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
5 This file is part of libDAI.
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.
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.
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
24 /// \brief Defines TProb<T> and Prob classes
25 /// \todo Rename to Vector<T>
28 #ifndef __defined_libdai_prob_h
29 #define __defined_libdai_prob_h
45 /// Represents a vector with entries of type \a T.
46 /** A TProb<T> is a std::vector<T> with an interface designed for dealing with probability mass functions.
47 * It is mainly used for representing measures on a finite outcome space, e.g., the probability
48 * distribution of a discrete random variable.
49 * \tparam T Should be a scalar that is castable from and to double and should support elementary arithmetic operations.
51 template <typename T
> class TProb
{
57 /// Enumerates different ways of normalizing a probability measure.
59 * - NORMPROB means that the sum of all entries should be 1;
60 * - NORMLINF means that the maximum absolute value of all entries should be 1.
62 typedef enum { NORMPROB
, NORMLINF
} NormType
;
63 /// Enumerates different distance measures between probability measures.
65 * - DISTL1 is the L-1 distance (sum of absolute values of pointwise difference);
66 * - DISTLINF is the L-inf distance (maximum absolute value of pointwise difference);
67 * - DISTTV is the Total Variation distance;
68 * - DISTKL is the Kullback-Leibler distance.
70 typedef enum { DISTL1
, DISTLINF
, DISTTV
, DISTKL
} DistType
;
72 /// Default constructor
75 /// Construct uniform distribution over n outcomes, i.e., a vector of length n with each entry set to 1/n
76 explicit TProb( size_t n
) : _p(std::vector
<T
>(n
, 1.0 / n
)) {}
78 /// Construct vector of length n with each entry set to p
79 explicit TProb( size_t n
, Real p
) : _p(n
, (T
)p
) {}
81 /// Construct vector from a range
82 /** \tparam Iterator Iterates over instances that can be cast to T.
83 * \param begin Points to first instance to be added.
84 * \param end Points just beyond last instance to be added.
85 * \param sizeHint For efficiency, the number of elements can be speficied by sizeHint.
87 template <typename Iterator
>
88 TProb( Iterator begin
, Iterator end
, size_t sizeHint
=0 ) : _p() {
89 _p
.reserve( sizeHint
);
90 _p
.insert( _p
.begin(), begin
, end
);
93 /// Returns a const reference to the vector
94 const std::vector
<T
> & p() const { return _p
; }
96 /// Returns a reference to the vector
97 std::vector
<T
> & p() { return _p
; }
99 /// Returns a copy of the i'th entry
100 T
operator[]( size_t i
) const {
108 /// Returns reference to the i'th entry
109 T
& operator[]( size_t i
) { return _p
[i
]; }
111 /// Sets all entries to x
112 TProb
<T
> & fill(T x
) {
113 std::fill( _p
.begin(), _p
.end(), x
);
117 /// Draws all entries i.i.d. from a uniform distribution on [0,1)
118 TProb
<T
> & randomize() {
119 std::generate(_p
.begin(), _p
.end(), rnd_uniform
);
123 /// Returns length of the vector, i.e., the number of entries
124 size_t size() const {
128 /// Sets entries that are smaller than epsilon to 0
129 TProb
<T
>& makeZero( Real epsilon
) {
130 for( size_t i
= 0; i
< size(); i
++ )
131 if( fabs(_p
[i
]) < epsilon
)
136 /// Sets entries that are smaller than epsilon to epsilon
137 TProb
<T
>& makePositive( Real epsilon
) {
138 for( size_t i
= 0; i
< size(); i
++ )
139 if( (0 < (Real
)_p
[i
]) && ((Real
)_p
[i
] < epsilon
) )
144 /// Multiplies each entry with scalar x
145 TProb
<T
>& operator*= (T x
) {
146 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::multiplies
<T
>(), x
) );
150 /// Returns product of *this with scalar x
151 TProb
<T
> operator* (T x
) const {
152 TProb
<T
> prod( *this );
157 /// Divides each entry by scalar x
158 TProb
<T
>& operator/= (T x
) {
162 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::divides
