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) 2006-2009 Joris Mooij [joris dot mooij at libdai dot org]
9 */
12 /// \file
13 /// \brief Defines TProb<> and Prob classes which represent (probability) vectors (e.g., probability distributions of discrete random variables)
16 #ifndef __defined_libdai_prob_h
17 #define __defined_libdai_prob_h
20 #include <cmath>
21 #include <vector>
22 #include <ostream>
23 #include <algorithm>
24 #include <numeric>
25 #include <functional>
26 #include <dai/util.h>
27 #include <dai/exceptions.h>
30 namespace dai {
33 /// Function object that returns the value itself
34 template<typename T> struct fo_id : public std::unary_function<T, T> {
35 /// Returns \a x
36 T operator()( const T &x ) const {
37 return x;
38 }
39 };
42 /// Function object that takes the absolute value
43 template<typename T> struct fo_abs : public std::unary_function<T, T> {
44 /// Returns abs(\a x)
45 T operator()( const T &x ) const {
46 if( x < (T)0 )
47 return -x;
48 else
49 return x;
50 }
51 };
54 /// Function object that takes the exponent
55 template<typename T> struct fo_exp : public std::unary_function<T, T> {
56 /// Returns exp(\a x)
57 T operator()( const T &x ) const {
58 return exp( x );
59 }
60 };
63 /// Function object that takes the logarithm
64 template<typename T> struct fo_log : public std::unary_function<T, T> {
65 /// Returns log(\a x)
66 T operator()( const T &x ) const {
67 return log( x );
68 }
69 };
72 /// Function object that takes the logarithm, except that log(0) is defined to be 0
73 template<typename T> struct fo_log0 : public std::unary_function<T, T> {
74 /// Returns (\a x == 0 ? 0 : log(\a x))
75 T operator()( const T &x ) const {
76 if( x )
77 return log( x );
78 else
79 return 0;
80 }
81 };
84 /// Function object that takes the inverse
85 template<typename T> struct fo_inv : public std::unary_function<T, T> {
86 /// Returns 1 / \a x
87 T operator()( const T &x ) const {
88 return 1 / x;
89 }
90 };
93 /// Function object that takes the inverse, except that 1/0 is defined to be 0
94 template<typename T> struct fo_inv0 : public std::unary_function<T, T> {
95 /// Returns (\a x == 0 ? 0 : (1 / \a x))
96 T operator()( const T &x ) const {
97 if( x )
98 return 1 / x;
99 else
100 return 0;
101 }
102 };
105 /// Function object that returns p*log0(p)
106 template<typename T> struct fo_plog0p : public std::unary_function<T, T> {
107 /// Returns \a p * log0(\a p)
108 T operator()( const T &p ) const {
109 return p * dai::log0(p);
110 }
111 };
114 /// Function object similar to std::divides(), but different in that dividing by zero results in zero
115 template<typename T> struct fo_divides0 : public std::binary_function<T, T, T> {
116 /// Returns (\a y == 0 ? 0 : (\a x / \a y))
117 T operator()( const T &x, const T &y ) const {
118 if( y == (T)0 )
119 return (T)0;
120 else
121 return x / y;
122 }
123 };
126 /// Function object useful for calculating the KL distance
127 template<typename T> struct fo_KL : public std::binary_function<T, T, T> {
128 /// Returns (\a p == 0 ? 0 : (\a p * (log(\a p) - log(\a q))))
129 T operator()( const T &p, const T &q ) const {
130 if( p == (T)0 )
131 return (T)0;
132 else
133 return p * (log(p) - log(q));
134 }
135 };
138 /// Function object useful for calculating the Hellinger distance
139 template<typename T> struct fo_Hellinger : public std::binary_function<T, T, T> {
140 /// Returns (sqrt(\a p) - sqrt(\a q))^2
141 T operator()( const T &p, const T &q ) const {
142 T x = sqrt(p) - sqrt(q);
143 return x * x;
144 }
