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 // predefine TFactor<T> class
  45 template<typename T> class      TFactor;
  46
  47
  48 /// Represents a factor with probability entries represented as Real
  49 typedef TFactor<Real>           Factor;
  50
  51
  52 /// Represents a probability factor.
  53 /** A \e factor is a function of the Cartesian product of the state
  54  *  spaces of some set of variables to the nonnegative real numbers.
  55  *  More formally, if \f$x_i \in X_i\f$ for all \f$i\f$, then a factor
  56  *  depending on the variables \f$\{x_i\}\f$ is a function defined
  57  *  on \f$\prod_i X_i\f$ with values in \f$[0,\infty)\f$.
  58  *
  59  *  A Factor has two components: a VarSet, defining the set of variables
  60  *  that the factor depends on, and a TProb<T>, containing the values of
  61  *  the factor for all possible joint states of the variables.
  62  *
  63  *  \tparam T Should be castable from and to double.
  64  */
  65 template <typename T> class TFactor {
  66     private:
  67         VarSet      _vs;
  68         TProb<T>    _p;
  69
  70     public:
  71         /// Construct Factor with empty VarSet
  72         TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
  73
  74         /// Construct Factor from VarSet
  75         TFactor( const VarSet& ns ) : _vs(ns), _p(_vs.nrStates()) {}
  76
  77         /// Construct Factor from VarSet and initial value
  78         TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(_vs.nrStates(),p) {}
  79
  80         /// Construct Factor from VarSet and initial array
  81         TFactor( const VarSet& ns, const Real *p ) : _vs(ns), _p(_vs.nrStates(),p) {}
  82
  83         /// Construct Factor from VarSet and TProb<T>
  84         TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
  85 #ifdef DAI_DEBUG
  86             assert( _vs.nrStates() == _p.size() );
  87 #endif
  88         }
  89
  90         /// Construct Factor from Var
  91         TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
  92
  93         /// Copy constructor
  94         TFactor( const TFactor<T> &x ) : _vs(x._vs), _p(x._p) {}
  95
  96         /// Assignment operator
  97         TFactor<T> & operator= (const TFactor<T> &x) {
  98             if( this != &x ) {
  99                 _vs = x._vs;
 100                 _p  = x._p;
 101             }
 102             return *this;
 103         }
 104
 105         /// Returns const reference to probability entries
 106         const TProb<T> & p() const { return _p; }
 107         /// Returns reference to probability entries
 108         TProb<T> & p() { return _p; }
 109
 110         /// Returns const reference to variables
 111         const VarSet & vars() const { return _vs; }
 112
 113         /// Returns the number of possible joint states of the variables
 114         size_t states() const { return _p.size(); }
 115
 116         /// Returns a copy of the i'th probability value
 117         T operator[] (size_t i) const { return _p[i]; }
 118
 119         /// Returns a reference to the i'th probability value
 120         T& operator[] (size_t i) { return _p[i]; }
 121
 122         /// Sets all probability entries to p
 123         TFactor<T> & fill (T p) { _p.fill( p ); return(*this); }
 124
 125         /// Fills all probability entries with random values
 126         TFactor<T> & randomize () { _p.randomize(); return(*this); }
 127
 128         /// Returns product of *this with x
 129         TFactor<T> operator* (T x) const {
 130             Factor result = *this;
 131             result.p() *= x;
 132             return result;
 133         }
 134
 135         /// Multiplies each probability entry with x
 136         TFactor<T>& operator*= (T x) {
 137             _p *= x;
 138             return *this;
 139         }
 140
 141         /// Returns quotient of *this with x
 142         TFactor<T> operator/ (T x) const {
 143             Factor result = *this;
 144             result.p() /= x;
 145             return result;
 146         }
 147
 148         /// Divides each probability entry by x
 149         TFactor<T>& operator/= (T x) {
