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 /// \file
  27 /// \brief Defines TFactor<T> and Factor classes
  28
  29
  30 #ifndef __defined_libdai_factor_h
  31 #define __defined_libdai_factor_h
  32
  33
  34 #include <iostream>
  35 #include <cmath>
  36 #include <dai/prob.h>
  37 #include <dai/varset.h>
  38 #include <dai/index.h>
  39
  40
  41 namespace dai {
  42
  43
  44 /// Represents a (probability) factor.
  45 /** Mathematically, a \e factor is a function mapping joint states of some
  46  *  variables to the nonnegative real numbers.
  47  *  More formally, denoting a discrete variable with label \f$l\f$ by
  48  *  \f$x_l\f$ and its state space by \f$X_l = \{0,1,\dots,S_l-1\}\f$,
  49  *  then a factor depending on the variables \f$\{x_l\}_{l\in L}\f$ is
  50  *  a function \f$f_L : \prod_{l\in L} X_l \to [0,\infty)\f$.
  51  *
  52  *  In libDAI, a factor is represented by a TFactor<\a T> object, which has two
  53  *  components:
  54  *  \arg a VarSet, corresponding with the set of variables \f$\{x_l\}_{l\in L}\f$
  55  *  that the factor depends on;
  56  *  \arg a TProb<\a T>, a vector containing the value of the factor for each possible
  57  *  joint state of the variables.
  58  *
  59  *  The factor values are stored in the entries of the TProb<\a T> in a particular
  60  *  ordering, which is defined by the one-to-one correspondence of a joint state
  61  *  in \f$\prod_{l\in L} X_l\f$ with a linear index in
  62  *  \f$\{0,1,\dots,\prod_{l\in L} S_l-1\}\f$ according to the mapping \f$\sigma\f$
  63  *  induced by VarSet::calcState(const std::map<Var,size_t> &).
  64  *
  65  *  \tparam T Should be a scalar that is castable from and to double and should support elementary arithmetic operations.
  66  *  \todo Define a better fileformat for .fg files (maybe using XML)?
  67  *  \todo Add support for sparse factors.
  68  */
  69 template <typename T> class TFactor {
  70     private:
  71         VarSet      _vs;
  72         TProb<T>    _p;
  73
  74     public:
  75         /// Iterator over factor entries
  76                 typedef typename TProb<T>::iterator iterator;
  77
  78         /// Const iterator over factor entries
  79                 typedef typename TProb<T>::const_iterator const_iterator;
  80
  81         /// Constructs TFactor depending on no variables, with value p
  82         TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
  83
  84         /// Constructs TFactor depending on variables in ns, with uniform distribution
  85         TFactor( const VarSet& ns ) : _vs(ns), _p(_vs.nrStates()) {}
  86
  87         /// Constructs TFactor depending on variables in ns, with all values set to p
  88         TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(_vs.nrStates(),p) {}
  89
  90         /// Constructs TFactor depending on variables in ns, copying the values from the range starting at begin
  91         /** \param ns contains the variables that the new TFactor should depend on.
  92          *  \tparam Iterator Iterates over instances of type T; should support addition of size_t.
  93          *  \param begin Points to first element to be added.
  94          */
  95         template<typename TIterator>
  96         TFactor( const VarSet& ns, TIterator begin ) : _vs(ns), _p(begin, begin + _vs.nrStates(), _vs.nrStates()) {}
  97
  98         /// Constructs TFactor depending on variables in ns, with values set to the TProb p
  99         TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
 100 #ifdef DAI_DEBUG
 101             assert( _vs.nrStates() == _p.size() );
 102 #endif
 103         }
 104
 105         /// Constructs TFactor depending on the variable n, with uniform distribution
 106         TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
 107
 108         /// Returns const reference to value vector
 109         const TProb<T> & p() const { return _p; }
 110         /// Returns reference to value vector
 111         TProb<T> & p() { return _p; }
 112
 113         /// Returns const reference to variable set
 114         const VarSet & vars() const { return _vs; }
 115
 116         /// Returns the number of possible joint states of the variables
 117         /** \note This is equal to the length of the value vector.