145 };
148 /// Function object that returns x to the power y
149 template<typename T> struct fo_pow : public std::binary_function<T, T, T> {
150 /// Returns (\a x ^ \a y)
151 T operator()( const T &x, const T &y ) const {
152 if( y != 1 )
153 return std::pow( x, y );
154 else
155 return x;
156 }
157 };
160 /// Function object that returns the maximum of two values
161 template<typename T> struct fo_max : public std::binary_function<T, T, T> {
162 /// Returns (\a x > y ? x : y)
163 T operator()( const T &x, const T &y ) const {
164 return (x > y) ? x : y;
165 }
166 };
169 /// Function object that returns the minimum of two values
170 template<typename T> struct fo_min : public std::binary_function<T, T, T> {
171 /// Returns (\a x > y ? y : x)
172 T operator()( const T &x, const T &y ) const {
173 return (x > y) ? y : x;
174 }
175 };
178 /// Function object that returns the absolute difference of x and y
179 template<typename T> struct fo_absdiff : public std::binary_function<T, T, T> {
180 /// Returns abs( \a x - \a y )
181 T operator()( const T &x, const T &y ) const {
182 return dai::abs( x - y );
183 }
184 };
187 /// Represents a vector with entries of type \a T.
188 /** It is simply a <tt>std::vector</tt><<em>T</em>> with an interface designed for dealing with probability mass functions.
189 *
190 * It is mainly used for representing measures on a finite outcome space, for example, the probability
191 * distribution of a discrete random variable. However, entries are not necessarily non-negative; it is also used to
192 * represent logarithms of probability mass functions.
193 *
194 * \tparam T Should be a scalar that is castable from and to dai::Real and should support elementary arithmetic operations.
195 */
196 template <typename T> class TProb {
197 private:
198 /// The vector
199 std::vector<T> _p;
201 public:
202 /// Enumerates different ways of normalizing a probability measure.
203 /**
204 * - NORMPROB means that the sum of all entries should be 1;
205 * - NORMLINF means that the maximum absolute value of all entries should be 1.
206 */
207 typedef enum { NORMPROB, NORMLINF } NormType;
208 /// Enumerates different distance measures between probability measures.
209 /**
210 * - DISTL1 is the \f$\ell_1\f$ distance (sum of absolute values of pointwise difference);
211 * - DISTLINF is the \f$\ell_\infty\f$ distance (maximum absolute value of pointwise difference);
212 * - DISTTV is the total variation distance (half of the \f$\ell_1\f$ distance);
213 * - DISTKL is the Kullback-Leibler distance (\f$\sum_i p_i (\log p_i - \log q_i)\f$).
214 * - DISTHEL is the Hellinger distance (\f$\frac{1}{2}\sum_i (\sqrt{p_i}-\sqrt{q_i})^2\f$).
215 */
216 typedef enum { DISTL1, DISTLINF, DISTTV, DISTKL, DISTHEL } DistType;
218 /// \name Constructors and destructors
219 //@{
220 /// Default constructor (constructs empty vector)
221 TProb() : _p() {}
223 /// Construct uniform probability distribution over \a n outcomes (i.e., a vector of length \a n with each entry set to \f$1/n\f$)
224 explicit TProb( size_t n ) : _p(std::vector<T>(n, (T)1 / n)) {}
226 /// Construct vector of length \a n with each entry set to \a p
227 explicit TProb( size_t n, T p ) : _p(n, p) {}
229 /// Construct vector from a range
230 /** \tparam TIterator Iterates over instances that can be cast to \a T
231 * \param begin Points to first instance to be added.
232 * \param end Points just beyond last instance to be added.
233 * \param sizeHint For efficiency, the number of entries can be speficied by \a sizeHint.
