/// \file
/// \brief Defines TProb<T> and Prob classes
-/// \todo Improve documentation
+/// \todo Rename to Vector<T>
#ifndef __defined_libdai_prob_h
#include <numeric>
#include <functional>
#include <dai/util.h>
+#include <dai/exceptions.h>
namespace dai {
-/// Real number (alias for double, could be changed to long double if necessary)
-typedef double Real;
-
-template<typename T> class TProb;
-
-/// Represents a probability measure, with entries of type Real.
-typedef TProb<Real> Prob;
-
-
-/// Represents a probability measure on a finite outcome space (i.e., corresponding to a discrete random variable).
-/** It is implemented as a std::vector<T> but adds a convenient interface.
- * It is not necessarily normalized at all times.
- * \tparam T Should be castable from and to double.
+/// Represents a vector with entries of type \a T.
+/** A TProb<T> is a std::vector<T> with an interface designed for dealing with probability mass functions.
+ * It is mainly used for representing measures on a finite outcome space, e.g., the probability
+ * distribution of a discrete random variable.
+ * \tparam T Should be a scalar that is castable from and to double and should support elementary arithmetic operations.
*/
template <typename T> class TProb {
private:
- /// The probability measure
+ /// The vector
std::vector<T> _p;
public:
+ /// Iterator over entries
+ typedef typename std::vector<T>::iterator iterator;
+ /// Const iterator over entries
+ typedef typename std::vector<T>::const_iterator const_iterator;
+
/// Enumerates different ways of normalizing a probability measure.
/**
* - NORMPROB means that the sum of all entries should be 1;
/// Default constructor
TProb() : _p() {}
- /// Construct uniform distribution of given length
+ /// Construct uniform distribution over n outcomes, i.e., a vector of length n with each entry set to 1/n
explicit TProb( size_t n ) : _p(std::vector<T>(n, 1.0 / n)) {}
- /// Construct from given length and initial value
- TProb( size_t n, Real p ) : _p(n, (T)p) {}
+ /// Construct vector of length n with each entry set to p
+ explicit TProb( size_t n, Real p ) : _p(n, (T)p) {}
- /// Construct from given length and initial array
- TProb( size_t n, const Real* p ) : _p(p, p + n ) {}
+ /// Construct vector from a range
+ /** \tparam Iterator Iterates over instances that can be cast to T.
+ * \param begin Points to first instance to be added.
+ * \param end Points just beyond last instance to be added.
+ * \param sizeHint For efficiency, the number of entries can be speficied by sizeHint.
+ */
+ template <typename Iterator>
+ TProb( Iterator begin, Iterator end, size_t sizeHint=0 ) : _p() {
+ _p.reserve( sizeHint );
+ _p.insert( _p.begin(), begin, end );
+ }
- /// Returns a const reference to the probability vector
+ /// Returns a const reference to the vector
const std::vector<T> & p() const { return _p; }
- /// Returns a reference to the probability vector
+ /// Returns a reference to the vector
std::vector<T> & p() { return _p; }
- /// Returns a copy of the i'th probability entry
+ /// Returns a copy of the i'th entry
T operator[]( size_t i ) const {
#ifdef DAI_DEBUG
return _p.at(i);
#endif
}
- /// Returns a reference to the i'th probability entry
+ /// Returns reference to the i'th entry
T& operator[]( size_t i ) { return _p[i]; }
+
+ /// Returns iterator pointing to first entry
+ iterator begin() { return _p.begin(); }
+
+ /// Returns const iterator pointing to first entry
+ const_iterator begin() const { return _p.begin(); }
+
+ /// Returns iterator pointing beyond last entry
+ iterator end() { return _p.end(); }
- /// Sets all elements to x
+ /// Returns const iterator pointing beyond last entry
+ const_iterator end() const { return _p.end(); }
+
+ /// Sets all entries to x
TProb<T> & fill(T x) {
std::fill( _p.begin(), _p.end(), x );
return *this;
}
- /// Sets all elements to i.i.d. random numbers from a uniform[0,1) distribution
+ /// Draws all entries i.i.d. from a uniform distribution on [0,1)
TProb<T> & randomize() {
std::generate(_p.begin(), _p.end(), rnd_uniform);
return *this;
}
- /// Returns number of elements
+ /// Returns length of the vector, i.e., the number of entries
size_t size() const {
return _p.size();
}
- /// Sets entries that are smaller than epsilon to zero