 150             _p /= x;
 151             return *this;
 152         }
 153
 154         /// Returns product of *this with another Factor
 155         TFactor<T> operator* (const TFactor<T>& Q) const;
 156
 157         /// Returns quotient of *this with another Factor
 158         TFactor<T> operator/ (const TFactor<T>& Q) const;
 159
 160         /// Multiplies *this with another Factor
 161         TFactor<T>& operator*= (const TFactor<T>& Q) { return( *this = (*this * Q) ); }
 162
 163         /// Divides *this by another Factor
 164         TFactor<T>& operator/= (const TFactor<T>& Q) { return( *this = (*this / Q) ); }
 165
 166         /// Returns sum of *this and another Factor (their vars() should be identical)
 167         TFactor<T> operator+ (const TFactor<T>& Q) const {
 168 #ifdef DAI_DEBUG
 169             assert( Q._vs == _vs );
 170 #endif
 171             TFactor<T> sum(*this);
 172             sum._p += Q._p;
 173             return sum;
 174         }
 175
 176         /// Returns difference of *this and another Factor (their vars() should be identical)
 177         TFactor<T> operator- (const TFactor<T>& Q) const {
 178 #ifdef DAI_DEBUG
 179             assert( Q._vs == _vs );
 180 #endif
 181             TFactor<T> sum(*this);
 182             sum._p -= Q._p;
 183             return sum;
 184         }
 185
 186         /// Adds another Factor to *this (their vars() should be identical)
 187         TFactor<T>& operator+= (const TFactor<T>& Q) {
 188 #ifdef DAI_DEBUG
 189             assert( Q._vs == _vs );
 190 #endif
 191             _p += Q._p;
 192             return *this;
 193         }
 194
 195         /// Subtracts another Factor from *this (their vars() should be identical)
 196         TFactor<T>& operator-= (const TFactor<T>& Q) {
 197 #ifdef DAI_DEBUG
 198             assert( Q._vs == _vs );
 199 #endif
 200             _p -= Q._p;
 201             return *this;
 202         }
 203
 204         /// Adds scalar to *this
 205         TFactor<T>& operator+= (T q) {
 206             _p += q;
 207             return *this;
 208         }
 209
 210         /// Subtracts scalar from *this
 211         TFactor<T>& operator-= (T q) {
 212             _p -= q;
 213             return *this;
 214         }
 215
 216         /// Returns sum of *this and a scalar
 217         TFactor<T> operator+ (T q) const {
 218             TFactor<T> result(*this);
 219             result._p += q;
 220             return result;
 221         }
 222
 223         /// Returns difference of *this with a scalar
 224         TFactor<T> operator- (T q) const {
 225             TFactor<T> result(*this);
 226             result._p -= q;
 227             return result;
 228         }
 229
 230         /// Returns *this raised to some power
 231         TFactor<T> operator^ (Real a) const { TFactor<T> x; x._vs = _vs; x._p = _p^a; return x; }
 232
 233         /// Raises *this to some power
 234         TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
 235
 236         /// Sets all entries that are smaller than epsilon to zero
 237         TFactor<T>& makeZero( Real epsilon ) {
 238             _p.makeZero( epsilon );
 239             return *this;
 240         }
 241
 242         /// Sets all entries that are smaller than epsilon to epsilon
 243         TFactor<T>& makePositive( Real epsilon ) {
 244             _p.makePositive( epsilon );
 245             return *this;
 246         }
 247
 248         /// Returns inverse of *this
 249         TFactor<T> inverse() const {
 250             TFactor<T> inv;
 251             inv._vs = _vs;
 252             inv._p = _p.inverse(true);  // FIXME
 253             return inv;
 254         }
 255
 256         /// Returns *this divided by another Factor
 257         TFactor<T> divided_by( const TFactor<T>& denom ) const {
 258 #ifdef DAI_DEBUG
 259             assert( denom._vs == _vs );
 260 #endif
 261             TFactor<T> quot(*this);
 262             quot._p /= denom._p;
 263             return quot;
 264         }
 265
 266         /// Divides *this by another Factor
 267         TFactor<T>& divide( const TFactor<T>& denom ) {
