1427002ba5ef6c8990680611dc0d166b81c06250
[libdai.git] / 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 <functional>
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 /// Function object similar to std::divides(), but different in that dividing by zero results in zero
46 template<typename T> struct divides0 : public std::binary_function<T, T, T> {
47 T operator()(const T& i, const T& j) const {
48 if( j == (T)0 )
49 return (T)0;
50 else
51 return i / j;
52 }
53 };
54
55
56 /// Represents a (probability) factor.
57 /** Mathematically, a \e factor is a function mapping joint states of some
58 * variables to the nonnegative real numbers.
59 * More formally, denoting a discrete variable with label \f$l\f$ by
60 * \f$x_l\f$ and its state space by \f$X_l = \{0,1,\dots,S_l-1\}\f$,
61 * then a factor depending on the variables \f$\{x_l\}_{l\in L}\f$ is
62 * a function \f$f_L : \prod_{l\in L} X_l \to [0,\infty)\f$.
63 *
64 * In libDAI, a factor is represented by a TFactor<\a T> object, which has two
65 * components:
66 * \arg a VarSet, corresponding with the set of variables \f$\{x_l\}_{l\in L}\f$
67 * that the factor depends on;
68 * \arg a TProb<\a T>, a vector containing the value of the factor for each possible
69 * joint state of the variables.
70 *
71 * The factor values are stored in the entries of the TProb<\a T> in a particular
72 * ordering, which is defined by the one-to-one correspondence of a joint state
73 * in \f$\prod_{l\in L} X_l\f$ with a linear index in
74 * \f$\{0,1,\dots,\prod_{l\in L} S_l-1\}\f$ according to the mapping \f$\sigma\f$
75 * induced by VarSet::calcState(const std::map<Var,size_t> &).
76 *
77 * \tparam T Should be a scalar that is castable from and to double and should support elementary arithmetic operations.
78 * \todo Define a better fileformat for .fg files (maybe using XML)?
79 * \todo Add support for sparse factors.
80 */
81 template <typename T> class TFactor {
82 private:
83 VarSet _vs;
84 TProb<T> _p;
85
86 public:
87 /// Iterator over factor entries
88 typedef typename TProb<T>::iterator iterator;
89
90 /// Const iterator over factor entries
91 typedef typename TProb<T>::const_iterator const_iterator;
92
93 /// Constructs TFactor depending on no variables, with value p
94 TFactor ( Real p = 1.0 ) : _vs(), _p(1,p) {}
95
96 /// Constructs TFactor depending on variables in ns, with uniform distribution
97 TFactor( const VarSet& ns ) : _vs(ns), _p(_vs.nrStates()) {}
98
99 /// Constructs TFactor depending on variables in ns, with all values set to p
100 TFactor( const VarSet& ns, Real p ) : _vs(ns), _p(_vs.nrStates(),p) {}
101
102 /// Constructs TFactor depending on variables in ns, copying the values from the range starting at begin
103 /** \param ns contains the variables that the new TFactor should depend on.
104 * \tparam Iterator Iterates over instances of type T; should support addition of size_t.
105 * \param begin Points to first element to be added.
106 */
107 template<typename TIterator>
108 TFactor( const VarSet& ns, TIterator begin ) : _vs(ns), _p(begin, begin + _vs.nrStates(), _vs.nrStates()) {}
109
110 /// Constructs TFactor depending on variables in ns, with values set to the TProb p
111 TFactor( const VarSet& ns, const TProb<T>& p ) : _vs(ns), _p(p) {
112 #ifdef DAI_DEBUG
113 assert( _vs.nrStates() == _p.size() );
114 #endif
115 }
116 TFactor( const std::vector< Var >& vars, const std::vector< T >& p ) : _vs(vars.begin(), vars.end(), vars.size()), _p(p.size()) {
117 Permute permindex(vars);
118 for (size_t li = 0; li < p.size(); ++li) {
119 _p[permindex.convert_linear_index(li)] = p[li];
120 }
121 }
122
123 /// Constructs TFactor depending on the variable n, with uniform distribution
124 TFactor( const Var& n ) : _vs(n), _p(n.states()) {}
125
126 /// Returns const reference to value vector
127 const TProb<T> & p() const { return _p; }
128 /// Returns reference to value vector
129 TProb<T> & p() { return _p; }
130
131 /// Returns const reference to variable set
132 const VarSet & vars() const { return _vs; }
133
134 /// Returns the number of possible joint states of the variables
135 /** \note This is equal to the length of the value vector.