234 */
235 template <typename TIterator>
236 TProb( TIterator begin, TIterator end, size_t sizeHint=0 ) : _p() {
237 _p.reserve( sizeHint );
238 _p.insert( _p.begin(), begin, end );
239 }
241 /// Construct vector from another vector
242 /** \tparam S type of elements in \a v (should be castable to type \a T)
243 * \param v vector used for initialization
244 */
245 template <typename S>
246 TProb( const std::vector<S> &v ) : _p() {
247 _p.reserve( v.size() );
248 _p.insert( _p.begin(), v.begin(), v.end() );
249 }
250 //@}
252 /// Constant iterator over the elements
253 typedef typename std::vector<T>::const_iterator const_iterator;
254 /// Iterator over the elements
255 typedef typename std::vector<T>::iterator iterator;
256 /// Constant reverse iterator over the elements
257 typedef typename std::vector<T>::const_reverse_iterator const_reverse_iterator;
258 /// Reverse iterator over the elements
259 typedef typename std::vector<T>::reverse_iterator reverse_iterator;
261 /// \name Iterator interface
262 //@{
263 /// Returns iterator that points to the first element
264 iterator begin() { return _p.begin(); }
265 /// Returns constant iterator that points to the first element
266 const_iterator begin() const { return _p.begin(); }
268 /// Returns iterator that points beyond the last element
269 iterator end() { return _p.end(); }
270 /// Returns constant iterator that points beyond the last element
271 const_iterator end() const { return _p.end(); }
273 /// Returns reverse iterator that points to the last element
274 reverse_iterator rbegin() { return _p.rbegin(); }
275 /// Returns constant reverse iterator that points to the last element
276 const_reverse_iterator rbegin() const { return _p.rbegin(); }
278 /// Returns reverse iterator that points beyond the first element
279 reverse_iterator rend() { return _p.rend(); }
280 /// Returns constant reverse iterator that points beyond the first element
281 const_reverse_iterator rend() const { return _p.rend(); }
282 //@}
284 /// \name Queries
285 //@{
286 /// Returns a const reference to the wrapped vector
287 const std::vector<T> & p() const { return _p; }
289 /// Returns a reference to the wrapped vector
290 std::vector<T> & p() { return _p; }
292 /// Returns a copy of the \a i 'th entry
293 T operator[]( size_t i ) const {
294 #ifdef DAI_DEBUG
295 return _p.at(i);
296 #else
297 return _p[i];
298 #endif
299 }
301 /// Returns reference to the \a i 'th entry
302 T& operator[]( size_t i ) { return _p[i]; }
304 /// Returns length of the vector (i.e., the number of entries)
305 size_t size() const { return _p.size(); }
307 /// Accumulate over all values, similar to std::accumulate
308 template<typename binOp, typename unOp> T accumulate( T init, binOp op1, unOp op2 ) const {
309 T t = init;
310 for( const_iterator it = begin(); it != end(); it++ )
311 t = op1( t, op2(*it) );
312 return t;
313 }
315 /// Returns the Shannon entropy of \c *this, \f$-\sum_i p_i \log p_i\f$
316 T entropy() const { return -accumulate( (T)0, std::plus<T>(), fo_plog0p<T>() ); }
318 /// Returns maximum value of all entries
319 T max() const { return accumulate( (T)(-INFINITY), fo_max<T>(), fo_id<T>() ); }
321 /// Returns minimum value of all entries
322 T min() const { return accumulate( (T)INFINITY, fo_min<T>(), fo_id<T>() ); }
324 /// Returns sum of all entries
325 T sum() const { return accumulate( (T)0, std::plus<T>(), fo_id<T>() ); }
327 /// Return sum of absolute value of all entries
328 T sumAbs() const { return accumulate( (T)0, std::plus<T>(), fo_abs<T>() ); }
330 /// Returns maximum absolute value of all entries
331 T maxAbs() const { return accumulate( (T)0, fo_max<T>(), fo_abs<T>() ); }
333 /// Returns \c true if one or more entries are NaN
334 bool hasNaNs() const {
335 bool foundnan = false;
