1 /* This file is part of libDAI - http://www.libdai.org/
2 *
4 * 2, or (at your option) any later version. libDAI is distributed without any
5 * warranty. See the file COPYING for more details.
6 *
7 * Copyright (C) 2002 Martijn Leisink [martijn@mbfys.kun.nl]
8 * Copyright (C) 2006-2009 Joris Mooij [joris dot mooij at libdai dot org]
10 */
13 /// \file
14 /// \brief Defines TFactor<T> and Factor classes
17 #ifndef __defined_libdai_factor_h
18 #define __defined_libdai_factor_h
21 #include <iostream>
22 #include <functional>
23 #include <cmath>
24 #include <dai/prob.h>
25 #include <dai/varset.h>
26 #include <dai/index.h>
27 #include <dai/util.h>
30 namespace dai {
33 // Function object similar to std::divides(), but different in that dividing by zero results in zero
34 template<typename T> struct divides0 : public std::binary_function<T, T, T> {
35 // Returns (j == 0 ? 0 : (i/j))
36 T operator()( const T &i, const T &j ) const {
37 if( j == (T)0 )
38 return (T)0;
39 else
40 return i / j;
41 }
42 };
45 /// Represents a (probability) factor.
46 /** Mathematically, a \e factor is a function mapping joint states of some
47 * 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$\{x_l\}_{l\in L}\f$ is
51 * a function \f$f_L : \prod_{l\in L} X_l \to [0,\infty)\f$.
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$\{x_l\}_{l\in L}\f$
56 * that the factor depends on;
57 * \arg a TProb<\a T>, a vector containing the value 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$\prod_{l\in L} X_l\f$ with a linear index in
63 * \f$\{0,1,\dots,\prod_{l\in L} S_l-1\}\f$ 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 * \todo Define a better fileformat for .fg files (maybe using XML)?
68 * \todo Add support for sparse factors.
69 */
70 template <typename T> class TFactor {
71 private:
72 VarSet _vs;
73 TProb<T> _p;
75 public:
76 /// Iterator over factor entries
77 typedef typename TProb<T>::iterator iterator;
79 /// Const iterator over factor entries
80 typedef typename TProb<T>::const_iterator const_iterator;
82 /// Constructs TFactor depending on no variables, with value p
83 TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
85 /// Constructs TFactor depending on variables in vars, with uniform distribution
86 TFactor( const VarSet& vars ) : _vs(vars), _p(_vs.nrStates()) {}
88 /// Constructs TFactor depending on variables in vars, with all values set to p
89 TFactor( const VarSet& vars, Real p ) : _vs(vars), _p(_vs.nrStates(),p) {}
91 /// Constructs TFactor depending on variables in vars, copying the values from the range starting at begin
92 /** \param vars contains the variables that the new TFactor should depend on.
93 * \tparam Iterator Iterates over instances of type T; should support addition of size_t.
94 * \param begin Points to first element to be added.
95 */
96 template<typename TIterator>
97 TFactor( const VarSet& vars, TIterator begin ) : _vs(vars), _p(begin, begin + _vs.nrStates(), _vs.nrStates()) {}
99 /// Constructs TFactor depending on variables in vars, with values set to the TProb p
100 TFactor( const VarSet& vars, const TProb<T> &p ) : _vs(vars), _p(p) {
101 DAI_DEBASSERT( _vs.nrStates() == _p.size() );
102 }
104 /// Constructs TFactor depending on variables in vars, permuting the values given in TProb p
105 TFactor( const std::vector<Var> &vars, const std::vector<T> &p ) : _vs(vars.begin(), vars.end(), vars.size()), _p(p.size()) {
106 Permute permindex(vars);
107 for( size_t li = 0; li < p.size(); ++li )
108 _p[permindex.convert_linear_index(li)] = p[li];
109 }
111 /// Constructs TFactor depending on the variable v, with uniform distribution
112 TFactor( const Var &v ) : _vs(v), _p(v.states()) {}
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; }
119 /// Returns const reference to variable set
120 const VarSet& vars() const { return _vs; }
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(); }
127 /// Returns a copy of the i'th entry of the value vector
128 T operator[] (size_t i) const { return _p[i]; }
130 /// Returns a reference to the i'th entry of the value vector
131 T& operator[] (size_t i) { return _p[i]; }
133 /// Returns iterator pointing to first entry
134 iterator begin() { return _p.begin(); }
135 /// Returns const iterator pointing to first entry
136 const_iterator begin() const { return _p.begin(); }