136 */
137 size_t states() const { return _p.size(); }
138
139 /// Returns a copy of the i'th entry of the value vector
140 T operator[] (size_t i) const { return _p[i]; }
141
142 /// Returns a reference to the i'th entry of the value vector
143 T& operator[] (size_t i) { return _p[i]; }
144
145 /// Returns iterator pointing to first entry
146 iterator begin() { return _p.begin(); }
147 /// Returns const iterator pointing to first entry
148 const_iterator begin() const { return _p.begin(); }
149 /// Returns iterator pointing beyond last entry
150 iterator end() { return _p.end(); }
151 /// Returns const iterator pointing beyond last entry
152 const_iterator end() const { return _p.end(); }
153
154 /// Sets all values to p
155 TFactor<T> & fill (T p) { _p.fill( p ); return(*this); }
156
157 /// Draws all values i.i.d. from a uniform distribution on [0,1)
158 TFactor<T> & randomize () { _p.randomize(); return(*this); }
159
160
161 /// Multiplies *this with scalar t
162 TFactor<T>& operator*= (T t) {
163 _p *= t;
164 return *this;
165 }
166
167 /// Divides *this by scalar t
168 TFactor<T>& operator/= (T t) {
169 _p /= t;
170 return *this;
171 }
172
173 /// Adds scalar t to *this
174 TFactor<T>& operator+= (T t) {
175 _p += t;
176 return *this;
177 }
178
179 /// Subtracts scalar t from *this
180 TFactor<T>& operator-= (T t) {
181 _p -= t;
182 return *this;
183 }
184
185 /// Raises *this to the power a
186 TFactor<T>& operator^= (Real a) { _p ^= a; return *this; }
187
188
189 /// Returns product of *this with scalar t
190 TFactor<T> operator* (T t) const {
191 TFactor<T> result = *this;
192 result.p() *= t;
193 return result;
194 }
195
196 /// Returns quotient of *this with scalar t
197 TFactor<T> operator/ (T t) const {
198 TFactor<T> result = *this;
199 result.p() /= t;
200 return result;
201 }
202
203 /// Returns sum of *this and scalar t
204 TFactor<T> operator+ (T t) const {
205 TFactor<T> result(*this);
206 result._p += t;
207 return result;
208 }
209
210 /// Returns *this minus scalar t
211 TFactor<T> operator- (T t) const {
212 TFactor<T> result(*this);
213 result._p -= t;
214 return result;
215 }
216
217 /// Returns *this raised to the power a
218 TFactor<T> operator^ (Real a) const {
219 TFactor<T> x;
220 x._vs = _vs;
221 x._p = _p^a;
222 return x;
223 }
224
225 /// Multiplies *this with the TFactor f
226 TFactor<T>& operator*= (const TFactor<T>& f) {
227 if( f._vs == _vs ) // optimize special case
228 _p *= f._p;
229 else
230 *this = (*this * f);
231 return *this;
232 }
233
234 /// Divides *this by the TFactor f
235 TFactor<T>& operator/= (const TFactor<T>& f) {
236 if( f._vs == _vs ) // optimize special case
237 _p /= f._p;
238 else
239 *this = (*this / f);
240 return *this;
241 }
242
243 /// Adds the TFactor f to *this
244 TFactor<T>& operator+= (const TFactor<T>& f) {
245 if( f._vs == _vs ) // optimize special case
246 _p += f._p;
247 else
248 *this = (*this + f);
249 return *this;
250 }
251
252 /// Subtracts the TFactor f from *this
253 TFactor<T>& operator-= (const TFactor<T>& f) {
254 if( f._vs == _vs ) // optimize special case
255 _p -= f._p;
256 else
257 *this = (*this - f);
258 return *this;
259 }
260
261 /// Returns product of *this with the TFactor f
262 /** The product of two factors is defined as follows: if
263 * \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
264 * \f[fg : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) g(x_M).\f]
265 */
266 TFactor<T> operator* (const TFactor<T>& f) const {
267 return pointwiseOp(*this,f,std::multiplies<T>());