336 for( typename std::vector<T>::const_iterator x = _p.begin(); x != _p.end(); x++ )
337 if( isnan( *x ) ) {
338 foundnan = true;
339 break;
340 }
341 return foundnan;
342 }
344 /// Returns \c true if one or more entries are negative
345 bool hasNegatives() const {
346 return (std::find_if( _p.begin(), _p.end(), std::bind2nd( std::less<T>(), (T)0 ) ) != _p.end());
347 }
349 /// Returns a pair consisting of the index of the maximum value and the maximum value itself
350 std::pair<size_t,T> argmax() const {
351 T max = _p[0];
352 size_t arg = 0;
353 for( size_t i = 1; i < size(); i++ ) {
354 if( _p[i] > max ) {
355 max = _p[i];
356 arg = i;
357 }
358 }
359 return std::make_pair(arg,max);
360 }
362 /// Returns a random index, according to the (normalized) distribution described by *this
363 size_t draw() {
364 Real x = rnd_uniform() * sum();
365 T s = 0;
366 for( size_t i = 0; i < size(); i++ ) {
367 s += _p[i];
368 if( s > x )
369 return i;
370 }
371 return( size() - 1 );
372 }
374 /// Lexicographical comparison
375 /** \pre <tt>this->size() == q.size()</tt>
376 */
377 bool operator<= (const TProb<T> & q) const {
378 DAI_DEBASSERT( size() == q.size() );
379 return lexicographical_compare( begin(), end(), q.begin(), q.end() );
380 }
381 //@}
383 /// \name Unary transformations
384 //@{
385 /// Returns the result of applying operation \a op pointwise on \c *this
386 template<typename unaryOp> TProb<T> pwUnaryTr( unaryOp op ) const {
387 TProb<T> r;
388 r._p.reserve( size() );
389 std::transform( _p.begin(), _p.end(), back_inserter( r._p ), op );
390 return r;
391 }
393 /// Returns negative of \c *this
394 TProb<T> operator- () const { return pwUnaryTr( std::negate<T>() ); }
396 /// Returns pointwise absolute value
397 TProb<T> abs() const { return pwUnaryTr( fo_abs<T>() ); }
399 /// Returns pointwise exponent
400 TProb<T> exp() const { return pwUnaryTr( fo_exp<T>() ); }
402 /// Returns pointwise logarithm
403 /** If \a zero == \c true, uses <tt>log(0)==0</tt>; otherwise, <tt>log(0)==-Inf</tt>.
404 */
405 TProb<T> log(bool zero=false) const {
406 if( zero )
407 return pwUnaryTr( fo_log0<T>() );
408 else
409 return pwUnaryTr( fo_log<T>() );
410 }
412 /// Returns pointwise inverse
413 /** If \a zero == \c true, uses <tt>1/0==0</tt>; otherwise, <tt>1/0==Inf</tt>.
414 */
415 TProb<T> inverse(bool zero=true) const {
416 if( zero )
417 return pwUnaryTr( fo_inv0<T>() );
418 else
419 return pwUnaryTr( fo_inv<T>() );
420 }
422 /// Returns normalized copy of \c *this, using the specified norm
423 /** \throw NOT_NORMALIZABLE if the norm is zero
424 */
425 TProb<T> normalized( NormType norm = NORMPROB ) const {
426 T Z = 0;
427 if( norm == NORMPROB )
428 Z = sum();
429 else if( norm == NORMLINF )
430 Z = maxAbs();
431 if( Z == (T)0 ) {
432 DAI_THROW(NOT_NORMALIZABLE);
433 return *this;
434 } else
435 return pwUnaryTr( std::bind2nd( std::divides<T>(), Z ) );
436 }
437 //@}
439 /// \name Unary operations
440 //@{
441 /// Applies unary operation \a op pointwise
442 template<typename unaryOp> TProb<T>& pwUnaryOp( unaryOp op ) {
443 std::transform( _p.begin(), _p.end(), _p.begin(), op );
444 return *this;
445 }
447 /// Draws all entries i.i.d. from a uniform distribution on [0,1)
448 TProb<T>& randomize() {
449 std::generate( _p.begin(), _p.end(), rnd_uniform );
450 return *this;
451 }
453 /// Sets all entries to \f$1/n\f$ where \a n is the length of the vector
454 TProb<T>& setUniform () {
455 fill( (T)1 / size() );
456 return *this;
457 }
459 /// Applies absolute value pointwise
460 const TProb<T>& takeAbs() { return pwUnaryOp( fo_abs<T>() ); }
462 /// Applies exponent pointwise
463 const TProb<T>& takeExp() { return pwUnaryOp( fo_exp<T>() ); }
465 /// Applies logarithm pointwise
466 /** If \a zero == \c true, uses <tt>log(0)==0</tt>; otherwise, <tt>log(0)==-Inf</tt>.
