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 <functional>
  36 #include <cmath>
  37 #include <dai/prob.h>
  38 #include <dai/varset.h>
  39 #include <dai/index.h>
  40
  41
  42 namespace dai {
  43
  44
  45 // Function object similar to std::divides(), but different in that dividing by zero results in zero
  46 template<typename T> struct divides0 : public std::binary_function<T, T, T> {
  47     T operator()(const T& i, const T& j) const {
  48         if( j == (T)0 )
  49             return (T)0;
  50         else
  51             return i / j;
  52     }
  53 };
  54
  55
  56 /// Represents a (probability) factor.
  57 /** Mathematically, a \e factor is a function mapping joint states of some
  58  *  variables to the nonnegative real numbers.
  59  *  More formally, denoting a discrete variable with label \f$l\f$ by
  60  *  \f$x_l\f$ and its state space by \f$X_l = \{0,1,\dots,S_l-1\}\f$,
  61  *  then a factor depending on the variables \f$\{x_l\}_{l\in L}\f$ is
  62  *  a function \f$f_L : \prod_{l\in L} X_l \to [0,\infty)\f$.
  63  *
  64  *  In libDAI, a factor is represented by a TFactor<\a T> object, which has two
  65  *  components:
  66  *  \arg a VarSet, corresponding with the set of variables \f$\{x_l\}_{l\in L}\f$
  67  *  that the factor depends on;
  68  *  \arg a TProb<\a T>, a vector containing the value of the factor for each possible
  69  *  joint state of the variables.
  70  *
  71  *  The factor values are stored in the entries of the TProb<\a T> in a particular
  72  *  ordering, which is defined by the one-to-one correspondence of a joint state
  73  *  in \f$\prod_{l\in L} X_l\f$ with a linear index in
  74  *  \f$\{0,1,\dots,\prod_{l\in L} S_l-1\}\f$ according to the mapping \f$\sigma\f$
  75  *  induced by VarSet::calcState(const std::map<Var,size_t> &).
  76  *
  77  *  \tparam T Should be a scalar that is castable from and to double and should support elementary arithmetic operations.
  78  *  \todo Define a better fileformat for .fg files (maybe using XML)?
  79  *  \todo Add support for sparse factors.
  80  */
  81 template <typename T> class TFactor {
  82     private:
  83         VarSet      _vs;
  84         TProb<T>    _p;
  85
  86     public:
  87         /// Iterator over factor entries
  88                 typedef typename TProb<T>::iterator iterator;
  89
  90         /// Const iterator over factor entries
  91                 typedef typename TProb<T>::const_iterator const_iterator;
  92
  93         /// Constructs TFactor depending on no variables, with value p
  94         TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
  95
  96         /// Constructs TFactor depending on variables in ns, with uniform distribution
  97         TFactor( const VarSet& ns ) : _vs(ns), _p(_vs.nrStates()) {}
  98
  99         /// Constructs TFactor depending on variables in ns, with all values set to p
 100         TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(_vs.nrStates(),p) {}
 101
 102         /// Constructs TFactor depending on variables in ns, copying the values from the range starting at begin
 103         /** \param ns contains the variables that the new TFactor should depend on.
 104          *  \tparam Iterator Iterates over instances of type T; should support addition of size_t.
 105          *  \param begin Points to first element to be added.
 106          */
 107         template<typename TIterator>
 108         TFactor( const VarSet& ns, TIterator begin ) : _vs(ns), _p(begin, begin + _vs.nrStates(), _vs.nrStates()) {}
 109
 110         /// Constructs TFactor depending on variables in ns, with values set to the TProb p
 111         TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
 112 #ifdef DAI_DEBUG
 113             assert( _vs.nrStates() == _p.size() );
 114 #endif
 115         }
 116
 117         /// Constructs TFactor depending on the variable n, with uniform distribution
 118         TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
 119
 120         /// Returns const reference to value vector
 121         const TProb<T> & p() const { return _p; }
 122         /// Returns reference to value vector
 123         TProb<T> & p() { return _p; }
 124
 125         /// Returns const reference to variable set
 126         const VarSet & vars() const { return _vs; }
 127
 128         /// Returns the number of possible joint states of the variables
 129         /** \note This is equal to the length of the value vector.