+ /// Sets entries that are smaller than epsilon to 0
TProb<T>& makeZero( Real epsilon ) {
for( size_t i = 0; i < size(); i++ )
if( fabs(_p[i]) < epsilon )
_p[i] = 0;
return *this;
}
+
+ /// Set all entries to 1.0/size()
+ TProb<T>& setUniform () {
+ fill(1.0/size());
+ return *this;
+ }
/// Sets entries that are smaller than epsilon to epsilon
- TProb<T>& makePositive (Real epsilon) {
+ TProb<T>& makePositive( Real epsilon ) {
for( size_t i = 0; i < size(); i++ )
if( (0 < (Real)_p[i]) && ((Real)_p[i] < epsilon) )
_p[i] = epsilon;
return *this;
}
- /// Multiplies each entry with x
+ /// Multiplies each entry with scalar x
TProb<T>& operator*= (T x) {
std::transform( _p.begin(), _p.end(), _p.begin(), std::bind2nd( std::multiplies<T>(), x) );
return *this;
}
- /// Returns product of *this with x
+ /// Returns product of *this with scalar x
TProb<T> operator* (T x) const {
TProb<T> prod( *this );
prod *= x;
return prod;
}
- /// Divides each entry by x
+ /// Divides each entry by scalar x
TProb<T>& operator/= (T x) {
#ifdef DAI_DEBUG
assert( x != 0.0 );
return *this;
}
- /// Returns quotient of *this and x
+ /// Returns quotient of *this and scalar x
TProb<T> operator/ (T x) const {
TProb<T> quot( *this );
quot /= x;
return quot;
}
- /// Adds x to each entry
+ /// Adds scalar x to each entry
TProb<T>& operator+= (T x) {
std::transform( _p.begin(), _p.end(), _p.begin(), std::bind2nd( std::plus<T>(), x ) );
return *this;
}
- /// Returns sum of *this and x
+ /// Returns sum of *this and scalar x
TProb<T> operator+ (T x) const {
TProb<T> sum( *this );
sum += x;
return sum;
}
- /// Subtracts x from each entry
+ /// Subtracts scalar x from each entry
TProb<T>& operator-= (T x) {
std::transform( _p.begin(), _p.end(), _p.begin(), std::bind2nd( std::minus<T>(), x ) );
return *this;
}
- /// Returns difference of *this and x
+ /// Returns difference of *this and scalar x
TProb<T> operator- (T x) const {
TProb<T> diff( *this );
diff -= x;
return diff;
}
- /// Pointwise comparison
+ /// Lexicographical comparison (sizes should be identical)
bool operator<= (const TProb<T> & q) const {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return true;
}
- /// Pointwise multiplication with q
+ /// Pointwise multiplication with q (sizes should be identical)
TProb<T>& operator*= (const TProb<T> & q) {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return *this;
}
- /// Return product of *this with q
+ /// Return product of *this with q (sizes should be identical)
TProb<T> operator* (const TProb<T> & q) const {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return prod;
}
- /// Pointwise addition with q
+ /// Pointwise addition with q (sizes should be identical)
TProb<T>& operator+= (const TProb<T> & q) {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return *this;
}
- /// Return sum of *this and q
+ /// Returns sum of *this and q (sizes should be identical)
TProb<T> operator+ (const TProb<T> & q) const {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return sum;
}
- /// Pointwise subtraction of q
+ /// Pointwise subtraction of q (sizes should be identical)
TProb<T>& operator-= (const TProb<T> & q) {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return *this;
}
- /// Return *this minus q
+ /// Return *this minus q (sizes should be identical)
TProb<T> operator- (const TProb<T> & q) const {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return diff;
}
- /// Pointwise division by q, where division by zero yields zero
+ /// Pointwise division by q, where division by 0 yields 0 (sizes should be identical)
TProb<T>& operator/= (const TProb<T> & q) {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return *this;
}
- /// Pointwise division by q, where division by zero yields infinity
+ /// Pointwise division by q, where division by 0 yields +Inf (sizes should be identical)
TProb<T>& divide (const TProb<T> & q) {
#ifdef DAI_DEBUG
assert( size() == q.size() );
return *this;
}
- /// Returns quotient of *this with q
+ /// Returns quotient of *this with q (sizes should be identical)
TProb<T> operator/ (const TProb<T> & q) const {
#ifdef DAI_DEBUG
assert( size() == q.size() );
}
/// Returns pointwise inverse
- TProb<T> inverse(bool zero = false) const {
+ /** If zero==true; uses 1/0==0, otherwise 1/0==Inf.
