include/dai/factor.h

   1 /*  Copyright (C) 2006-2008  Joris Mooij  [j dot mooij at science dot ru dot nl]
   2     Copyright (C) 2002  Martijn Leisink  [martijn@mbfys.kun.nl]
   3     Radboud University Nijmegen, The Netherlands
   4
   5     This file is part of libDAI.
   6
   7     libDAI is free software; you can redistribute it and/or modify
   8     it under the terms of the GNU General Public License as published by
   9     the Free Software Foundation; either version 2 of the License, or
  10     (at your option) any later version.
  11
  12     libDAI is distributed in the hope that it will be useful,
  13     but WITHOUT ANY WARRANTY; without even the implied warranty of
  14     MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
  15     GNU General Public License for more details.
  16
  17     You should have received a copy of the GNU General Public License
  18     along with libDAI; if not, write to the Free Software
  19     Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, MA  02110-1301  USA
  20 */
  21
  22
  23 #ifndef __defined_libdai_factor_h
  24 #define __defined_libdai_factor_h
  25
  26
  27 #include <iostream>
  28 #include <cmath>
  29 #include <dai/prob.h>
  30 #include <dai/varset.h>
  31 #include <dai/index.h>
  32
  33
  34 namespace dai {
  35
  36
  37 template<typename T> class      TFactor;
  38 typedef TFactor<Real>           Factor;
  39
  40
  41 // predefine friends
  42 template<typename T> Real           dist( const TFactor<T> & x, const TFactor<T> & y, Prob::DistType dt );
  43 template<typename T> Real           KL_dist( const TFactor<T> & p, const TFactor<T> & q );
  44 template<typename T> Real           MutualInfo( const TFactor<T> & p );
  45 template<typename T> TFactor<T>     max( const TFactor<T> & P, const TFactor<T> & Q );
  46 template<typename T> TFactor<T>     min( const TFactor<T> & P, const TFactor<T> & Q );
  47 template<typename T> std::ostream&  operator<< (std::ostream& os, const TFactor<T>& P);
  48
  49
  50 // T should be castable from and to double
  51 template <typename T> class TFactor {
  52     private:
  53         VarSet      _vs;
  54         TProb<T>    _p;
  55
  56     public:
  57         // Construct Factor with empty VarSet but nonempty _p
  58         TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
  59
  60         // Construct Factor from VarSet
  61         TFactor( const VarSet& ns ) : _vs(ns), _p(nrStates(_vs)) {}
  62
  63         // Construct Factor from VarSet and initial value
  64         TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(nrStates(_vs),p) {}
  65
  66         // Construct Factor from VarSet and initial array
  67         TFactor( const VarSet& ns, const Real* p ) : _vs(ns), _p(nrStates(_vs),p) {}
  68
  69         // Construct Factor from VarSet and TProb<T>
  70         TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
  71 #ifdef DAI_DEBUG
  72             assert( nrStates(_vs) == _p.size() );
  73 #endif
  74         }
  75
  76         // Construct Factor from Var
  77         TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
  78
  79         // Copy constructor
  80         TFactor( const TFactor<T> &x ) : _vs(x._vs), _p(x._p) {}
  81
  82         // Assignment operator
  83         TFactor<T> & operator= (const TFactor<T> &x) {
  84             if( this != &x ) {
  85                 _vs = x._vs;
  86                 _p  = x._p;
  87             }
  88             return *this;
  89         }
  90
  91         const TProb<T> & p() const { return _p; }
  92         TProb<T> & p() { return _p; }
  93         const VarSet & vars() const { return _vs; }
  94         size_t states() const { return _p.size(); }
  95
  96         T operator[] (size_t i) const { return _p[i]; }
  97         T& operator[] (size_t i) { return _p[i]; }
  98         TFactor<T> & fill (T p)
  99             { _p.fill( p ); return(*this); }
