include/dai/factor.h

   1 /*  Copyright (C) 2006-2008  Joris Mooij  [joris dot mooij at tuebingen dot mpg dot de]
   2     Radboud University Nijmegen, The Netherlands /
   3     Max Planck Institute for Biological Cybernetics, Germany
   4
   5     Copyright (C) 2002  Martijn Leisink  [martijn@mbfys.kun.nl]
   6     Radboud University Nijmegen, The Netherlands
   7
   8     This file is part of libDAI.
   9
  10     libDAI is free software; you can redistribute it and/or modify
  11     it under the terms of the GNU General Public License as published by
  12     the Free Software Foundation; either version 2 of the License, or
  13     (at your option) any later version.
  14
  15     libDAI is distributed in the hope that it will be useful,
  16     but WITHOUT ANY WARRANTY; without even the implied warranty of
  17     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  18     GNU General Public License for more details.
  19
  20     You should have received a copy of the GNU General Public License
  21     along with libDAI; if not, write to the Free Software
  22     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  23 */
  24
  25
  26 #ifndef __defined_libdai_factor_h
  27 #define __defined_libdai_factor_h
  28
  29
  30 #include <iostream>
  31 #include <cmath>
  32 #include <dai/prob.h>
  33 #include <dai/varset.h>
  34 #include <dai/index.h>
  35
  36
  37 namespace dai {
  38
  39
  40 template<typename T> class      TFactor;
  41 typedef TFactor<Real>           Factor;
  42
  43
  44 // predefine friends
  45 template<typename T> Real           dist( const TFactor<T> & x, const TFactor<T> & y, Prob::DistType dt );
  46 template<typename T> Real           KL_dist( const TFactor<T> & p, const TFactor<T> & q );
  47 template<typename T> Real           MutualInfo( const TFactor<T> & p );
  48 template<typename T> TFactor<T>     max( const TFactor<T> & P, const TFactor<T> & Q );
  49 template<typename T> TFactor<T>     min( const TFactor<T> & P, const TFactor<T> & Q );
  50 template<typename T> std::ostream&  operator<< (std::ostream& os, const TFactor<T>& P);
  51
  52
  53 // T should be castable from and to double
  54 template <typename T> class TFactor {
  55     private:
  56         VarSet      _vs;
  57         TProb<T>    _p;
  58
  59     public:
  60         // Construct Factor with empty VarSet but nonempty _p
  61         TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
  62
  63         // Construct Factor from VarSet
  64         TFactor( const VarSet& ns ) : _vs(ns), _p(nrStates(_vs)) {}
  65
  66         // Construct Factor from VarSet and initial value
  67         TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(nrStates(_vs),p) {}
  68
  69         // Construct Factor from VarSet and initial array
  70         TFactor( const VarSet& ns, const Real* p ) : _vs(ns), _p(nrStates(_vs),p) {}
  71
  72         // Construct Factor from VarSet and TProb<T>
  73         TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
  74 #ifdef DAI_DEBUG
  75             assert( nrStates(_vs) == _p.size() );
  76 #endif
  77         }
  78
  79         // Construct Factor from Var
  80         TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
  81
  82         // Copy constructor
  83         TFactor( const TFactor<T> &x ) : _vs(x._vs), _p(x._p) {}
  84
  85         // Assignment operator
  86         TFactor<T> & operator= (const TFactor<T> &x) {
  87             if( this != &x ) {
  88                 _vs = x._vs;
  89                 _p  = x._p;
  90             }
  91             return *this;
  92         }
  93
  94         const TProb<T> & p() const { return _p; }
  95         TProb<T> & p() { return _p; }
  96         const VarSet & vars() const { return _vs; }
  97         size_t states() const { return _p.size(); }
  98
  99         T operator[] (size_t i) const { return _p[i]; }
 100         T& operator[] (size_t i) { return _p[i]; }