 118          */
 119         size_t states() const { return _p.size(); }
 120
 121         /// Returns a copy of the i'th entry of the value vector
 122         T operator[] (size_t i) const { return _p[i]; }
 123
 124         /// Returns a reference to the i'th entry of the value vector
 125         T& operator[] (size_t i) { return _p[i]; }
 126
 127         /// Returns iterator pointing to first entry
 128         iterator begin() { return _p.begin(); }
 129         /// Returns const iterator pointing to first entry
 130                 const_iterator begin() const { return _p.begin(); }
 131                 /// Returns iterator pointing beyond last entry
 132                 iterator end() { return _p.end(); }
 133                 /// Returns const iterator pointing beyond last entry
 134                 const_iterator end() const { return _p.end(); }
 135
 136         /// Sets all values to p
 137         TFactor<T> & fill (T p) { _p.fill( p ); return(*this); }
 138
 139         /// Draws all values i.i.d. from a uniform distribution on [0,1)
 140         TFactor<T> & randomize () { _p.randomize(); return(*this); }
 141
 142
 143         /// Multiplies *this with scalar t
 144         TFactor<T>& operator*= (T t) {
 145             _p *= t;
 146             return *this;
 147         }
 148
 149         /// Divides *this by scalar t
 150         TFactor<T>& operator/= (T t) {
 151             _p /= t;
 152             return *this;
 153         }
 154
 155         /// Adds scalar t to *this
 156         TFactor<T>& operator+= (T t) {
 157             _p += t;
 158             return *this;
 159         }
 160
 161         /// Subtracts scalar t from *this
 162         TFactor<T>& operator-= (T t) {
 163             _p -= t;
 164             return *this;
 165         }
 166
 167         /// Raises *this to the power a
 168         TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
 169
 170
 171         /// Returns product of *this with scalar t
 172         TFactor<T> operator* (T t) const {
 173             TFactor<T> result = *this;
 174             result.p() *= t;
 175             return result;
 176         }
 177
 178         /// Returns quotient of *this with scalar t
 179         TFactor<T> operator/ (T t) const {
 180             TFactor<T> result = *this;
 181             result.p() /= t;
 182             return result;
 183         }
 184
 185         /// Returns sum of *this and scalar t
 186         TFactor<T> operator+ (T t) const {
 187             TFactor<T> result(*this);
 188             result._p += t;
 189             return result;
 190         }
 191
 192         /// Returns *this minus scalar t
 193         TFactor<T> operator- (T t) const {
 194             TFactor<T> result(*this);
 195             result._p -= t;
 196             return result;
 197         }
 198
 199         /// Returns *this raised to the power a
 200         TFactor<T> operator^ (Real a) const {
 201             TFactor<T> x;
 202             x._vs = _vs;
 203             x._p = _p^a;
 204             return x;
 205         }
 206
 207         /// Multiplies *this with the TFactor f
 208         TFactor<T>& operator*= (const TFactor<T>& f) {
 209             if( f._vs == _vs ) // optimize special case
 210                 _p *= f._p;
 211             else
 212                 *this = (*this * f);
 213             return *this;
 214         }
 215
 216         /// Divides *this by the TFactor f
 217         TFactor<T>& operator/= (const TFactor<T>& f) {
 218             if( f._vs == _vs ) // optimize special case
 219                 _p /= f._p;
 220             else
 221                 *this = (*this / f);
 222             return *this;
 223         }
 224
 225         /// Returns product of *this with the TFactor f
 226         /** The product of two factors is defined as follows: if
 227          *  \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$g : \prod_{m\in M} X_m \to [0,\infty)\f$, then
 228          *  \f[fg : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) g(x_M).\f]
 229          */
 230         TFactor<T> operator* (const TFactor<T>& f) const;
 231
 232         /// Returns quotient of *this by the TFactor f
 233         /** The quotient of two factors is defined as follows: if
 234          *  \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$g : \prod_{m\in M} X_m \to [0,\infty)\f$, then
 235          *  \f[\frac{f}{g} : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto \frac{f(x_L)}{g(x_M)}.\f]
 236          */
 237         TFactor<T> operator/ (const TFactor<T>& f) const;