 268 #ifdef DAI_DEBUG
 269             assert( denom._vs == _vs );
 270 #endif
 271             _p /= denom._p;
 272             return *this;
 273         }
 274
 275         /// Returns exp of *this
 276         TFactor<T> exp() const {
 277             TFactor<T> e;
 278             e._vs = _vs;
 279             e._p = _p.exp();
 280             return e;
 281         }
 282
 283         /// Returns absolute value of *this
 284         TFactor<T> abs() const {
 285             TFactor<T> e;
 286             e._vs = _vs;
 287             e._p = _p.abs();
 288             return e;
 289         }
 290
 291         /// Returns logarithm of *this
 292         TFactor<T> log() const {
 293             TFactor<T> l;
 294             l._vs = _vs;
 295             l._p = _p.log();
 296             return l;
 297         }
 298
 299         /// Returns logarithm of *this (defining log(0)=0)
 300         TFactor<T> log0() const {
 301             TFactor<T> l0;
 302             l0._vs = _vs;
 303             l0._p = _p.log0();
 304             return l0;
 305         }
 306
 307         /// Normalizes *this Factor
 308         T normalize( typename Prob::NormType norm = Prob::NORMPROB ) { return _p.normalize( norm ); }
 309
 310         /// Returns a normalized copy of *this
 311         TFactor<T> normalized( typename Prob::NormType norm = Prob::NORMPROB ) const {
 312             TFactor<T> result;
 313             result._vs = _vs;
 314             result._p = _p.normalized( norm );
 315             return result;
 316         }
 317
 318         /// Returns a slice of this factor, where the subset ns is in state ns_state
 319         Factor slice( const VarSet & ns, size_t ns_state ) const {
 320             assert( ns << _vs );
 321             VarSet nsrem = _vs / ns;
 322             Factor result( nsrem, 0.0 );
 323
 324             // OPTIMIZE ME
 325             IndexFor i_ns (ns, _vs);
 326             IndexFor i_nsrem (nsrem, _vs);
 327             for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
 328                 if( (size_t)i_ns == ns_state )
 329                     result._p[i_nsrem] = _p[i];
 330
 331             return result;
 332         }
 333
 334         /// Returns unnormalized marginal; ns should be a subset of vars()
 335         TFactor<T> partSum(const VarSet & ns) const;
 336
 337         /// Returns (normalized by default) marginal; ns should be a subset of vars()
 338         TFactor<T> marginal(const VarSet & ns, bool normed = true) const { if(normed) return partSum(ns).normalized(); else return partSum(ns); }
 339
 340         /// Sums out all variables except those in ns
 341         TFactor<T> notSum(const VarSet & ns) const { return partSum(vars() ^ ns); }
 342
 343         /// Embeds this factor in a larger VarSet
 344         TFactor<T> embed(const VarSet & ns) const {
 345             VarSet vs = vars();
 346             assert( ns >> vs );
 347             if( vs == ns )
 348                 return *this;
 349             else
 350                 return (*this) * Factor(ns / vs, 1.0);
 351         }
 352
 353         /// Returns true if *this has NANs
 354         bool hasNaNs() const { return _p.hasNaNs(); }
 355
 356         /// Returns true if *this has negative entries
 357         bool hasNegatives() const { return _p.hasNegatives(); }
 358
 359         /// Returns total sum of probability entries
 360         T totalSum() const { return _p.totalSum(); }
 361
 362         /// Returns maximum absolute value of probability entries
 363         T maxAbs() const { return _p.maxAbs(); }
 364
 365         /// Returns maximum value of probability entries
 366         T maxVal() const { return _p.maxVal(); }
 367
 368         /// Returns minimum value of probability entries
 369         T minVal() const { return _p.minVal(); }
 370
 371         /// Returns entropy of *this
 372         Real entropy() const { return _p.entropy(); }
 373
 374         /// Returns strength of *this, between variables i and j, using (52) of [\ref MoK07b]
 375         T strength( const Var &i, const Var &j ) const;
 376 };
 377
 378