467 */
468 const TProb<T>& takeLog(bool zero=false) {
469 if( zero ) {
470 return pwUnaryOp( fo_log0<T>() );
471 } else
472 return pwUnaryOp( fo_log<T>() );
473 }
475 /// Normalizes vector using the specified norm
476 /** \throw NOT_NORMALIZABLE if the norm is zero
477 */
478 T normalize( NormType norm=NORMPROB ) {
479 T Z = 0;
480 if( norm == NORMPROB )
481 Z = sum();
482 else if( norm == NORMLINF )
483 Z = maxAbs();
484 if( Z == (T)0 )
485 DAI_THROW(NOT_NORMALIZABLE);
486 else
487 *this /= Z;
488 return Z;
489 }
490 //@}
492 /// \name Operations with scalars
493 //@{
494 /// Sets all entries to \a x
495 TProb<T> & fill(T x) {
496 std::fill( _p.begin(), _p.end(), x );
497 return *this;
498 }
500 /// Adds scalar \a x to each entry
501 TProb<T>& operator+= (T x) {
502 if( x != 0 )
503 return pwUnaryOp( std::bind2nd( std::plus<T>(), x ) );
504 else
505 return *this;
506 }
508 /// Subtracts scalar \a x from each entry
509 TProb<T>& operator-= (T x) {
510 if( x != 0 )
511 return pwUnaryOp( std::bind2nd( std::minus<T>(), x ) );
512 else
513 return *this;
514 }
516 /// Multiplies each entry with scalar \a x
517 TProb<T>& operator*= (T x) {
518 if( x != 1 )
519 return pwUnaryOp( std::bind2nd( std::multiplies<T>(), x ) );
520 else
521 return *this;
522 }
524 /// Divides each entry by scalar \a x
525 TProb<T>& operator/= (T x) {
526 DAI_DEBASSERT( x != 0 );
527 if( x != 1 )
528 return pwUnaryOp( std::bind2nd( std::divides<T>(), x ) );
529 else
530 return *this;
531 }
533 /// Raises entries to the power \a x
534 TProb<T>& operator^= (T x) {
535 if( x != (T)1 )
536 return pwUnaryOp( std::bind2nd( fo_pow<T>(), x) );
537 else
538 return *this;
539 }
540 //@}
542 /// \name Transformations with scalars
543 //@{
544 /// Returns sum of \c *this and scalar \a x
545 TProb<T> operator+ (T x) const { return pwUnaryTr( std::bind2nd( std::plus<T>(), x ) ); }
547 /// Returns difference of \c *this and scalar \a x
548 TProb<T> operator- (T x) const { return pwUnaryTr( std::bind2nd( std::minus<T>(), x ) ); }
550 /// Returns product of \c *this with scalar \a x
551 TProb<T> operator* (T x) const { return pwUnaryTr( std::bind2nd( std::multiplies<T>(), x ) ); }
553 /// Returns quotient of \c *this and scalar \a x, where division by 0 yields 0
554 TProb<T> operator/ (T x) const { return pwUnaryTr( std::bind2nd( fo_divides0<T>(), x ) ); }
556 /// Returns \c *this raised to the power \a x
557 TProb<T> operator^ (T x) const { return pwUnaryTr( std::bind2nd( fo_pow<T>(), x ) ); }
558 //@}
560 /// \name Operations with other equally-sized vectors
561 //@{
562 /// Applies binary operation pointwise on two vectors
563 /** \tparam binaryOp Type of function object that accepts two arguments of type \a T and outputs a type \a T
564 * \param q Right operand
565 * \param op Operation of type \a binaryOp