<T
>(), x
) );
166 /// Returns quotient of *this and scalar x
167 TProb
<T
> operator/ (T x
) const {
168 TProb
<T
> quot( *this );
173 /// Adds scalar x to each entry
174 TProb
<T
>& operator+= (T x
) {
175 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::plus
<T
>(), x
) );
179 /// Returns sum of *this and scalar x
180 TProb
<T
> operator+ (T x
) const {
181 TProb
<T
> sum( *this );
186 /// Subtracts scalar x from each entry
187 TProb
<T
>& operator-= (T x
) {
188 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::minus
<T
>(), x
) );
192 /// Returns difference of *this and scalar x
193 TProb
<T
> operator- (T x
) const {
194 TProb
<T
> diff( *this );
199 /// Lexicographical comparison (sizes should be identical)
200 bool operator<= (const TProb
<T
> & q
) const {
202 assert( size() == q
.size() );
204 for( size_t i
= 0; i
< size(); i
++ )
205 if( !(_p
[i
] <= q
[i
]) )
210 /// Pointwise multiplication with q (sizes should be identical)
211 TProb
<T
>& operator*= (const TProb
<T
> & q
) {
213 assert( size() == q
.size() );
215 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::multiplies
<T
>() );
219 /// Return product of *this with q (sizes should be identical)
220 TProb
<T
> operator* (const TProb
<T
> & q
) const {
222 assert( size() == q
.size() );
224 TProb
<T
> prod( *this );
229 /// Pointwise addition with q (sizes should be identical)
230 TProb
<T
>& operator+= (const TProb
<T
> & q
) {
232 assert( size() == q
.size() );
234 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::plus
<T
>() );
238 /// Returns sum of *this and q (sizes should be identical)
239 TProb
<T
> operator+ (const TProb
<T
> & q
) const {
241 assert( size() == q
.size() );
243 TProb
<T
> sum( *this );
248 /// Pointwise subtraction of q (sizes should be identical)
249 TProb
<T
>& operator-= (const TProb
<T
> & q
) {
251 assert( size() == q
.size() );
253 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::minus
<T
>() );
257 /// Return *this minus q (sizes should be identical)
258 TProb
<T
> operator- (const TProb
<T
> & q
) const {
260 assert( size() == q
.size() );
262 TProb
<T
> diff( *this );
267 /// Pointwise division by q, where division by 0 yields 0 (sizes should be identical)
268 TProb
<T
>& operator/= (const TProb
<T
> & q
) {
270 assert( size() == q
.size() );
272 for( size_t i
= 0; i
< size(); i
++ ) {
281 /// Pointwise division by q, where division by 0 yields +Inf (sizes should be identical)
282 TProb
<T
>& divide (const TProb
<T
> & q
) {
284 assert( size() == q
.size() );
286 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::divides
<T
>() );
290 /// Returns quotient of *this with q (sizes should be identical)
291 TProb
<T
> operator/ (const TProb
<T
> & q
) const {
293 assert( size() == q
.size() );
295 TProb
<T
> quot( *this );
300 /// Returns pointwise inverse
301 /** If zero==true; uses 1/0==0, otherwise 1/0==Inf.
303 TProb
<T
> inverse(bool zero
=true) const {
305 inv
._p
.reserve( size() );
307 for( size_t i
= 0; i
< size(); i
++ )
308 inv
._p
.push_back( _p
[i
] == 0.0 ? 0.0 : 1.0 / _p
[i
] );
310 for( size_t i
= 0; i
< size(); i
++ )
311 inv
._p
.push_back( 1.0 / _p
[i
] );
315 /// Raises entries to the power a
316 TProb
<T
>& operator^= (Real a
) {
318 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::ptr_fun
<T
, Real
, T
>(std::pow
), a
) );
322 /// Returns *this raised to the power a
323 TProb
<T
> operator^ (Real a
) const {
324 TProb
<T
> power(*this);
329 /// Returns pointwise signum
330 TProb
<T
> sgn() const {
332 x
._p
.reserve( size() );
333 for( size_t i
= 0; i
< size(); i
++ ) {
344 /// Returns pointwise absolute value
345 TProb
<T
> abs() const {
347 x
._p
.reserve( size() );
348 for( size_t i
= 0; i
< size(); i
++ )
349 x
._p
.push_back( _p
[i
] < 0 ? (-p
[i
]) : p
[i
] );
353 /// Applies exp pointwise
354 const TProb
<T