 130          */
 131         size_t states() const { return _p.size(); }
 132
 133         /// Returns a copy of the i'th entry of the value vector
 134         T operator[] (size_t i) const { return _p[i]; }
 135
 136         /// Returns a reference to the i'th entry of the value vector
 137         T& operator[] (size_t i) { return _p[i]; }
 138
 139         /// Returns iterator pointing to first entry
 140         iterator begin() { return _p.begin(); }
 141         /// Returns const iterator pointing to first entry
 142                 const_iterator begin() const { return _p.begin(); }
 143                 /// Returns iterator pointing beyond last entry
 144                 iterator end() { return _p.end(); }
 145                 /// Returns const iterator pointing beyond last entry
 146                 const_iterator end() const { return _p.end(); }
 147
 148         /// Sets all values to p
 149         TFactor<T> & fill (T p) { _p.fill( p ); return(*this); }
 150
 151         /// Draws all values i.i.d. from a uniform distribution on [0,1)
 152         TFactor<T> & randomize () { _p.randomize(); return(*this); }
 153
 154
 155         /// Multiplies *this with scalar t
 156         TFactor<T>& operator*= (T t) {
 157             _p *= t;
 158             return *this;
 159         }
 160
 161         /// Divides *this by scalar t
 162         TFactor<T>& operator/= (T t) {
 163             _p /= t;
 164             return *this;
 165         }
 166
 167         /// Adds scalar t to *this
 168         TFactor<T>& operator+= (T t) {
 169             _p += t;
 170             return *this;
 171         }
 172
 173         /// Subtracts scalar t from *this
 174         TFactor<T>& operator-= (T t) {
 175             _p -= t;
 176             return *this;
 177         }
 178
 179         /// Raises *this to the power a
 180         TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
 181
 182
 183         /// Returns product of *this with scalar t
 184         TFactor<T> operator* (T t) const {
 185             TFactor<T> result = *this;
 186             result.p() *= t;
 187             return result;
 188         }
 189
 190         /// Returns quotient of *this with scalar t
 191         TFactor<T> operator/ (T t) const {
 192             TFactor<T> result = *this;
 193             result.p() /= t;
 194             return result;
 195         }
 196
 197         /// Returns sum of *this and scalar t
 198         TFactor<T> operator+ (T t) const {
 199             TFactor<T> result(*this);
 200             result._p += t;
 201             return result;
 202         }
 203
 204         /// Returns *this minus scalar t
 205         TFactor<T> operator- (T t) const {
 206             TFactor<T> result(*this);
 207             result._p -= t;
 208             return result;
 209         }
 210
 211         /// Returns *this raised to the power a
 212         TFactor<T> operator^ (Real a) const {
 213             TFactor<T> x;
 214             x._vs = _vs;
 215             x._p = _p^a;
 216             return x;
 217         }
 218
 219         /// Multiplies *this with the TFactor f
 220         TFactor<T>& operator*= (const TFactor<T>& f) {
 221             if( f._vs == _vs ) // optimize special case
 222                 _p *= f._p;
 223             else
 224                 *this = (*this * f);
 225             return *this;
 226         }
 227
 228         /// Divides *this by the TFactor f
 229         TFactor<T>& operator/= (const TFactor<T>& f) {
 230             if( f._vs == _vs ) // optimize special case
 231                 _p /= f._p;
 232             else
 233                 *this = (*this / f);
 234             return *this;
 235         }
 236
 237         /// Adds the TFactor f to *this
 238         TFactor<T>& operator+= (const TFactor<T>& f) {
 239             if( f._vs == _vs ) // optimize special case
 240                 _p += f._p;
 241             else
 242                 *this = (*this + f);
 243             return *this;
 244         }
 245
 246         /// Subtracts the TFactor f from *this
 247         TFactor<T>& operator-= (const TFactor<T>& f) {
 248             if( f._vs == _vs ) // optimize special case
 249                 _p -= f._p;
 250             else
 251                 *this = (*this - f);
 252             return *this;
 253         }
 254
 255         /// Returns product of *this with the TFactor f
 256         /** The product of two factors is defined as follows: if
 257          *  \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
 258          *  \f[fg : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) g(x_M).\f]