137 /// Returns iterator pointing beyond last entry
138 iterator end() { return _p.end(); }
139 /// Returns const iterator pointing beyond last entry
140 const_iterator end() const { return _p.end(); }
142 /// Sets all values to p
143 TFactor<T> & fill (T p) { _p.fill( p ); return(*this); }
145 /// Draws all values i.i.d. from a uniform distribution on [0,1)
146 TFactor<T> & randomize () { _p.randomize(); return(*this); }
149 /// Multiplies *this with scalar t
150 TFactor<T>& operator*= (T t) {
151 _p *= t;
152 return *this;
153 }
155 /// Divides *this by scalar t
156 TFactor<T>& operator/= (T t) {
157 _p /= t;
158 return *this;
159 }
161 /// Adds scalar t to *this
162 TFactor<T>& operator+= (T t) {
163 _p += t;
164 return *this;
165 }
167 /// Subtracts scalar t from *this
168 TFactor<T>& operator-= (T t) {
169 _p -= t;
170 return *this;
171 }
173 /// Raises *this to the power a
174 TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
177 /// Returns product of *this with scalar t
178 TFactor<T> operator* (T t) const {
179 TFactor<T> result = *this;
180 result.p() *= t;
181 return result;
182 }
184 /// Returns quotient of *this with scalar t
185 TFactor<T> operator/ (T t) const {
186 TFactor<T> result = *this;
187 result.p() /= t;
188 return result;
189 }
191 /// Returns sum of *this and scalar t
192 TFactor<T> operator+ (T t) const {
193 TFactor<T> result(*this);
194 result._p += t;
195 return result;
196 }
198 /// Returns *this minus scalar t
199 TFactor<T> operator- (T t) const {
200 TFactor<T> result(*this);
201 result._p -= t;
202 return result;
203 }
205 /// Returns *this raised to the power a
206 TFactor<T> operator^ (Real a) const {
207 TFactor<T> x;
208 x._vs = _vs;
209 x._p = _p^a;
210 return x;
211 }
213 /// Multiplies *this with 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 }
222 /// Divides *this by the TFactor f
223 TFactor<T>& operator/= (const TFactor<T>& f) {
224 if( f._vs == _vs ) // optimize special case
225 _p /= f._p;
226 else
227 *this = (*this / f);
228 return *this;
229 }
231 /// Adds the TFactor f to *this
232 TFactor<T>& operator+= (const TFactor<T>& f) {
233 if( f._vs == _vs ) // optimize special case
234 _p += f._p;
235 else
236 *this = (*this + f);
237 return *this;
238 }
240 /// Subtracts the TFactor f from *this
241 TFactor<T>& operator-= (const TFactor<T>& f) {
242 if( f._vs == _vs ) // optimize special case
243 _p -= f._p;
244 else
245 *this = (*this - f);
246 return *this;
247 }
249 /// Returns product of *this with the TFactor f
250 /** The product of two factors is defined as follows: if
251 * \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
252 * \f[fg : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) g(x_M).\f]
253 */
254 TFactor<T> operator* (const TFactor<T>& f) const {
255 return pointwiseOp(*this,f,std::multiplies<T>());
256 }
258 /// Returns quotient of *this by the TFactor f
259 /** The quotient of two factors is defined as follows: if
260 * \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
261 * \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]
262 */
263 TFactor<T> operator/ (const TFactor<T>& f) const {
264 return pointwiseOp(*this,f,divides0<T>());
265 }
267 /// Returns sum of *this and the TFactor f
268 /** The sum of two factors is defined as follows: if
269 * \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
270 * \f[f+g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) + g(x_M).\f]
271 */
272 TFactor<T> operator+ (const TFactor<T>& f) const {
273 return pointwiseOp(*this,f,std::plus<T>());
274 }
276 /// Returns *this minus the TFactor f
277 /** The difference of two factors is defined as follows: if
278 * \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
279 * \f[f-g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) - g(x_M).\f]
280 */
281 TFactor<T> operator- (const TFactor<T>& f) const {
282 return pointwiseOp(*this,f,std::minus<T>());
283 }
286 /// Sets all values that are smaller than epsilon to 0
287 TFactor<T>& makeZero( T epsilon ) {
288 _p.makeZero( epsilon );
289 return *this;
290 }
292 /// Sets all values that are smaller than epsilon to epsilon
293 TFactor<T>& makePositive( T epsilon ) {
294 _p.makePositive( epsilon );
295 return *this;
296 }
298 /// Returns pointwise inverse of *this.
299 /** If zero == true, uses 1 / 0 == 0; otherwise 1 / 0 == Inf.