 100         TFactor<T> & randomize ()
 101             { _p.randomize(); return(*this); }
 102         TFactor<T> operator* (T x) const {
 103             Factor result = *this;
 104             result.p() *= x;
 105             return result;
 106         }
 107         TFactor<T>& operator*= (T x) {
 108             _p *= x;
 109             return *this;
 110         }
 111         TFactor<T> operator/ (T x) const {
 112             Factor result = *this;
 113             result.p() /= x;
 114             return result;
 115         }
 116         TFactor<T>& operator/= (T x) {
 117             _p /= x;
 118             return *this;
 119         }
 120         TFactor<T> operator* (const TFactor<T>& Q) const;
 121         TFactor<T> operator/ (const TFactor<T>& Q) const;
 122         TFactor<T>& operator*= (const TFactor<T>& Q) { return( *this = (*this * Q) ); }
 123         TFactor<T>& operator/= (const TFactor<T>& Q) { return( *this = (*this / Q) ); }
 124         TFactor<T> operator+ (const TFactor<T>& Q) const {
 125 #ifdef DAI_DEBUG
 126             assert( Q._vs == _vs );
 127 #endif
 128             TFactor<T> sum(*this);
 129             sum._p += Q._p;
 130             return sum;
 131         }
 132         TFactor<T> operator- (const TFactor<T>& Q) const {
 133 #ifdef DAI_DEBUG
 134             assert( Q._vs == _vs );
 135 #endif
 136             TFactor<T> sum(*this);
 137             sum._p -= Q._p;
 138             return sum;
 139         }
 140         TFactor<T>& operator+= (const TFactor<T>& Q) {
 141 #ifdef DAI_DEBUG
 142             assert( Q._vs == _vs );
 143 #endif
 144             _p += Q._p;
 145             return *this;
 146         }
 147         TFactor<T>& operator-= (const TFactor<T>& Q) {
 148 #ifdef DAI_DEBUG
 149             assert( Q._vs == _vs );
 150 #endif
 151             _p -= Q._p;
 152             return *this;
 153         }
 154         TFactor<T>& operator+= (T q) {
 155             _p += q;
 156             return *this;
 157         }
 158         TFactor<T>& operator-= (T q) {
 159             _p -= q;
 160             return *this;
 161         }
 162         TFactor<T> operator+ (T q) const {
 163             TFactor<T> result(*this);
 164             result._p += q;
 165             return result;
 166         }
 167         TFactor<T> operator- (T q) const {
 168             TFactor<T> result(*this);
 169             result._p -= q;
 170             return result;
 171         }
 172
 173         TFactor<T> operator^ (Real a) const { TFactor<T> x; x._vs = _vs; x._p = _p^a; return x; }
 174         TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
 175
 176         TFactor<T>& makeZero( Real epsilon ) {
 177             _p.makeZero( epsilon );
 178             return *this;
 179         }
 180
 181         TFactor<T>& makePositive( Real epsilon ) {
 182             _p.makePositive( epsilon );
 183             return *this;
 184         }
 185
 186         TFactor<T> inverse() const {
 187             TFactor<T> inv;
 188             inv._vs = _vs;
 189             inv._p = _p.inverse(true);  // FIXME
 190             return inv;
 191         }
 192
 193         TFactor<T> divided_by( const TFactor<T>& denom ) const {
 194 #ifdef DAI_DEBUG
 195             assert( denom._vs == _vs );
 196 #endif
 197             TFactor<T> quot(*this);
 198             quot._p /= denom._p;
 199             return quot;
 200         }
 201
 202         TFactor<T>& divide( const TFactor<T>& denom ) {
 203 #ifdef DAI_DEBUG
 204             assert( denom._vs == _vs );
 205 #endif
 206             _p /= denom._p;
 207             return *this;
 208         }
 209
 210         TFactor<T> exp() const {
 211             TFactor<T> e;
 212             e._vs = _vs;
 213             e._p = _p.exp();
 214             return e;
 215         }
 216
 217         TFactor<T> abs() const {
 218             TFactor<T> e;