 259          */
 260         TFactor<T> operator* (const TFactor<T>& f) const {
 261             return pointwiseOp(*this,f,std::multiplies<T>());
 262         }
 263
 264         /// Returns quotient of *this by the TFactor f
 265         /** The quotient of two factors is defined as follows: if
 266          *  \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
 267          *  \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]
 268          */
 269         TFactor<T> operator/ (const TFactor<T>& f) const {
 270             return pointwiseOp(*this,f,divides0<T>());
 271         }
 272
 273         /// Returns sum of *this and the TFactor f
 274         /** The sum of two factors is defined as follows: if
 275          *  \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
 276          *  \f[f+g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) + g(x_M).\f]
 277          */
 278         TFactor<T> operator+ (const TFactor<T>& f) const {
 279             return pointwiseOp(*this,f,std::plus<T>());
 280         }
 281
 282         /// Returns *this minus the TFactor f
 283         /** The difference of two factors is defined as follows: if
 284          *  \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
 285          *  \f[f-g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) - g(x_M).\f]
 286          */
 287         TFactor<T> operator- (const TFactor<T>& f) const {
 288             return pointwiseOp(*this,f,std::minus<T>());
 289         }
 290
 291
 292         /// Sets all values that are smaller than epsilon to 0
 293         TFactor<T>& makeZero( T epsilon ) {
 294             _p.makeZero( epsilon );
 295             return *this;
 296         }
 297
 298         /// Sets all values that are smaller than epsilon to epsilon
 299         TFactor<T>& makePositive( T epsilon ) {
 300             _p.makePositive( epsilon );
 301             return *this;
 302         }
 303
 304         /// Returns pointwise inverse of *this.
 305         /** If zero == true, uses 1 / 0 == 0; otherwise 1 / 0 == Inf.
 306          */
 307         TFactor<T> inverse(bool zero=true) const {
 308             TFactor<T> inv;
 309             inv._vs = _vs;
 310             inv._p = _p.inverse(zero);
 311             return inv;
 312         }
 313
 314         /// Returns pointwise exp of *this
 315         TFactor<T> exp() const {
 316             TFactor<T> e;
 317             e._vs = _vs;
 318             e._p = _p.exp();
 319             return e;
 320         }
 321
 322         /// Returns pointwise logarithm of *this
 323         /** If zero==true, uses log(0)==0; otherwise, log(0)=-Inf.
 324          */
 325         TFactor<T> log(bool zero=false) const {
 326             TFactor<T> l;
 327             l._vs = _vs;
 328             l._p = _p.log(zero);
 329             return l;
 330         }
 331
 332         /// Returns pointwise absolute value of *this
 333         TFactor<T> abs() const {
 334             TFactor<T> e;
 335             e._vs = _vs;
 336             e._p = _p.abs();
 337             return e;
 338         }
 339
 340         /// Normalizes *this TFactor according to the specified norm
 341         T normalize( typename Prob::NormType norm=Prob::NORMPROB ) { return _p.normalize( norm ); }
 342
 343         /// Returns a normalized copy of *this, according to the specified norm
 344         TFactor<T> normalized( typename Prob::NormType norm=Prob::NORMPROB ) const {
 345             TFactor<T> result;
 346             result._vs = _vs;
 347             result._p = _p.normalized( norm );
 348             return result;
 349         }
 350
 351         /// Returns a slice of this TFactor, where the subset ns is in state nsState
 352         /** \pre \a ns sould be a subset of vars()
 353          *  \pre \a nsState < ns.states()
 354          *
 355          *  The result is a TFactor that depends on the variables in this->vars() except those in \a ns,
 356          *  obtained by setting the variables in \a ns to the joint state specified by the linear index
 357          *  \a nsState. Formally, if *this corresponds with the factor \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$,
 358          *  \f$M \subset L\f$ corresponds with \a ns and \a nsState corresponds with a mapping \f$s\f$ that
 359          *  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
 360          *  returned corresponds with the factor \f$g : \prod_{l \in L \setminus M} X_l \to [0,\infty)\f$
 361          *  defined by \f$g(\{x_l\}_{l\in L \setminus M}) = f(\{x_l\}_{l\in L \setminus M}, \{s(x_m)\}_{m\in M})\f$.
