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