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 of length n by copying the elements between p and p+n
82 TProb( size_t n
, const Real
* p
) : _p(p
, p
+ n
) {}
84 /// Returns a const reference to the vector
85 const std::vector
<T
> & p() const { return _p
; }
87 /// Returns a reference to the vector
88 std::vector
<T
> & p() { return _p
; }
90 /// Returns a copy of the i'th entry
91 T
operator[]( size_t i
) const {
99 /// Returns reference to the i'th entry
100 T
& operator[]( size_t i
) { return _p
[i
]; }
102 /// Sets all entries to x
103 TProb
<T
> & fill(T x
) {
104 std::fill( _p
.begin(), _p
.end(), x
);
108 /// Draws all entries i.i.d. from a uniform distribution on [0,1)
109 TProb
<T
> & randomize() {
110 std::generate(_p
.begin(), _p
.end(), rnd_uniform
);
114 /// Returns length of the vector, i.e., the number of entries
115 size_t size() const {
119 /// Sets entries that are smaller than epsilon to 0
120 TProb
<T
>& makeZero( Real epsilon
) {
121 for( size_t i
= 0; i
< size(); i
++ )
122 if( fabs(_p
[i
]) < epsilon
)
127 /// Sets entries that are smaller than epsilon to epsilon
128 TProb
<T
>& makePositive( Real epsilon
) {
129 for( size_t i
= 0; i
< size(); i
++ )
130 if( (0 < (Real
)_p
[i
]) && ((Real
)_p
[i
] < epsilon
) )
135 /// Multiplies each entry with scalar x
136 TProb
<T
>& operator*= (T x
) {
137 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::multiplies
<T
>(), x
) );
141 /// Returns product of *this with scalar x
142 TProb
<T
> operator* (T x
) const {
143 TProb
<T
> prod( *this );
148 /// Divides each entry by scalar x
149 TProb
<T
>& operator/= (T x
) {
153 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::divides
<T
>(), x
) );
157 /// Returns quotient of *this and scalar x
158 TProb
<T
> operator/ (T x
) const {
159 TProb
<T
> quot( *this );
164 /// Adds scalar x to each entry
165 TProb
<T
>& operator+= (T x
) {
166 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::plus
<T
>(), x
) );
170 /// Returns sum of *this and scalar x
171 TProb
<T
> operator+ (T x
) const {
172 TProb
<T
> sum( *this );
177 /// Subtracts scalar x from each entry
178 TProb
<T
>& operator-= (T x
) {
179 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::minus
<T
>(), x
) );
183 /// Returns difference of *this and scalar x
184 TProb
<T
> operator- (T x
) const {
185 TProb
<T
> diff( *this );
190 /// Lexicographical comparison (sizes should be identical)
191 bool operator<= (const TProb
<T
> & q
) const {
193 assert( size() == q
.size() );
195 for( size_t i
= 0; i
< size(); i
++ )
196 if( !(_p
[i
] <= q
[i
]) )
201 /// Pointwise multiplication with q (sizes should be identical)
202 TProb
<T
>& operator*= (const TProb
<T
> & q
) {
204 assert( size() == q
.size() );
206 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::multiplies
<T
>() );
210 /// Return product of *this with q (sizes should be identical)
211 TProb
<T
> operator* (const TProb
<T
> & q
) const {
213 assert( size() == q
.size() );
215 TProb
<T
> prod( *this );
220 /// Pointwise addition with q (sizes should be identical)
221 TProb
<T
>& operator+= (const TProb
<T
> & q
) {
223 assert( size() == q
.size() );
225 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::plus
<T
>() );
229 /// Returns sum of *this and q (sizes should be identical)
230 TProb
<T
> operator+ (const TProb
<T
> & q
) const {
232 assert( size() == q
.size() );
234 TProb
<T
> sum( *this );
239 /// Pointwise subtraction of q (sizes should be identical)
240 TProb
<T
>& operator-= (const TProb
<T
> & q
) {
242 assert( size() == q
.size() );
244 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::minus
<T
>() );
248 /// Return *this minus q (sizes should be identical)
249 TProb
<T
> operator- (const TProb
<T
> & q
) const {
251 assert( size() == q
.size() );
253 TProb
<T
> diff( *this );
258 /// Pointwise division by q, where division by 0 yields 0 (sizes should be identical)
259 TProb
<T
>& operator/= (const TProb
<T
> & q
) {
261 assert( size() == q
.size() );
263 for( size_t i
= 0; i
< size(); i
++ ) {
272 /// Pointwise division by q, where division by 0 yields +Inf (sizes should be identical)
273 TProb
<T
>& divide (const TProb
<T
> & q
) {
275 assert( size() == q
.size() );
277 std::transform( _p
.begin(), _p
.end(), q
._p
.begin(), _p
.begin(), std::divides
<T
>() );
281 /// Returns quotient of *this with q (sizes should be identical)
282 TProb
<T
> operator/ (const TProb
<T
> & q
) const {
284 assert( size() == q
.size() );
286 TProb
<T
> quot( *this );
291 /// Returns pointwise inverse
292 /** If zero==true; uses 1/0==0, otherwise 1/0==Inf.
