th[i] += 0.5 * log(psi[1] / psi[0]);
 652         } else if( psi.vars().size() == 2 ) {
 653             size_t i = fg.findVar( *(psi.vars().begin()) );
 654             VarSet::const_iterator jit = psi.vars().begin();
 655             size_t j = fg.findVar( *(++jit) );
 656
 657             w[i*Nin+j] += 0.25 * log(psi[3] * psi[0] / (psi[2] * psi[1]));
 658             w[j*Nin+i] += 0.25 * log(psi[3] * psi[0] / (psi[2] * psi[1]));
 659
 660             th[i] += 0.25 * log(psi[3] / psi[2] * psi[1] / psi[0]);
 661             th[j] += 0.25 * log(psi[3] / psi[1] * psi[2] / psi[0]);
 662         }
 663     }
 664
 665     init(Nin, w, th);
 666
 667     delete th;
 668     delete w;
 669 }
 670
 671
 672 } // end of namespace dai