 219             e._vs = _vs;
 220             e._p = _p.abs();
 221             return e;
 222         }
 223
 224         TFactor<T> log() const {
 225             TFactor<T> l;
 226             l._vs = _vs;
 227             l._p = _p.log();
 228             return l;
 229         }
 230
 231         TFactor<T> log0() const {
 232             TFactor<T> l0;
 233             l0._vs = _vs;
 234             l0._p = _p.log0();
 235             return l0;
 236         }
 237
 238         T normalize( typename Prob::NormType norm = Prob::NORMPROB ) { return _p.normalize( norm ); }
 239         TFactor<T> normalized( typename Prob::NormType norm = Prob::NORMPROB ) const {
 240             TFactor<T> result;
 241             result._vs = _vs;
 242             result._p = _p.normalized( norm );
 243             return result;
 244         }
 245
 246         // returns slice of this factor where the subset ns is in state ns_state
 247         Factor slice( const VarSet & ns, size_t ns_state ) const {
 248             assert( ns << _vs );
 249             VarSet nsrem = _vs / ns;
 250             Factor result( nsrem, 0.0 );
 251
 252             // OPTIMIZE ME
 253             IndexFor i_ns (ns, _vs);
 254             IndexFor i_nsrem (nsrem, _vs);
 255             for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
 256                 if( (size_t)i_ns == ns_state )
 257                     result._p[i_nsrem] = _p[i];
 258
 259             return result;
 260         }
 261
 262         // returns unnormalized marginal; ns should be a subset of vars()
 263         TFactor<T> partSum(const VarSet & ns) const;
 264         // returns (normalized by default) marginal; ns should be a subset of vars()
 265         TFactor<T> marginal(const VarSet & ns, bool normed = true) const { if(normed) return partSum(ns).normalized(); else return partSum(ns); }
 266         // sums out all variables except those in ns
 267         TFactor<T> notSum(const VarSet & ns) const { return partSum(vars() ^ ns); }
 268
 269         // embeds this factor in larger varset ns
 270         TFactor<T> embed(const VarSet & ns) const {
 271             VarSet vs = vars();
 272             assert( ns >> vs );
 273             if( vs == ns )
 274                 return *this;
 275             else
 276                 return (*this) * Factor(ns / vs, 1.0);
 277         }
 278
 279         bool hasNaNs() const { return _p.hasNaNs(); }
 280         bool hasNegatives() const { return _p.hasNegatives(); }
 281         T totalSum() const { return _p.totalSum(); }
 282         T maxAbs() const { return _p.maxAbs(); }
 283         T maxVal() const { return _p.maxVal(); }
 284         T minVal() const { return _p.minVal(); }
 285         Real entropy() const { return _p.entropy(); }
 286         T strength( const Var &i, const Var &j ) const;
 287
 288         friend Real dist( const TFactor<T> & x, const TFactor<T> & y, Prob::DistType dt ) {
 289             if( x._vs.empty() || y._vs.empty() )
 290                 return -1;
 291             else {
 292 #ifdef DAI_DEBUG
 293                 assert( x._vs == y._vs );
 294 #endif
 295                 return dist( x._p, y._p, dt );
 296             }
 297         }
 298         friend Real KL_dist <> (const TFactor<T> & p, const TFactor<T> & q);
 299         friend Real MutualInfo <> ( const TFactor<T> & P );
 300         template<class U> friend std::ostream& operator<< (std::ostream& os, const TFactor<U>& P);
 301 };
 302
 303
 304 template<typename T> TFactor<T> TFactor<T>::partSum(const VarSet & ns) const {
 305 #ifdef DAI_DEBUG
 306     assert( ns << _vs );
 307 #endif
 308
 309     TFactor<T> res( ns, 0.0 );
 310
 311     IndexFor i_res( ns, _vs );
 312     for( size_t i = 0; i < _p.size(); i++, ++i_res )
 313         res._p[i_res] += _p[i];
 314
 315     return res;
 316 }
 317
 318
 319 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
