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