 101         TFactor<T> & fill (T p)
 102             { _p.fill( p ); return(*this); }
 103         TFactor<T> & randomize ()
 104             { _p.randomize(); return(*this); }
 105         TFactor<T> operator* (T x) const {
 106             Factor result = *this;
 107             result.p() *= x;
 108             return result;
 109         }
 110         TFactor<T>& operator*= (T x) {
 111             _p *= x;
 112             return *this;
 113         }
 114         TFactor<T> operator/ (T x) const {
 115             Factor result = *this;
 116             result.p() /= x;
 117             return result;
 118         }
 119         TFactor<T>& operator/= (T x) {
 120             _p /= x;
 121             return *this;
 122         }
 123         TFactor<T> operator* (const TFactor<T>& Q) const;
 124         TFactor<T> operator/ (const TFactor<T>& Q) const;
 125         TFactor<T>& operator*= (const TFactor<T>& Q) { return( *this = (*this * Q) ); }
 126         TFactor<T>& operator/= (const TFactor<T>& Q) { return( *this = (*this / Q) ); }
 127         TFactor<T> operator+ (const TFactor<T>& Q) const {
 128 #ifdef DAI_DEBUG
 129             assert( Q._vs == _vs );
 130 #endif
 131             TFactor<T> sum(*this);
 132             sum._p += Q._p;
 133             return sum;
 134         }
 135         TFactor<T> operator- (const TFactor<T>& Q) const {
 136 #ifdef DAI_DEBUG
 137             assert( Q._vs == _vs );
 138 #endif
 139             TFactor<T> sum(*this);
 140             sum._p -= Q._p;
 141             return sum;
 142         }
 143         TFactor<T>& operator+= (const TFactor<T>& Q) {
 144 #ifdef DAI_DEBUG
 145             assert( Q._vs == _vs );
 146 #endif
 147             _p += Q._p;
 148             return *this;
 149         }
 150         TFactor<T>& operator-= (const TFactor<T>& Q) {
 151 #ifdef DAI_DEBUG
 152             assert( Q._vs == _vs );
 153 #endif
 154             _p -= Q._p;
 155             return *this;
 156         }
 157         TFactor<T>& operator+= (T q) {
 158             _p += q;
 159             return *this;
 160         }
 161         TFactor<T>& operator-= (T q) {
 162             _p -= q;
 163             return *this;
 164         }
 165         TFactor<T> operator+ (T q) const {
 166             TFactor<T> result(*this);
 167             result._p += q;
 168             return result;
 169         }
 170         TFactor<T> operator- (T q) const {
 171             TFactor<T> result(*this);
 172             result._p -= q;
 173             return result;
 174         }
 175
 176         TFactor<T> operator^ (Real a) const { TFactor<T> x; x._vs = _vs; x._p = _p^a; return x; }
 177         TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
 178
 179         TFactor<T>& makeZero( Real epsilon ) {
 180             _p.makeZero( epsilon );
 181             return *this;
 182         }
 183
 184         TFactor<T>& makePositive( Real epsilon ) {
 185             _p.makePositive( epsilon );
 186             return *this;
 187         }
 188
 189         TFactor<T> inverse() const {
 190             TFactor<T> inv;
 191             inv._vs = _vs;
 192             inv._p = _p.inverse(true);  // FIXME
 193             return inv;
 194         }
 195
 196         TFactor<T> divided_by( const TFactor<T>& denom ) const {
 197 #ifdef DAI_DEBUG
 198             assert( denom._vs == _vs );
 199 #endif
 200             TFactor<T> quot(*this);
 201             quot._p /= denom._p;
 202             return quot;
 203         }
 204
 205         TFactor<T>& divide( const TFactor<T>& denom ) {
 206 #ifdef DAI_DEBUG
 207             assert( denom._vs == _vs );
 208 #endif
 209             _p /= denom._p;
 210             return *this;
 211         }
 212
 213         TFactor<T> exp() const {
 214             TFactor<T> e;
 215             e._vs = _vs;
 216             e._p = _p.exp();
 217             return e;
 218         }
 219
 220         TFactor<T> abs() const {