300 */
301 TFactor<T> inverse(bool zero=true) const {
302 TFactor<T> inv;
303 inv._vs = _vs;
304 inv._p = _p.inverse(zero);
305 return inv;
306 }
308 /// Returns pointwise exp of *this
309 TFactor<T> exp() const {
310 TFactor<T> e;
311 e._vs = _vs;
312 e._p = _p.exp();
313 return e;
314 }
316 /// Returns pointwise logarithm of *this
317 /** If zero==true, uses log(0)==0; otherwise, log(0)=-Inf.
318 */
319 TFactor<T> log(bool zero=false) const {
320 TFactor<T> l;
321 l._vs = _vs;
322 l._p = _p.log(zero);
323 return l;
324 }
326 /// Returns pointwise absolute value of *this
327 TFactor<T> abs() const {
328 TFactor<T> e;
329 e._vs = _vs;
330 e._p = _p.abs();
331 return e;
332 }
334 /// Normalizes *this TFactor according to the specified norm
335 T normalize( typename Prob::NormType norm=Prob::NORMPROB ) { return _p.normalize( norm ); }
337 /// Returns a normalized copy of *this, according to the specified norm
338 TFactor<T> normalized( typename Prob::NormType norm=Prob::NORMPROB ) const {
339 TFactor<T> result;
340 result._vs = _vs;
341 result._p = _p.normalized( norm );
342 return result;
343 }
345 /// Returns a slice of this TFactor, where the subset ns is in state nsState
346 /** \pre \a ns sould be a subset of vars()
347 * \pre \a nsState < ns.states()
348 *
349 * The result is a TFactor that depends on the variables in this->vars() except those in \a ns,
350 * obtained by setting the variables in \a ns to the joint state specified by the linear index
351 * \a nsState. Formally, if *this corresponds with the factor \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$,
352 * \f$M \subset L\f$ corresponds with \a ns and \a nsState corresponds with a mapping \f$s\f$ that
353 * 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
354 * returned corresponds with the factor \f$g : \prod_{l \in L \setminus M} X_l \to [0,\infty)\f$
355 * defined by \f$g(\{x_l\}_{l\in L \setminus M}) = f(\{x_l\}_{l\in L \setminus M}, \{s(x_m)\}_{m\in M})\f$.
356 */
357 TFactor<T> slice( const VarSet& ns, size_t nsState ) const {
358 DAI_ASSERT( ns << _vs );
359 VarSet nsrem = _vs / ns;
360 TFactor<T> result( nsrem, T(0) );
362 // OPTIMIZE ME
363 IndexFor i_ns (ns, _vs);
364 IndexFor i_nsrem (nsrem, _vs);
365 for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
366 if( (size_t)i_ns == nsState )
367 result._p[i_nsrem] = _p[i];
369 return result;
370 }
372 /// Returns marginal on ns, obtained by summing out all variables except those in ns, and normalizing the result if normed==true
373 TFactor<T> marginal(const VarSet & ns, bool normed=true) const;
375 /// Returns max-marginal on ns, obtained by maximizing all variables except those in ns, and normalizing the result if normed==true
376 TFactor<T> maxMarginal(const VarSet & ns, bool normed=true) const;
378 /// Embeds this factor in a larger VarSet
379 /** \pre vars() should be a subset of ns
380 *
381 * If *this corresponds with \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$L \subset M\f$, then
382 * the embedded factor corresponds with \f$g : \prod_{m\in M} X_m \to [0,\infty) : x \mapsto f(x_L)\f$.