 238
 239         /// Adds the TFactor f to *this
 240         /** \pre this->vars() == f.vars()
 241          */
 242         TFactor<T>& operator+= (const TFactor<T>& f) {
 243 #ifdef DAI_DEBUG
 244             assert( f._vs == _vs );
 245 #endif
 246             _p += f._p;
 247             return *this;
 248         }
 249
 250         /// Subtracts the TFactor f from *this
 251         /** \pre this->vars() == f.vars()
 252          */
 253         TFactor<T>& operator-= (const TFactor<T>& f) {
 254 #ifdef DAI_DEBUG
 255             assert( f._vs == _vs );
 256 #endif
 257             _p -= f._p;
 258             return *this;
 259         }
 260
 261         /// Returns sum of *this and the TFactor f
 262         /** \pre this->vars() == f.vars()
 263          */
 264         TFactor<T> operator+ (const TFactor<T>& f) const {
 265 #ifdef DAI_DEBUG
 266             assert( f._vs == _vs );
 267 #endif
 268             TFactor<T> sum(*this);
 269             sum._p += f._p;
 270             return sum;
 271         }
 272
 273         /// Returns *this minus the TFactor f
 274         /** \pre this->vars() == f.vars()
 275          */
 276         TFactor<T> operator- (const TFactor<T>& f) const {
 277 #ifdef DAI_DEBUG
 278             assert( f._vs == _vs );
 279 #endif
 280             TFactor<T> sum(*this);
 281             sum._p -= f._p;
 282             return sum;
 283         }
 284
 285
 286         /// Sets all values that are smaller than epsilon to 0
 287         TFactor<T>& makeZero( T epsilon ) {
 288             _p.makeZero( epsilon );
 289             return *this;
 290         }
 291
 292         /// Sets all values that are smaller than epsilon to epsilon
 293         TFactor<T>& makePositive( T epsilon ) {
 294             _p.makePositive( epsilon );
 295             return *this;
 296         }
 297
 298         /// Returns pointwise inverse of *this.
 299         /** If zero == true, uses 1 / 0 == 0; otherwise 1 / 0 == Inf.
 300          */
 301         TFactor<T> inverse(bool zero=true) const {
 302             TFactor<T> inv;
 303             inv._vs = _vs;
 304             inv._p = _p.inverse(zero);
 305             return inv;
 306         }
 307
 308         /// Returns pointwise exp of *this
 309         TFactor<T> exp() const {
 310             TFactor<T> e;
 311             e._vs = _vs;
 312             e._p = _p.exp();
 313             return e;
 314         }
 315
 316         /// Returns pointwise logarithm of *this
 317         /** If zero==true, uses log(0)==0; otherwise, log(0)=-Inf.
 318          */
 319         TFactor<T> log(bool zero=false) const {
 320             TFactor<T> l;
 321             l._vs = _vs;
 322             l._p = _p.log(zero);
 323             return l;
 324         }
 325
 326         /// Returns pointwise absolute value of *this
 327         TFactor<T> abs() const {
 328             TFactor<T> e;
 329             e._vs = _vs;
 330             e._p = _p.abs();
 331             return e;
 332         }
 333
 334         /// Normalizes *this TFactor according to the specified norm
 335         T normalize( typename Prob::NormType norm=Prob::NORMPROB ) { return _p.normalize( norm ); }
 336
 337         /// Returns a normalized copy of *this, according to the specified norm
 338         TFactor<T> normalized( typename Prob::NormType norm=Prob::NORMPROB ) const {
 339             TFactor<T> result;
 340             result._vs = _vs;
 341             result._p = _p.normalized( norm );
 342             return result;
 343         }
 344
 345         /// Returns a slice of this TFactor, where the subset ns is in state nsState
 346         /** \pre \a ns sould be a subset of vars()
 347          *  \pre \a nsState < ns.states()
 348          *
 349          *  The result is a TFactor that depends on the variables in this->vars() except those in \a ns,
 350          *  obtained by setting the variables in \a ns to the joint state specified by the linear index
 351          *  \a nsState. Formally, if *this corresponds with the factor \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$,
 352          *  \f$M \subset L\f$ corresponds with \a ns and \a nsState corresponds with a mapping \f$s\f$ that
 353          *  maps a variable \f$x_m\f$ with \f$m\in M\f$ to its state \f$s(x_m) \in X_m\f$, then the slice
 354          *  returned corresponds with the factor \f$g : \prod_{l \in L \setminus M} X_l \to [0,\infty)\f$
 355          *  defined by \f$g(\{x_l\}_{l\in L \setminus M}) = f(\{x_l\}_{l\in L \setminus M}, \{s(x_m)\}_{m\in M})\f$.