566 */
567 template<typename binaryOp> TProb<T>& pwBinaryOp( const TProb<T> &q, binaryOp op ) {
568 DAI_DEBASSERT( size() == q.size() );
569 std::transform( _p.begin(), _p.end(), q._p.begin(), _p.begin(), op );
570 return *this;
571 }
573 /// Pointwise addition with \a q
574 /** \pre <tt>this->size() == q.size()</tt>
575 */
576 TProb<T>& operator+= (const TProb<T> & q) { return pwBinaryOp( q, std::plus<T>() ); }
578 /// Pointwise subtraction of \a q
579 /** \pre <tt>this->size() == q.size()</tt>
580 */
581 TProb<T>& operator-= (const TProb<T> & q) { return pwBinaryOp( q, std::minus<T>() ); }
583 /// Pointwise multiplication with \a q
584 /** \pre <tt>this->size() == q.size()</tt>
585 */
586 TProb<T>& operator*= (const TProb<T> & q) { return pwBinaryOp( q, std::multiplies<T>() ); }
588 /// Pointwise division by \a q, where division by 0 yields 0
589 /** \pre <tt>this->size() == q.size()</tt>
590 * \see divide(const TProb<T> &)
591 */
592 TProb<T>& operator/= (const TProb<T> & q) { return pwBinaryOp( q, fo_divides0<T>() ); }
594 /// Pointwise division by \a q, where division by 0 yields +Inf
595 /** \pre <tt>this->size() == q.size()</tt>
596 * \see operator/=(const TProb<T> &)
597 */
598 TProb<T>& divide (const TProb<T> & q) { return pwBinaryOp( q, std::divides<T>() ); }
600 /// Pointwise power
601 /** \pre <tt>this->size() == q.size()</tt>
602 */
603 TProb<T>& operator^= (const TProb<T> & q) { return pwBinaryOp( q, fo_pow<T>() ); }
604 //@}
606 /// \name Transformations with other equally-sized vectors
607 //@{
608 /// Returns the result of applying binary operation \a op pointwise on \c *this and \a q
609 /** \tparam binaryOp Type of function object that accepts two arguments of type \a T and outputs a type \a T
610 * \param q Right operand
611 * \param op Operation of type \a binaryOp
612 */
613 template<typename binaryOp> TProb<T> pwBinaryTr( const TProb<T> &q, binaryOp op ) const {
614 DAI_DEBASSERT( size() == q.size() );
615 TProb<T> r;
616 r._p.reserve( size() );
617 std::transform( _p.begin(), _p.end(), q._p.begin(), back_inserter( r._p ), op );
618 return r;
619 }
621 /// Returns sum of \c *this and \a q
622 /** \pre <tt>this->size() == q.size()</tt>
623 */
624 TProb<T> operator+ ( const TProb<T>& q ) const { return pwBinaryTr( q, std::plus<T>() ); }
626 /// Return \c *this minus \a q
627 /** \pre <tt>this->size() == q.size()</tt>
628 */
629 TProb<T> operator- ( const TProb<T>& q ) const { return pwBinaryTr( q, std::minus<T>() ); }
631 /// Return product of \c *this with \a q
632 /** \pre <tt>this->size() == q.size()</tt>
633 */
634 TProb<T> operator* ( const TProb<T> &q ) const { return pwBinaryTr( q, std::multiplies<T>() ); }
636 /// Returns quotient of \c *this with \a q, where division by 0 yields 0
637 /** \pre <tt>this->size() == q.size()</tt>