383 */
384 TFactor<T> embed(const VarSet & ns) const {
385 DAI_ASSERT( ns >> _vs );
386 if( _vs == ns )
387 return *this;
388 else
389 return (*this) * TFactor<T>(ns / _vs, (T)1);
390 }
392 /// Returns true if *this has NaN values
393 bool hasNaNs() const { return _p.hasNaNs(); }
395 /// Returns true if *this has negative values
396 bool hasNegatives() const { return _p.hasNegatives(); }
398 /// Returns total sum of values
399 T sum() const { return _p.sum(); }
401 /// Returns maximum absolute value
402 T maxAbs() const { return _p.maxAbs(); }
404 /// Returns maximum value
405 T max() const { return _p.max(); }
407 /// Returns minimum value
408 T min() const { return _p.min(); }
410 /// Returns entropy of *this TFactor
411 Real entropy() const { return _p.entropy(); }
413 /// Returns strength of *this TFactor (between variables i and j), as defined in eq. (52) of [\ref MoK07b]
414 T strength( const Var &i, const Var &j ) const;
415 };
418 template<typename T> TFactor<T> TFactor<T>::marginal(const VarSet & ns, bool normed) const {
419 VarSet res_ns = ns & _vs;
421 TFactor<T> res( res_ns, 0.0 );
423 IndexFor i_res( res_ns, _vs );
424 for( size_t i = 0; i < _p.size(); i++, ++i_res )
425 res._p[i_res] += _p[i];
427 if( normed )
428 res.normalize( Prob::NORMPROB );
430 return res;
431 }
434 template<typename T> TFactor<T> TFactor<T>::maxMarginal(const VarSet & ns, bool normed) const {
435 VarSet res_ns = ns & _vs;
437 TFactor<T> res( res_ns, 0.0 );
439 IndexFor i_res( res_ns, _vs );
440 for( size_t i = 0; i < _p.size(); i++, ++i_res )
441 if( _p[i] > res._p[i_res] )
442 res._p[i_res] = _p[i];
444 if( normed )
445 res.normalize( Prob::NORMPROB );
447 return res;
448 }
451 /// Apply binary operator pointwise on two factors
452 template<typename T, typename binaryOp> TFactor<T> pointwiseOp( const TFactor<T> &f, const TFactor<T> &g, binaryOp op ) {
453 if( f.vars() == g.vars() ) { // optimizate special case
454 TFactor<T> result(f);
455 for( size_t i = 0; i < result.states(); i++ )
456 result[i] = op( result[i], g[i] );
457 return result;
458 } else {
459 TFactor<T> result( f.vars() | g.vars(), 0.0 );
461 IndexFor i1(f.vars(), result.vars());
462 IndexFor i2(g.vars(), result.vars());
464 for( size_t i = 0; i < result.states(); i++, ++i1, ++i2 )
465 result[i] = op( f[i1], g[i2] );
467 return result;
468 }
469 }
472 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
473 DAI_DEBASSERT( _vs.contains( i ) );
474 DAI_DEBASSERT( _vs.contains( j ) );
475 DAI_DEBASSERT( i != j );
476 VarSet ij(i, j);
478 T max = 0.0;
479 for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
480 for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
481 if( alpha2 != alpha1 )
482 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
483 for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
484 if( beta2 != beta1 ) {
485 size_t as = 1, bs = 1;
486 if( i < j )
487 bs = i.states();
488 else
489 as = j.states();
490 T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).max();
491 T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).max();
492 T f = f1 * f2;
493 if( f > max )
494 max = f;
495 }
497 return std::tanh( 0.25 * std::log( max ) );
498 }
501 /// Writes a TFactor to an output stream
502 /** \relates TFactor
503 */
504 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
505 os << "(" << P.vars() << ", (";
506 for( size_t i = 0; i < P.states(); i++ )
507 os << (i == 0 ? "" : ", ") << P[i];
508 os << "))";
509 return os;
510 }
513 /// Returns distance between two TFactors f and g, according to the distance measure dt
514 /** \relates TFactor
515 * \pre f.vars() == g.vars()
516 */
517 template<typename T> Real dist( const TFactor<T> &f, const TFactor<T> &g, Prob::DistType dt ) {
518 if( f.vars().empty() || g.vars().empty() )
519 return -1;
520 else {
521 DAI_DEBASSERT( f.vars() == g.vars() );
522 return dist( f.p(), g.p(), dt );
523 }
524 }
527 /// Returns the pointwise maximum of two TFactors
528 /** \relates TFactor
529 * \pre f.vars() == g.vars()
530 */
531 template<typename T> TFactor<T> max( const TFactor<T> &f, const TFactor<T> &g ) {
532 DAI_ASSERT( f._vs == g._vs );
533 return TFactor<T>( f._vs, min( f.p(), g.p() ) );
534 }
537 /// Returns the pointwise minimum of two TFactors
538 /** \relates TFactor
539 * \pre f.vars() == g.vars()
540 */
541 template<typename T> TFactor<T> min( const TFactor<T> &f, const TFactor<T> &g ) {
542 DAI_ASSERT( f._vs == g._vs );
543 return TFactor<T>( f._vs, max( f.p(), g.p() ) );
544 }
547 /// Calculates the mutual information between the two variables that f depends on, under the distribution given by f
548 /** \relates TFactor
549 * \pre f.vars().size() == 2
550 */
551 template<typename T> Real MutualInfo(const TFactor<T> &f) {
552 DAI_ASSERT( f.vars().size() == 2 );
553 VarSet::const_iterator it = f.vars().begin();
554 Var i = *it; it++; Var j = *it;
555 TFactor<T> projection = f.marginal(i) * f.marginal(j);
556 return dist( f.normalized(), projection, Prob::DISTKL );
557 }
560 /// Represents a factor with values of type Real.
561 typedef TFactor<Real> Factor;
564 } // end of namespace dai
567 #endif