 221             TFactor<T> e;
 222             e._vs = _vs;
 223             e._p = _p.abs();
 224             return e;
 225         }
 226
 227         TFactor<T> log() const {
 228             TFactor<T> l;
 229             l._vs = _vs;
 230             l._p = _p.log();
 231             return l;
 232         }
 233
 234         TFactor<T> log0() const {
 235             TFactor<T> l0;
 236             l0._vs = _vs;
 237             l0._p = _p.log0();
 238             return l0;
 239         }
 240
 241         T normalize( typename Prob::NormType norm = Prob::NORMPROB ) { return _p.normalize( norm ); }
 242         TFactor<T> normalized( typename Prob::NormType norm = Prob::NORMPROB ) const {
 243             TFactor<T> result;
 244             result._vs = _vs;
 245             result._p = _p.normalized( norm );
 246             return result;
 247         }
 248
 249         // returns slice of this factor where the subset ns is in state ns_state
 250         Factor slice( const VarSet & ns, size_t ns_state ) const {
 251             assert( ns << _vs );
 252             VarSet nsrem = _vs / ns;
 253             Factor result( nsrem, 0.0 );
 254
 255             // OPTIMIZE ME
 256             IndexFor i_ns (ns, _vs);
 257             IndexFor i_nsrem (nsrem, _vs);
 258             for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
 259                 if( (size_t)i_ns == ns_state )
 260                     result._p[i_nsrem] = _p[i];
 261
 262             return result;
 263         }
 264
 265         // returns unnormalized marginal; ns should be a subset of vars()
 266         TFactor<T> partSum(const VarSet & ns) const;
 267         // returns (normalized by default) marginal; ns should be a subset of vars()
 268         TFactor<T> marginal(const VarSet & ns, bool normed = true) const { if(normed) return partSum(ns).normalized(); else return partSum(ns); }
 269         // sums out all variables except those in ns
 270         TFactor<T> notSum(const VarSet & ns) const { return partSum(vars() ^ ns); }
 271
 272         // embeds this factor in larger varset ns
 273         TFactor<T> embed(const VarSet & ns) const {
 274             VarSet vs = vars();
 275             assert( ns >> vs );
 276             if( vs == ns )
 277                 return *this;
 278             else
 279                 return (*this) * Factor(ns / vs, 1.0);
 280         }
 281
 282         bool hasNaNs() const { return _p.hasNaNs(); }
 283         bool hasNegatives() const { return _p.hasNegatives(); }
 284         T totalSum() const { return _p.totalSum(); }
 285         T maxAbs() const { return _p.maxAbs(); }
 286         T maxVal() const { return _p.maxVal(); }
 287         T minVal() const { return _p.minVal(); }
 288         Real entropy() const { return _p.entropy(); }
 289         T strength( const Var &i, const Var &j ) const;
 290
 291         friend Real dist( const TFactor<T> & x, const TFactor<T> & y, Prob::DistType dt ) {
 292             if( x._vs.empty() || y._vs.empty() )
 293                 return -1;
 294             else {
 295 #ifdef DAI_DEBUG
 296                 assert( x._vs == y._vs );
 297 #endif
 298                 return dist( x._p, y._p, dt );
 299             }
 300         }
 301         friend Real KL_dist <> (const TFactor<T> & p, const TFactor<T> & q);
 302         friend Real MutualInfo <> ( const TFactor<T> & P );
 303         template<class U> friend std::ostream& operator<< (std::ostream& os, const TFactor<U>& P);
 304 };
 305
 306
 307 template<typename T> TFactor<T> TFactor<T>::partSum(const VarSet & ns) const {
 308 #ifdef DAI_DEBUG
 309     assert( ns << _vs );
 310 #endif
 311
 312     TFactor<T> res( ns, 0.0 );
 313
 314     IndexFor i_res( ns, _vs );
 315     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 316         res._p[i_res] += _p[i];
 317
 318     return res;
 319 }
 320
 321
 322 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