268 }
269
270 /// Returns quotient of *this by the TFactor f
271 /** The quotient of two factors is defined as follows: if
272 * \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
273 * \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]
274 */
275 TFactor<T> operator/ (const TFactor<T>& f) const {
276 return pointwiseOp(*this,f,divides0<T>());
277 }
278
279 /// Returns sum of *this and the TFactor f
280 /** The sum of two factors is defined as follows: if
281 * \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
282 * \f[f+g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) + g(x_M).\f]
283 */
284 TFactor<T> operator+ (const TFactor<T>& f) const {
285 return pointwiseOp(*this,f,std::plus<T>());
286 }
287
288 /// Returns *this minus the TFactor f
289 /** The difference of two factors is defined as follows: if
290 * \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
291 * \f[f-g : \prod_{l\in L\cup M} X_l \to [0,\infty) : x \mapsto f(x_L) - g(x_M).\f]
292 */
293 TFactor<T> operator- (const TFactor<T>& f) const {
294 return pointwiseOp(*this,f,std::minus<T>());
295 }
296
297
298 /// Sets all values that are smaller than epsilon to 0
299 TFactor<T>& makeZero( T epsilon ) {
300 _p.makeZero( epsilon );
301 return *this;
302 }
303
304 /// Sets all values that are smaller than epsilon to epsilon
305 TFactor<T>& makePositive( T epsilon ) {
306 _p.makePositive( epsilon );
307 return *this;
308 }
309
310 /// Returns pointwise inverse of *this.
311 /** If zero == true, uses 1 / 0 == 0; otherwise 1 / 0 == Inf.
312 */
313 TFactor<T> inverse(bool zero=true) const {
314 TFactor<T> inv;
315 inv._vs = _vs;
316 inv._p = _p.inverse(zero);
317 return inv;
318 }
319
320 /// Returns pointwise exp of *this
321 TFactor<T> exp() const {
322 TFactor<T> e;
323 e._vs = _vs;
324 e._p = _p.exp();
325 return e;
326 }
327
328 /// Returns pointwise logarithm of *this
329 /** If zero==true, uses log(0)==0; otherwise, log(0)=-Inf.
330 */
331 TFactor<T> log(bool zero=false) const {
332 TFactor<T> l;
333 l._vs = _vs;
334 l._p = _p.log(zero);
335 return l;
336 }
337
338 /// Returns pointwise absolute value of *this
339 TFactor<T> abs() const {
340 TFactor<T> e;
341 e._vs = _vs;
342 e._p = _p.abs();
343 return e;
344 }
345
346 /// Normalizes *this TFactor according to the specified norm
347 T normalize( typename Prob::NormType norm=Prob::NORMPROB ) { return _p.normalize( norm ); }
348
349 /// Returns a normalized copy of *this, according to the specified norm
350 TFactor<T> normalized( typename Prob::NormType norm=Prob::NORMPROB ) const {
351 TFactor<T> result;
352 result._vs = _vs;
353 result._p = _p.normalized( norm );
354 return result;
355 }
356
357 /// Returns a slice of this TFactor, where the subset ns is in state nsState
358 /** \pre \a ns sould be a subset of vars()
359 * \pre \a nsState < ns.states()
360 *
361 * The result is a TFactor that depends on the variables in this->vars() except those in \a ns,
362 * obtained by setting the variables in \a ns to the joint state specified by the linear index
363 * \a nsState. Formally, if *this corresponds with the factor \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$,
364 * \f$M \subset L\f$ corresponds with \a ns and \a nsState corresponds with a mapping \f$s\f$ that
365 * 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
366 * returned corresponds with the factor \f$g : \prod_{l \in L \setminus M} X_l \to [0,\infty)\f$
367 * defined by \f$g(\{x_l\}_{l\in L \setminus M}) = f(\{x_l\}_{l\in L \setminus M}, \{s(x_m)\}_{m\in M})\f$.