 356          */
 357         TFactor<T> slice( const VarSet& ns, size_t nsState ) const {
 358             assert( ns << _vs );
 359             VarSet nsrem = _vs / ns;
 360             TFactor<T> result( nsrem, T(0) );
 361
 362             // OPTIMIZE ME
 363             IndexFor i_ns (ns, _vs);
 364             IndexFor i_nsrem (nsrem, _vs);
 365             for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
 366                 if( (size_t)i_ns == nsState )
 367                     result._p[i_nsrem] = _p[i];
 368
 369             return result;
 370         }
 371
 372         /// Returns marginal on ns, obtained by summing out all variables except those in ns, and normalizing the result if normed==true
 373         TFactor<T> marginal(const VarSet & ns, bool normed=true) const;
 374
 375         /// Embeds this factor in a larger VarSet
 376         /** \pre vars() should be a subset of ns
 377          *
 378          *  If *this corresponds with \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$L \subset M\f$, then
 379          *  the embedded factor corresponds with \f$g : \prod_{m\in M} X_m \to [0,\infty) : x \mapsto f(x_L)\f$.
 380          */
 381         TFactor<T> embed(const VarSet & ns) const {
 382             assert( ns >> _vs );
 383             if( _vs == ns )
 384                 return *this;
 385             else
 386                 return (*this) * TFactor<T>(ns / _vs, 1);
 387         }
 388
 389         /// Returns true if *this has NaN values
 390         bool hasNaNs() const { return _p.hasNaNs(); }
 391
 392         /// Returns true if *this has negative values
 393         bool hasNegatives() const { return _p.hasNegatives(); }
 394
 395         /// Returns total sum of values
 396         T totalSum() const { return _p.totalSum(); }
 397
 398         /// Returns maximum absolute value
 399         T maxAbs() const { return _p.maxAbs(); }
 400
 401         /// Returns maximum value
 402         T maxVal() const { return _p.maxVal(); }
 403
 404         /// Returns minimum value
 405         T minVal() const { return _p.minVal(); }
 406
 407         /// Returns entropy of *this TFactor
 408         Real entropy() const { return _p.entropy(); }
 409
 410         /// Returns strength of *this TFactor (between variables i and j), as defined in eq. (52) of [\ref MoK07b]
 411         T strength( const Var &i, const Var &j ) const;
 412 };
 413
 414
 415 template<typename T> TFactor<T> TFactor<T>::marginal(const VarSet & ns, bool normed) const {
 416     VarSet res_ns = ns & _vs;
 417
 418     TFactor<T> res( res_ns, 0.0 );
 419
 420     IndexFor i_res( res_ns, _vs );
 421     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 422         res._p[i_res] += _p[i];
 423
 424     if( normed )
 425         res.normalize( Prob::NORMPROB );
 426
 427     return res;
 428 }
 429
 430
 431 template<typename T> TFactor<T> TFactor<T>::operator* (const TFactor<T>& f) const {
 432     if( f._vs == _vs ) { // optimizate special case
 433         TFactor<T> prod(*this);
 434         prod._p *= f._p;
 435         return prod;
 436     } else {
 437         TFactor<T> prod( _vs | f._vs, 0.0 );
 438
 439         IndexFor i1(_vs, prod._vs);
 440         IndexFor i2(f._vs, prod._vs);
 441
 442         for( size_t i = 0; i < prod._p.size(); i++, ++i1, ++i2 )
 443             prod._p[i] += _p[i1] * f._p[i2];
 444
 445         return prod;
 446     }
 447 }
 448
 449
 450 template<typename T> TFactor<T> TFactor<T>::operator/ (const TFactor<T>& f) const {
 451     if( f._vs == _vs ) { // optimizate special case
 452         TFactor<T> quot(*this);
 453         quot._p /= f._p;
 454         return quot;
 455     } else {
 456         TFactor<T> quot( _vs | f._vs, 0.0 );
 457