294 TProb
<T
> inverse(bool zero
=true) const {
296 inv
._p
.reserve( size() );
298 for( size_t i
= 0; i
< size(); i
++ )
299 inv
._p
.push_back( _p
[i
] == 0.0 ? 0.0 : 1.0 / _p
[i
] );
301 for( size_t i
= 0; i
< size(); i
++ )
302 inv
._p
.push_back( 1.0 / _p
[i
] );
306 /// Raises entries to the power a
307 TProb
<T
>& operator^= (Real a
) {
309 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::bind2nd( std::ptr_fun
<T
, Real
, T
>(std::pow
), a
) );
313 /// Returns *this raised to the power a
314 TProb
<T
> operator^ (Real a
) const {
315 TProb
<T
> power(*this);
320 /// Returns pointwise signum
321 TProb
<T
> sgn() const {
323 x
._p
.reserve( size() );
324 for( size_t i
= 0; i
< size(); i
++ ) {
335 /// Returns pointwise absolute value
336 TProb
<T
> abs() const {
338 x
._p
.reserve( size() );
339 for( size_t i
= 0; i
< size(); i
++ )
340 x
._p
.push_back( _p
[i
] < 0 ? (-p
[i
]) : p
[i
] );
344 /// Applies exp pointwise
345 const TProb
<T
>& takeExp() {
346 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::ptr_fun
<T
, T
>(std::exp
) );
350 /// Applies log pointwise
351 /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
353 const TProb
<T
>& takeLog(bool zero
=false) {
355 for( size_t i
= 0; i
< size(); i
++ )
356 _p
[i
] = ( (_p
[i
] == 0.0) ? 0.0 : std::log( _p
[i
] ) );
358 std::transform( _p
.begin(), _p
.end(), _p
.begin(), std::ptr_fun
<T
, T
>(std::log
) );
362 /// Returns pointwise exp
363 TProb
<T
> exp() const {
369 /// Returns pointwise log
370 /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
372 TProb
<T
> log(bool zero
=false) const {
378 /// Returns sum of all entries
380 T Z
= std::accumulate( _p
.begin(), _p
.end(), (T
)0 );
384 /// Returns maximum absolute value of all entries
387 for( size_t i
= 0; i
< size(); i
++ ) {
388 Real mag
= fabs( (Real
) _p
[i
] );
395 /// Returns maximum value of all entries
397 T Z
= *std::max_element( _p
.begin(), _p
.end() );
401 /// Returns minimum value of all entries
403 T Z
= *std::min_element( _p
.begin(), _p
.end() );
407 /// Normalizes vector using the specified norm
408 T
normalize( NormType norm
=NORMPROB
) {
410 if( norm
== NORMPROB
)
412 else if( norm
== NORMLINF
)
421 /// Returns normalized copy of *this, using the specified norm
422 TProb
<T
> normalized( NormType norm
= NORMPROB
) const {
423 TProb
<T
> result(*this);
424 result
.normalize( norm
);
428 /// Returns true if one or more entries are NaN
429 bool hasNaNs() const {
430 return (std::find_if( _p
.begin(), _p
.end(), isnan
) != _p
.end());
433 /// Returns true if one or more entries are negative
434 bool hasNegatives() const {
435 return (std::find_if( _p
.begin(), _p
.end(), std::bind2nd( std::less
<Real
>(), 0.0 ) ) != _p
.end());
438 /// Returns entropy of *this
439 Real
entropy() const {
441 for( size_t i
= 0; i
< size(); i
++ )
442 S
-= (_p
[i
] == 0 ? 0 : _p
[i
] * std::log(_p
[i
]));
448 /// Returns distance of p and q (sizes should be identical), measured using distance measure dt
451 template<typename T
> Real
dist( const TProb
<T
> &p
, const TProb
<T
> &q
, typename TProb
<T
>::DistType dt
) {
453 assert( p
.size() == q
.size() );
457 case TProb
<T
>::DISTL1
:
458 for( size_t i
= 0; i
< p
.size(); i
++ )
459 result
+= fabs((Real
)p
[i
] - (Real
)q
[i
]);
462 case TProb
<T
>::DISTLINF
:
463 for( size_t i
= 0; i
< p
.size(); i
++ ) {
464 Real z
= fabs((Real
)p
[i
] - (Real
)q
[i
]);
470 case TProb
<T
>::DISTTV
:
471 for( size_t i
= 0; i
< p
.size(); i
++ )
472 result
+= fabs((Real
)p
[i
] - (Real
)q
[i
]);
476 case TProb
<T
>::DISTKL
:
477 for( size_t i
= 0; i
< p
.size(); i
++ ) {
479 result
+= p
[i
] * (std::log(p
[i
]) - std::log(q
[i
]));
486 /// Writes a TProb<T> to an output stream
489 template<typename T
> std::ostream
& operator<< (std::ostream
& os
, const TProb
<T
>& P
) {
491 std::copy( P
.p().begin(), P
.p().end(), std::ostream_iterator
<T
>(os
, " ") );
497 /// Returns the TProb<T> containing the pointwise minimum of a and b (which should have equal size)
500 template<typename T
> TProb
<T
> min( const TProb
<T
> &a
, const TProb
<T
> &b
) {
501 assert( a
.size() == b
.size() );
502 TProb
<T
> result( a
.size() );
503 for( size_t i
= 0; i
< a
.size(); i
++ )
512 /// Returns the TProb<T> containing the pointwise maximum of a and b (which should have equal size)
515 template<typename T
> TProb
<T
> max( const TProb
<T
> &a
, const TProb
<T
> &b
) {
516 assert( a
.size() == b
.size() );
517 TProb
<T
> result( a
.size() );
518 for( size_t i
= 0; i
< a
.size(); i
++ )
527 /// Represents a vector with entries of type Real.
528 typedef TProb
<Real
> Prob
;
531 } // end of namespace dai