368 */
369 TFactor<T> slice( const VarSet& ns, size_t nsState ) const {
370 assert( ns << _vs );
371 VarSet nsrem = _vs / ns;
372 TFactor<T> result( nsrem, T(0) );
373
374 // OPTIMIZE ME
375 IndexFor i_ns (ns, _vs);
376 IndexFor i_nsrem (nsrem, _vs);
377 for( size_t i = 0; i < states(); i++, ++i_ns, ++i_nsrem )
378 if( (size_t)i_ns == nsState )
379 result._p[i_nsrem] = _p[i];
380
381 return result;
382 }
383
384 /// Returns marginal on ns, obtained by summing out all variables except those in ns, and normalizing the result if normed==true
385 TFactor<T> marginal(const VarSet & ns, bool normed=true) const;
386
387 /// Returns max-marginal on ns, obtained by maximizing all variables except those in ns, and normalizing the result if normed==true
388 TFactor<T> maxMarginal(const VarSet & ns, bool normed=true) const;
389
390 /// Embeds this factor in a larger VarSet
391 /** \pre vars() should be a subset of ns
392 *
393 * If *this corresponds with \f$f : \prod_{l\in L} X_l \to [0,\infty)\f$ and \f$L \subset M\f$, then
394 * the embedded factor corresponds with \f$g : \prod_{m\in M} X_m \to [0,\infty) : x \mapsto f(x_L)\f$.
395 */
396 TFactor<T> embed(const VarSet & ns) const {
397 assert( ns >> _vs );
398 if( _vs == ns )
399 return *this;
400 else
401 return (*this) * TFactor<T>(ns / _vs, (T)1);
402 }
403
404 /// Returns true if *this has NaN values
405 bool hasNaNs() const { return _p.hasNaNs(); }
406
407 /// Returns true if *this has negative values
408 bool hasNegatives() const { return _p.hasNegatives(); }
409
410 /// Returns total sum of values
411 T sum() const { return _p.sum(); }
412
413 /// Returns maximum absolute value
414 T maxAbs() const { return _p.maxAbs(); }
415
416 /// Returns maximum value
417 T max() const { return _p.max(); }
418
419 /// Returns minimum value
420 T min() const { return _p.min(); }
421
422 /// Returns entropy of *this TFactor
423 Real entropy() const { return _p.entropy(); }
424
425 /// Returns strength of *this TFactor (between variables i and j), as defined in eq. (52) of [\ref MoK07b]
426 T strength( const Var &i, const Var &j ) const;
427 };
428
429
430 template<typename T> TFactor<T> TFactor<T>::marginal(const VarSet & ns, bool normed) const {
431 VarSet res_ns = ns & _vs;
432
433 TFactor<T> res( res_ns, 0.0 );
434
435 IndexFor i_res( res_ns, _vs );
436 for( size_t i = 0; i < _p.size(); i++, ++i_res )
437 res._p[i_res] += _p[i];
438
439 if( normed )
440 res.normalize( Prob::NORMPROB );
441
442 return res;
443 }
444
445
446 template<typename T> TFactor<T> TFactor<T>::maxMarginal(const VarSet & ns, bool normed) const {
447 VarSet res_ns = ns & _vs;
448
449 TFactor<T> res( res_ns, 0.0 );
450
451 IndexFor i_res( res_ns, _vs );
452 for( size_t i = 0; i < _p.size(); i++, ++i_res )
453 if( _p[i] > res._p[i_res] )
454 res._p[i_res] = _p[i];
455
456 if( normed )
457 res.normalize( Prob::NORMPROB );
458
459 return res;
460 }
461
462
463 template<typename T, typename binaryOp> TFactor<T> pointwiseOp( const TFactor<T> &f, const TFactor<T> &g, binaryOp op ) {
464 if( f.vars() == g.vars() ) { // optimizate special case
465 TFactor<T> result(f);
466 for( size_t i = 0; i < result.states(); i++ )
467 result[i] = op( result[i], g[i] );
468 return result;
469 } else {
470 TFactor<T> result( f.vars() | g.vars(), 0.0 );
