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