 362          */
 363         TFactor<T> slice( const VarSet& ns, size_t nsState ) const {
 364             assert( ns << _vs );
 365             VarSet nsrem = _vs / ns;
 366             TFactor<T> result( nsrem, T(0) );
 367
 368             // OPTIMIZE ME
 369             IndexFor i_ns (ns, _vs);
 370             IndexFor i_nsrem (nsrem, _vs);
 371             for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
 372                 if( (size_t)i_ns == nsState )
 373                     result._p[i_nsrem] = _p[i];
 374
 375             return result;
 376         }
 377
 378         /// Returns marginal on ns, obtained by summing out all variables except those in ns, and normalizing the result if normed==true
 379         TFactor<T> marginal(const VarSet & ns, bool normed=true) const;
 380
 381         /// Returns max-marginal on ns, obtained by maximizing all variables except those in ns, and normalizing the result if normed==true
 382         TFactor<T> maxMarginal(const VarSet & ns, bool normed=true) const;
 383
 384         /// Embeds this factor in a larger VarSet
 385         /** \pre vars() should be a subset of ns
 386          *
 387          *  If *this corresponds with \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$L \subset M\f$, then
 388          *  the embedded factor corresponds with \f$g : \prod_{m\in M} X_m \to [0,\infty) : x \mapsto f(x_L)\f$.
 389          */
 390         TFactor<T> embed(const VarSet & ns) const {
 391             assert( ns >> _vs );
 392             if( _vs == ns )
 393                 return *this;
 394             else
 395                 return (*this) * TFactor<T>(ns / _vs, (T)1);
 396         }
 397
 398         /// Returns true if *this has NaN values
 399         bool hasNaNs() const { return _p.hasNaNs(); }
 400
 401         /// Returns true if *this has negative values
 402         bool hasNegatives() const { return _p.hasNegatives(); }
 403
 404         /// Returns total sum of values
 405         T sum() const { return _p.sum(); }
 406
 407         /// Returns maximum absolute value
 408         T maxAbs() const { return _p.maxAbs(); }
 409
 410         /// Returns maximum value
 411         T max() const { return _p.max(); }
 412
 413         /// Returns minimum value
 414         T min() const { return _p.min(); }
 415
 416         /// Returns entropy of *this TFactor
 417         Real entropy() const { return _p.entropy(); }
 418
 419         /// Returns strength of *this TFactor (between variables i and j), as defined in eq. (52) of [\ref MoK07b]
 420         T strength( const Var &i, const Var &j ) const;
 421 };
 422
 423
 424 template<typename T> TFactor<T> TFactor<T>::marginal(const VarSet & ns, bool normed) const {
 425     VarSet res_ns = ns & _vs;
 426
 427     TFactor<T> res( res_ns, 0.0 );
 428
 429     IndexFor i_res( res_ns, _vs );
 430     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 431         res._p[i_res] += _p[i];
 432
 433     if( normed )
 434         res.normalize( Prob::NORMPROB );
 435
 436     return res;
 437 }
 438
 439
 440 template<typename T> TFactor<T> TFactor<T>::maxMarginal(const VarSet & ns, bool normed) const {
 441     VarSet res_ns = ns & _vs;
 442
 443     TFactor<T> res( res_ns, 0.0 );
 444
 445     IndexFor i_res( res_ns, _vs );
 446     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 447         if( _p[i] > res._p[i_res] )
 448             res._p[i_res] = _p[i];
 449
 450     if( normed )
 451         res.normalize( Prob::NORMPROB );
 452
 453     return res;
 454 }
 455
 456
 457 template<typename T, typename binaryOp> TFactor<T> pointwiseOp( const TFactor<T> &f, const TFactor<T> &g, binaryOp op ) {
 458     if( f.vars() == g.vars() ) { // optimizate special case
 459         TFactor<T> result(f);
 460         for( size_t i = 0; i < result.states(); i++ )
 461             result[i] = op( result[i], g[i] );