 323     os << "(" << P.vars() << " <";
 324     for( size_t i = 0; i < P._p.size(); i++ )
 325         os << P._p[i] << " ";
 326     os << ">)";
 327     return os;
 328 }
 329
 330
 331 template<typename T> TFactor<T> TFactor<T>::operator* (const TFactor<T>& Q) const {
 332     TFactor<T> prod( _vs | Q._vs, 0.0 );
 333
 334     IndexFor i1(_vs, prod._vs);
 335     IndexFor i2(Q._vs, prod._vs);
 336
 337     for( size_t i = 0; i < prod._p.size(); i++, ++i1, ++i2 )
 338         prod._p[i] += _p[i1] * Q._p[i2];
 339
 340     return prod;
 341 }
 342
 343
 344 template<typename T> TFactor<T> TFactor<T>::operator/ (const TFactor<T>& Q) const {
 345     TFactor<T> quot( _vs + Q._vs, 0.0 );
 346
 347     IndexFor i1(_vs, quot._vs);
 348     IndexFor i2(Q._vs, quot._vs);
 349
 350     for( size_t i = 0; i < quot._p.size(); i++, ++i1, ++i2 )
 351         quot._p[i] += _p[i1] / Q._p[i2];
 352
 353     return quot;
 354 }
 355
 356
 357 template<typename T> Real KL_dist(const TFactor<T> & P, const TFactor<T> & Q) {
 358     if( P._vs.empty() || Q._vs.empty() )
 359         return -1;
 360     else {
 361 #ifdef DAI_DEBUG
 362         assert( P._vs == Q._vs );
 363 #endif
 364         return KL_dist( P._p, Q._p );
 365     }
 366 }
 367
 368
 369 // calculate mutual information of x_i and x_j where P.vars() = \{x_i,x_j\}
 370 template<typename T> Real MutualInfo(const TFactor<T> & P) {
 371     assert( P._vs.size() == 2 );
 372     VarSet::const_iterator it = P._vs.begin();
 373     Var i = *it; it++; Var j = *it;
 374     TFactor<T> projection = P.marginal(i) * P.marginal(j);
 375     return real( KL_dist( P.normalized(), projection ) );
 376 }
 377
 378
 379 template<typename T> TFactor<T> max( const TFactor<T> & P, const TFactor<T> & Q ) {
 380     assert( P._vs == Q._vs );
 381     return TFactor<T>( P._vs, min( P.p(), Q.p() ) );
 382 }
 383
 384 template<typename T> TFactor<T> min( const TFactor<T> & P, const TFactor<T> & Q ) {
 385     assert( P._vs == Q._vs );
 386     return TFactor<T>( P._vs, max( P.p(), Q.p() ) );
 387 }
 388
 389 // calculate N(psi, i, j)
 390 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
 391 #ifdef DAI_DEBUG
 392     assert( _vs.contains( i ) );
 393     assert( _vs.contains( j ) );
 394     assert( i != j );
 395 #endif
 396     VarSet ij(i, j);
 397
 398     T max = 0.0;
 399     for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
 400         for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
 401             if( alpha2 != alpha1 )
 402                 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
 403                     for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
 404                         if( beta2 != beta1 ) {
 405                             size_t as = 1, bs = 1;
 406                             if( i < j )
 407                                 bs = i.states();
 408                             else
 409                                 as = j.states();
 410                             T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).maxVal();
 411                             T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).maxVal();
 412                             T f = f1 * f2;
 413                             if( f > max )
 414                                 max = f;
 415                         }
 416
 417     return std::tanh( 0.25 * std::log( max ) );
 418 }
 419
 420
 421 template<typename T> TFactor<T> RemoveFirstOrderInteractions( const TFactor<T> & psi ) {
 422     TFactor<T> result = psi;
 423
 424     VarSet vars = psi.vars();
 425     for( size_t iter = 0; iter < 100; iter++ ) {
 426         for( VarSet::const_iterator n = vars.begin(); n != vars.end(); n++ )
 427             result = result * result.partSum(*n).inverse();
 428         result.normalize();
 429     }
 430
 431     return result;
 432 }
 433
 434
 435 } // end of namespace dai
 436
 437
 438 #endif