638 * \see divided_by(const TProb<T> &)
639 */
640 TProb<T> operator/ ( const TProb<T> &q ) const { return pwBinaryTr( q, fo_divides0<T>() ); }
642 /// Pointwise division by \a q, where division by 0 yields +Inf
643 /** \pre <tt>this->size() == q.size()</tt>
644 * \see operator/(const TProb<T> &)
645 */
646 TProb<T> divided_by( const TProb<T> &q ) const { return pwBinaryTr( q, std::divides<T>() ); }
648 /// Returns \c *this to the power \a q
649 /** \pre <tt>this->size() == q.size()</tt>
650 */
651 TProb<T> operator^ ( const TProb<T> &q ) const { return pwBinaryTr( q, fo_pow<T>() ); }
652 //@}
654 /// Performs a generalized inner product, similar to std::inner_product
655 /** \pre <tt>this->size() == q.size()</tt>
656 */
657 template<typename binOp1, typename binOp2> T innerProduct( const TProb<T> &q, T init, binOp1 binaryOp1, binOp2 binaryOp2 ) const {
658 DAI_DEBASSERT( size() == q.size() );
659 return std::inner_product( begin(), end(), q.begin(), init, binaryOp1, binaryOp2 );
660 }
661 };
664 /// Returns distance between \a p and \a q, measured using distance measure \a dt
665 /** \relates TProb
666 * \pre <tt>this->size() == q.size()</tt>
667 */
668 template<typename T> T dist( const TProb<T> &p, const TProb<T> &q, typename TProb<T>::DistType dt ) {
669 switch( dt ) {
670 case TProb<T>::DISTL1:
671 return p.innerProduct( q, (T)0, std::plus<T>(), fo_absdiff<T>() );
672 case TProb<T>::DISTLINF:
673 return p.innerProduct( q, (T)0, fo_max<T>(), fo_absdiff<T>() );
674 case TProb<T>::DISTTV:
675 return p.innerProduct( q, (T)0, std::plus<T>(), fo_absdiff<T>() ) / 2;
676 case TProb<T>::DISTKL:
677 return p.innerProduct( q, (T)0, std::plus<T>(), fo_KL<T>() );
678 case TProb<T>::DISTHEL:
679 return p.innerProduct( q, (T)0, std::plus<T>(), fo_Hellinger<T>() ) / 2;
680 default:
681 DAI_THROW(UNKNOWN_ENUM_VALUE);
682 return INFINITY;
683 }
684 }
687 /// Writes a TProb<T> to an output stream
688 /** \relates TProb
689 */
690 template<typename T> std::ostream& operator<< (std::ostream& os, const TProb<T>& p) {
691 os << "[";
692 std::copy( p.p().begin(), p.p().end(), std::ostream_iterator<T>(os, " ") );
693 os << "]";
694 return os;
695 }
698 /// Returns the pointwise minimum of \a a and \a b
699 /** \relates TProb
700 * \pre <tt>this->size() == q.size()</tt>
701 */
702 template<typename T> TProb<T> min( const TProb<T> &a, const TProb<T> &b ) {
703 return a.pwBinaryTr( b, fo_min<T>() );
704 }
707 /// Returns the pointwise maximum of \a a and \a b
708 /** \relates TProb
709 * \pre <tt>this->size() == q.size()</tt>
710 */
711 template<typename T> TProb<T> max( const TProb<T> &a, const TProb<T> &b ) {
712 return a.pwBinaryTr( b, fo_max<T>() );
713 }
716 /// Represents a vector with entries of type dai::Real.
717 typedef TProb<Real> Prob;
720 } // end of namespace dai
723 #endif