 379 template<typename T> TFactor<T> TFactor<T>::partSum(const VarSet & ns) const {
 380 #ifdef DAI_DEBUG
 381     assert( ns << _vs );
 382 #endif
 383
 384     TFactor<T> res( ns, 0.0 );
 385
 386     IndexFor i_res( ns, _vs );
 387     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 388         res._p[i_res] += _p[i];
 389
 390     return res;
 391 }
 392
 393
 394 template<typename T> TFactor<T> TFactor<T>::operator* (const TFactor<T>& Q) const {
 395     TFactor<T> prod( _vs | Q._vs, 0.0 );
 396
 397     IndexFor i1(_vs, prod._vs);
 398     IndexFor i2(Q._vs, prod._vs);
 399
 400     for( size_t i = 0; i < prod._p.size(); i++, ++i1, ++i2 )
 401         prod._p[i] += _p[i1] * Q._p[i2];
 402
 403     return prod;
 404 }
 405
 406
 407 template<typename T> TFactor<T> TFactor<T>::operator/ (const TFactor<T>& Q) const {
 408     TFactor<T> quot( _vs + Q._vs, 0.0 );
 409
 410     IndexFor i1(_vs, quot._vs);
 411     IndexFor i2(Q._vs, quot._vs);
 412
 413     for( size_t i = 0; i < quot._p.size(); i++, ++i1, ++i2 )
 414         quot._p[i] += _p[i1] / Q._p[i2];
 415
 416     return quot;
 417 }
 418
 419
 420 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
 421 #ifdef DAI_DEBUG
 422     assert( _vs.contains( i ) );
 423     assert( _vs.contains( j ) );
 424     assert( i != j );
 425 #endif
 426     VarSet ij(i, j);
 427
 428     T max = 0.0;
 429     for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
 430         for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
 431             if( alpha2 != alpha1 )
 432                 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
 433                     for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
 434                         if( beta2 != beta1 ) {
 435                             size_t as = 1, bs = 1;
 436                             if( i < j )
 437                                 bs = i.states();
 438                             else
 439                                 as = j.states();
 440                             T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).maxVal();
 441                             T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).maxVal();
 442                             T f = f1 * f2;
 443                             if( f > max )
 444                                 max = f;
 445                         }
 446
 447     return std::tanh( 0.25 * std::log( max ) );
 448 }
 449
 450
 451 /// Writes a Factor to an output stream
 452 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
 453     os << "(" << P.vars() << " <";
 454     for( size_t i = 0; i < P.states(); i++ )
 455         os << P[i] << " ";
 456     os << ">)";
 457     return os;
 458 }
 459
 460
 461 /// Returns distance between two Factors (with identical vars())
 462 template<typename T> Real dist( const TFactor<T> & x, const TFactor<T> & y, Prob::DistType dt ) {
 463     if( x.vars().empty() || y.vars().empty() )
 464         return -1;
 465     else {
 466 #ifdef DAI_DEBUG
 467         assert( x.vars() == y.vars() );
 468 #endif
 469         return dist( x.p(), y.p(), dt );
 470     }
 471 }
 472
 473
 474 /// Returns the pointwise maximum of two Factors
 475 template<typename T> TFactor<T> max( const TFactor<T> & P, const TFactor<T> & Q ) {
 476     assert( P._vs == Q._vs );
 477     return TFactor<T>( P._vs, min( P.p(), Q.p() ) );
 478 }
 479
 480
 481 /// Returns the pointwise minimum of two Factors
 482 template<typename T> TFactor<T> min( const TFactor<T> & P, const TFactor<T> & Q ) {
 483     assert( P._vs == Q._vs );
 484     return TFactor<T>( P._vs, max( P.p(), Q.p() ) );
 485 }
 486
 487
 488 /// Calculates the mutual information between the two variables in P
 489 template<typename T> Real MutualInfo(const TFactor<T> & P) {
 490     assert( P.vars().size() == 2 );
 491     VarSet::const_iterator it = P.vars().begin();
 492     Var i = *it; it++; Var j = *it;
 493     TFactor<T> projection = P.marginal(i) * P.marginal(j);
 494     return real( dist( P.normalized(), projection, Prob::DISTKL ) );
 495 }
 496
 497
 498 } // end of namespace dai
 499
 500
 501 #endif