471
472 IndexFor i1(f.vars(), result.vars());
473 IndexFor i2(g.vars(), result.vars());
474
475 for( size_t i = 0; i < result.states(); i++, ++i1, ++i2 )
476 result[i] = op( f[i1], g[i2] );
477
478 return result;
479 }
480 }
481
482
483 template<typename T> T TFactor<T>::strength( const Var &i, const Var &j ) const {
484 #ifdef DAI_DEBUG
485 assert( _vs.contains( i ) );
486 assert( _vs.contains( j ) );
487 assert( i != j );
488 #endif
489 VarSet ij(i, j);
490
491 T max = 0.0;
492 for( size_t alpha1 = 0; alpha1 < i.states(); alpha1++ )
493 for( size_t alpha2 = 0; alpha2 < i.states(); alpha2++ )
494 if( alpha2 != alpha1 )
495 for( size_t beta1 = 0; beta1 < j.states(); beta1++ )
496 for( size_t beta2 = 0; beta2 < j.states(); beta2++ )
497 if( beta2 != beta1 ) {
498 size_t as = 1, bs = 1;
499 if( i < j )
500 bs = i.states();
501 else
502 as = j.states();
503 T f1 = slice( ij, alpha1 * as + beta1 * bs ).p().divide( slice( ij, alpha2 * as + beta1 * bs ).p() ).max();
504 T f2 = slice( ij, alpha2 * as + beta2 * bs ).p().divide( slice( ij, alpha1 * as + beta2 * bs ).p() ).max();
505 T f = f1 * f2;
506 if( f > max )
507 max = f;
508 }
509
510 return std::tanh( 0.25 * std::log( max ) );
511 }
512
513
514 /// Writes a TFactor to an output stream
515 /** \relates TFactor
516 */
517 template<typename T> std::ostream& operator<< (std::ostream& os, const TFactor<T>& P) {
518 os << "(" << P.vars() << ", (";
519 for( size_t i = 0; i < P.states(); i++ )
520 os << (i == 0 ? "" : ", ") << P[i];
521 os << "))";
522 return os;
523 }
524
525
526 /// Returns distance between two TFactors f and g, according to the distance measure dt
527 /** \relates TFactor
528 * \pre f.vars() == g.vars()
529 */
530 template<typename T> Real dist( const TFactor<T> &f, const TFactor<T> &g, Prob::DistType dt ) {
531 if( f.vars().empty() || g.vars().empty() )
532 return -1;
533 else {
534 #ifdef DAI_DEBUG
535 assert( f.vars() == g.vars() );
536 #endif
537 return dist( f.p(), g.p(), dt );
538 }
539 }
540
541
542 /// Returns the pointwise maximum of two TFactors
543 /** \relates TFactor
544 * \pre f.vars() == g.vars()
545 */
546 template<typename T> TFactor<T> max( const TFactor<T> &f, const TFactor<T> &g ) {
547 assert( f._vs == g._vs );
548 return TFactor<T>( f._vs, min( f.p(), g.p() ) );
549 }
550
551
552 /// Returns the pointwise minimum of two TFactors
553 /** \relates TFactor
554 * \pre f.vars() == g.vars()
555 */
556 template<typename T> TFactor<T> min( const TFactor<T> &f, const TFactor<T> &g ) {
557 assert( f._vs == g._vs );
558 return TFactor<T>( f._vs, max( f.p(), g.p() ) );
559 }
560
561
562 /// Calculates the mutual information between the two variables that f depends on, under the distribution given by f
563 /** \relates TFactor
564 * \pre f.vars().size() == 2
565 */
566 template<typename T> Real MutualInfo(const TFactor<T> &f) {
567 assert( f.vars().size() == 2 );
568 VarSet::const_iterator it = f.vars().begin();
569 Var i = *it; it++; Var j = *it;
570 TFactor<T> projection = f.marginal(i) * f.marginal(j);
571 return dist( f.normalized(), projection, Prob::DISTKL );
572 }
573
574
575 /// Represents a factor with values of type Real.
576 typedef TFactor<Real> Factor;
577
578
579 } // end of namespace dai
580
581
582 #endif