 458         IndexFor i1(_vs, quot._vs);
 459         IndexFor i2(f._vs, quot._vs);
 460
 461         for( size_t i = 0; i < quot._p.size(); i++, ++i1, ++i2 )
 462             quot._p[i] += _p[i1] / f._p[i2];
 463
 464         return quot;
 465     }
 466 }
 467
 468
 469 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
 470 #ifdef DAI_DEBUG
 471     assert( _vs.contains( i ) );
 472     assert( _vs.contains( j ) );
 473     assert( i != j );
 474 #endif
 475     VarSet ij(i, j);
 476
 477     T max = 0.0;
 478     for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
 479         for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
 480             if( alpha2 != alpha1 )
 481                 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
 482                     for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
 483                         if( beta2 != beta1 ) {
 484                             size_t as = 1, bs = 1;
 485                             if( i < j )
 486                                 bs = i.states();
 487                             else
 488                                 as = j.states();
 489                             T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).maxVal();
 490                             T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).maxVal();
 491                             T f = f1 * f2;
 492                             if( f > max )
 493                                 max = f;
 494                         }
 495
 496     return std::tanh( 0.25 * std::log( max ) );
 497 }
 498
 499
 500 /// Writes a TFactor to an output stream
 501 /** \relates TFactor
 502  */
 503 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
 504     os << "(" << P.vars() << ", (";
 505     for( size_t i = 0; i < P.states(); i++ )
 506         os << (i == 0 ? "" : ", ") << P[i];
 507     os << "))";
 508     return os;
 509 }
 510
 511
 512 /// Returns distance between two TFactors f and g, according to the distance measure dt
 513 /** \relates TFactor
 514  *  \pre f.vars() == g.vars()
 515  */
 516 template<typename T> Real dist( const TFactor<T> &f, const TFactor<T> &g, Prob::DistType dt ) {
 517     if( f.vars().empty() || g.vars().empty() )
 518         return -1;
 519     else {
 520 #ifdef DAI_DEBUG
 521         assert( f.vars() == g.vars() );
 522 #endif
 523         return dist( f.p(), g.p(), dt );
 524     }
 525 }
 526
 527
 528 /// Returns the pointwise maximum of two TFactors
 529 /** \relates TFactor
 530  *  \pre f.vars() == g.vars()
 531  */
 532 template<typename T> TFactor<T> max( const TFactor<T> &f, const TFactor<T> &g ) {
 533     assert( f._vs == g._vs );
 534     return TFactor<T>( f._vs, min( f.p(), g.p() ) );
 535 }
 536
 537
 538 /// Returns the pointwise minimum of two TFactors
 539 /** \relates TFactor
 540  *  \pre f.vars() == g.vars()
 541  */
 542 template<typename T> TFactor<T> min( const TFactor<T> &f, const TFactor<T> &g ) {
 543     assert( f._vs == g._vs );
 544     return TFactor<T>( f._vs, max( f.p(), g.p() ) );
 545 }
 546
 547
 548 /// Calculates the mutual information between the two variables that f depends on, under the distribution given by f
 549 /** \relates TFactor
 550  *  \pre f.vars().size() == 2
 551  */
 552 template<typename T> Real MutualInfo(const TFactor<T> &f) {
 553     assert( f.vars().size() == 2 );
 554     VarSet::const_iterator it = f.vars().begin();
 555     Var i = *it; it++; Var j = *it;
 556     TFactor<T> projection = f.marginal(i) * f.marginal(j);
 557     return real( dist( f.normalized(), projection, Prob::DISTKL ) );
 558 }
 559
 560
 561 /// Represents a factor with values of type Real.
 562 typedef TFactor<Real> Factor;
 563
 564
 565 } // end of namespace dai
 566
 567
 568 #endif