 462         return result;
 463     } else {
 464         TFactor<T> result( f.vars() | g.vars(), 0.0 );
 465
 466         IndexFor i1(f.vars(), result.vars());
 467         IndexFor i2(g.vars(), result.vars());
 468
 469         for( size_t i = 0; i < result.states(); i++, ++i1, ++i2 )
 470             result[i] = op( f[i1], g[i2] );
 471
 472         return result;
 473     }
 474 }
 475
 476
 477 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
 478 #ifdef DAI_DEBUG
 479     assert( _vs.contains( i ) );
 480     assert( _vs.contains( j ) );
 481     assert( i != j );
 482 #endif
 483     VarSet ij(i, j);
 484
 485     T max = 0.0;
 486     for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
 487         for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
 488             if( alpha2 != alpha1 )
 489                 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
 490                     for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
 491                         if( beta2 != beta1 ) {
 492                             size_t as = 1, bs = 1;
 493                             if( i < j )
 494                                 bs = i.states();
 495                             else
 496                                 as = j.states();
 497                             T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).max();
 498                             T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).max();
 499                             T f = f1 * f2;
 500                             if( f > max )
 501                                 max = f;
 502                         }
 503
 504     return std::tanh( 0.25 * std::log( max ) );
 505 }
 506
 507
 508 /// Writes a TFactor to an output stream
 509 /** \relates TFactor
 510  */
 511 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
 512     os << "(" << P.vars() << ", (";
 513     for( size_t i = 0; i < P.states(); i++ )
 514         os << (i == 0 ? "" : ", ") << P[i];
 515     os << "))";
 516     return os;
 517 }
 518
 519
 520 /// Returns distance between two TFactors f and g, according to the distance measure dt
 521 /** \relates TFactor
 522  *  \pre f.vars() == g.vars()
 523  */
 524 template<typename T> Real dist( const TFactor<T> &f, const TFactor<T> &g, Prob::DistType dt ) {
 525     if( f.vars().empty() || g.vars().empty() )
 526         return -1;
 527     else {
 528 #ifdef DAI_DEBUG
 529         assert( f.vars() == g.vars() );
 530 #endif
 531         return dist( f.p(), g.p(), dt );
 532     }
 533 }
 534
 535
 536 /// Returns the pointwise maximum of two TFactors
 537 /** \relates TFactor
 538  *  \pre f.vars() == g.vars()
 539  */
 540 template<typename T> TFactor<T> max( const TFactor<T> &f, const TFactor<T> &g ) {
 541     assert( f._vs == g._vs );
 542     return TFactor<T>( f._vs, min( f.p(), g.p() ) );
 543 }
 544
 545
 546 /// Returns the pointwise minimum of two TFactors
 547 /** \relates TFactor
 548  *  \pre f.vars() == g.vars()
 549  */
 550 template<typename T> TFactor<T> min( const TFactor<T> &f, const TFactor<T> &g ) {
 551     assert( f._vs == g._vs );
 552     return TFactor<T>( f._vs, max( f.p(), g.p() ) );
 553 }
 554
 555
 556 /// Calculates the mutual information between the two variables that f depends on, under the distribution given by f
 557 /** \relates TFactor
 558  *  \pre f.vars().size() == 2
 559  */
 560 template<typename T> Real MutualInfo(const TFactor<T> &f) {
 561     assert( f.vars().size() == 2 );
 562     VarSet::const_iterator it = f.vars().begin();
 563     Var i = *it; it++; Var j = *it;
 564     TFactor<T> projection = f.marginal(i) * f.marginal(j);
 565     return real( dist( f.normalized(), projection, Prob::DISTKL ) );
 566 }
 567
 568
 569 /// Represents a factor with values of type Real.
 570 typedef TFactor<Real> Factor;
 571
 572
 573 } // end of namespace dai
 574
 575
 576 #endif