 320     os << "(" << P.vars() << " <";
 321     for( size_t i = 0; i < P._p.size(); i++ )
 322         os << P._p[i] << " ";
 323     os << ">)";
 324     return os;
 325 }
 326
 327
 328 template<typename T> TFactor<T> TFactor<T>::operator* (const TFactor<T>& Q) const {
 329     TFactor<T> prod( _vs | Q._vs, 0.0 );
 330
 331     IndexFor i1(_vs, prod._vs);
 332     IndexFor i2(Q._vs, prod._vs);
 333
 334     for( size_t i = 0; i < prod._p.size(); i++, ++i1, ++i2 )
 335         prod._p[i] += _p[i1] * Q._p[i2];
 336
 337     return prod;
 338 }
 339
 340
 341 template<typename T> TFactor<T> TFactor<T>::operator/ (const TFactor<T>& Q) const {
 342     TFactor<T> quot( _vs + Q._vs, 0.0 );
 343
 344     IndexFor i1(_vs, quot._vs);
 345     IndexFor i2(Q._vs, quot._vs);
 346
 347     for( size_t i = 0; i < quot._p.size(); i++, ++i1, ++i2 )
 348         quot._p[i] += _p[i1] / Q._p[i2];
 349
 350     return quot;
 351 }
 352
 353
 354 template<typename T> Real KL_dist(const TFactor<T> & P, const TFactor<T> & Q) {
 355     if( P._vs.empty() || Q._vs.empty() )
 356         return -1;
 357     else {
 358 #ifdef DAI_DEBUG
 359         assert( P._vs == Q._vs );
 360 #endif
 361         return KL_dist( P._p, Q._p );
 362     }
 363 }
 364
 365
 366 // calculate mutual information of x_i and x_j where P.vars() = \{x_i,x_j\}
 367 template<typename T> Real MutualInfo(const TFactor<T> & P) {
 368     assert( P._vs.size() == 2 );
 369     VarSet::const_iterator it = P._vs.begin();
 370     Var i = *it; it++; Var j = *it;
 371     TFactor<T> projection = P.marginal(i) * P.marginal(j);
 372     return real( KL_dist( P.normalized(), projection ) );
 373 }
 374
 375
 376 template<typename T> TFactor<T> max( const TFactor<T> & P, const TFactor<T> & Q ) {
 377     assert( P._vs == Q._vs );
 378     return TFactor<T>( P._vs, min( P.p(), Q.p() ) );
 379 }
 380
 381 template<typename T> TFactor<T> min( const TFactor<T> & P, const TFactor<T> & Q ) {
 382     assert( P._vs == Q._vs );
 383     return TFactor<T>( P._vs, max( P.p(), Q.p() ) );
 384 }
 385
 386 // calculate N(psi, i, j)
 387 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
 388 #ifdef DAI_DEBUG
 389     assert( _vs.contains( i ) );
 390     assert( _vs.contains( j ) );
 391     assert( i != j );
 392 #endif
 393     VarSet ij(i, j);
 394
 395     T max = 0.0;
 396     for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
 397         for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
 398             if( alpha2 != alpha1 )
 399                 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
 400                     for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
 401                         if( beta2 != beta1 ) {
 402                             size_t as = 1, bs = 1;
 403                             if( i < j )
 404                                 bs = i.states();
 405                             else
 406                                 as = j.states();
 407                             T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).maxVal();
 408                             T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).maxVal();
 409                             T f = f1 * f2;
 410                             if( f > max )
 411                                 max = f;
 412                         }
 413
 414     return std::tanh( 0.25 * std::log( max ) );
 415 }
 416
 417
 418 template<typename T> TFactor<T> RemoveFirstOrderInteractions( const TFactor<T> & psi ) {
 419     TFactor<T> result = psi;
 420
 421     VarSet vars = psi.vars();
 422     for( size_t iter = 0; iter < 100; iter++ ) {
 423         for( VarSet::const_iterator n = vars.begin(); n != vars.end(); n++ )
 424             result = result * result.partSum(*n).inverse();
 425         result.normalize();
 426     }
 427
 428     return result;
 429 }
 430
 431
 432 } // end of namespace dai
 433
 434
 435 #endif