>& takeExp() {
355 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::ptr_fun
<T
, T
>(std::exp
) );
359 /// Applies log pointwise
360 /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
362 const TProb
<T
>& takeLog(bool zero
=false) {
364 for( size_t i
= 0; i
< size(); i
++ )
365 _p
[i
] = ( (_p
[i
] == 0.0) ? 0.0 : std::log( _p
[i
] ) );
367 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::ptr_fun
<T
, T
>(std::log
) );
371 /// Returns pointwise exp
372 TProb
<T
> exp() const {
378 /// Returns pointwise log
379 /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
381 TProb
<T
> log(bool zero
=false) const {
387 /// Returns sum of all entries
389 T Z
= std::accumulate( _p
.begin(), _p
.end(), (T
)0 );
393 /// Returns maximum absolute value of all entries
396 for( size_t i
= 0; i
< size(); i
++ ) {
397 Real mag
= fabs( (Real
) _p
[i
] );
404 /// Returns maximum value of all entries
406 T Z
= *std::max_element( _p
.begin(), _p
.end() );
410 /// Returns minimum value of all entries
412 T Z
= *std::min_element( _p
.begin(), _p
.end() );
416 /// Normalizes vector using the specified norm
417 T
normalize( NormType norm
=NORMPROB
) {
419 if( norm
== NORMPROB
)
421 else if( norm
== NORMLINF
)
430 /// Returns normalized copy of *this, using the specified norm
431 TProb
<T
> normalized( NormType norm
= NORMPROB
) const {
432 TProb
<T
> result(*this);
433 result
.normalize( norm
);
437 /// Returns true if one or more entries are NaN
438 bool hasNaNs() const {
439 return (std::find_if( _p
.begin(), _p
.end(), isnan
) != _p
.end());
442 /// Returns true if one or more entries are negative
443 bool hasNegatives() const {
444 return (std::find_if( _p
.begin(), _p
.end(), std::bind2nd( std::less
<Real
>(), 0.0 ) ) != _p
.end());
447 /// Returns entropy of *this
448 Real
entropy() const {
450 for( size_t i
= 0; i
< size(); i
++ )
451 S
-= (_p
[i
] == 0 ? 0 : _p
[i
] * std::log(_p
[i
]));
455 /// Returns a random index, according to the (normalized) distribution described by *this
457 double x
= rnd_uniform() * totalSum();
459 for( size_t i
= 0; i
< size(); i
++ ) {
464 return( size() - 1 );
469 /// Returns distance of p and q (sizes should be identical), measured using distance measure dt
472 template<typename T
> Real
dist( const TProb
<T
> &p
, const TProb
<T
> &q
, typename TProb
<T
>::DistType dt
) {
474 assert( p
.size() == q
.size() );
478 case TProb
<T
>::DISTL1
:
479 for( size_t i
= 0; i
< p
.size(); i
++ )
480 result
+= fabs((Real
)p
[i
] - (Real
)q
[i
]);
483 case TProb
<T
>::DISTLINF
:
484 for( size_t i
= 0; i
< p
.size(); i
++ ) {
485 Real z
= fabs((Real
)p
[i
] - (Real
)q
[i
]);
491 case TProb
<T
>::DISTTV
:
492 for( size_t i
= 0; i
< p
.size(); i
++ )
493 result
+= fabs((Real
)p
[i
] - (Real
)q
[i
]);
497 case TProb
<T
>::DISTKL
:
498 for( size_t i
= 0; i
< p
.size(); i
++ ) {
500 result
+= p
[i
] * (std::log(p
[i
]) - std::log(q
[i
]));
507 /// Writes a TProb<T> to an output stream
510 template<typename T
> std::ostream
& operator<< (std::ostream
& os
, const TProb
<T
>& P
) {
512 std::copy( P
.p().begin(), P
.p().end(), std::ostream_iterator
<T
>(os
, " ") );
518 /// Returns the TProb<T> containing the pointwise minimum of a and b (which should have equal size)
521 template<typename T
> TProb
<T
> min( const TProb
<T
> &a
, const TProb
<T
> &b
) {
522 assert( a
.size() == b
.size() );
523 TProb
<T
> result( a
.size() );
524 for( size_t i
= 0; i
< a
.size(); i
++ )
533 /// Returns the TProb<T> containing the pointwise maximum of a and b (which should have equal size)
536 template<typename T
> TProb
<T
> max( const TProb
<T
> &a
, const TProb
<T
> &b
) {
537 assert( a
.size() == b
.size() );
538 TProb
<T
> result( a
.size() );
539 for( size_t i
= 0; i
< a
.size(); i
++ )
548 /// Represents a vector with entries of type Real.
549 typedef TProb
<Real
> Prob
;
552 } // end of namespace dai