+ */
+ TProb<T> inverse(bool zero=true) const {
TProb<T> inv;
inv._p.reserve( size() );
if( zero )
for( size_t i = 0; i < size(); i++ )
inv._p.push_back( _p[i] == 0.0 ? 0.0 : 1.0 / _p[i] );
else
- for( size_t i = 0; i < size(); i++ ) {
-#ifdef DAI_DEBUG
- assert( _p[i] != 0.0 );
-#endif
+ for( size_t i = 0; i < size(); i++ )
inv._p.push_back( 1.0 / _p[i] );
- }
return inv;
}
- /// Raises elements to the power a
+ /// Raises entries to the power a
TProb<T>& operator^= (Real a) {
if( a != 1.0 )
std::transform( _p.begin(), _p.end(), _p.begin(), std::bind2nd( std::ptr_fun<T, Real, T>(std::pow), a) );
TProb<T> x;
x._p.reserve( size() );
for( size_t i = 0; i < size(); i++ )
- x._p.push_back( _p[i] < 0 ? (-p[i]) : p[i] );
+ x._p.push_back( _p[i] < 0 ? (-_p[i]) : _p[i] );
return x;
}
}
/// Applies log pointwise
- const TProb<T>& takeLog() {
- std::transform( _p.begin(), _p.end(), _p.begin(), std::ptr_fun<T, T>(std::log) );
- return *this;
- }
-
- /// Applies log pointwise (defining log(0)=0)
- const TProb<T>& takeLog0() {
- for( size_t i = 0; i < size(); i++ )
- _p[i] = ( (_p[i] == 0.0) ? 0.0 : std::log( _p[i] ) );
+ /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
+ */
+ const TProb<T>& takeLog(bool zero=false) {
+ if( zero ) {
+ for( size_t i = 0; i < size(); i++ )
+ _p[i] = ( (_p[i] == 0.0) ? 0.0 : std::log( _p[i] ) );
+ } else
+ std::transform( _p.begin(), _p.end(), _p.begin(), std::ptr_fun<T, T>(std::log) );
return *this;
}
}
/// Returns pointwise log
- TProb<T> log() const {
+ /** If zero==true, uses log(0)==0; otherwise, log(0)==-Inf.
+ */
+ TProb<T> log(bool zero=false) const {
TProb<T> l(*this);
- l.takeLog();
+ l.takeLog(zero);
return l;
}
- /// Returns pointwise log (defining log(0)=0)
- TProb<T> log0() const {
- TProb<T> l0(*this);
- l0.takeLog0();
- return l0;
- }
-
- /// Returns distance of p and q, measured using dt
- friend Real dist( const TProb<T> &p, const TProb<T> &q, DistType dt ) {
-#ifdef DAI_DEBUG
- assert( p.size() == q.size() );
-#endif
- Real result = 0.0;
- switch( dt ) {
- case DISTL1:
- for( size_t i = 0; i < p.size(); i++ )
- result += fabs((Real)p[i] - (Real)q[i]);
- break;
-
- case DISTLINF:
- for( size_t i = 0; i < p.size(); i++ ) {
- Real z = fabs((Real)p[i] - (Real)q[i]);
- if( z > result )
- result = z;
- }
- break;
-
- case DISTTV:
- for( size_t i = 0; i < p.size(); i++ )
- result += fabs((Real)p[i] - (Real)q[i]);
- result *= 0.5;
- break;
-
- case DISTKL:
- for( size_t i = 0; i < p.size(); i++ ) {
- if( p[i] != 0.0 )
- result += p[i] * (std::log(p[i]) - std::log(q[i]));
- }
- }
- return result;
- }
-
/// Returns sum of all entries
- T totalSum() const {
+ T sum() const {
T Z = std::accumulate( _p.begin(), _p.end(), (T)0 );
return Z;
}
- /// Returns maximum absolute value of entries
+ /// Return sum of absolute value of all entries
+ T sumAbs() const {
+ T s = 0;
+ for( size_t i = 0; i < size(); i++ )
+ s += fabs( (Real) _p[i] );
+ return s;
+ }
+
+ /// Returns maximum absolute value of all entries
T maxAbs() const {
T Z = 0;
for( size_t i = 0; i < size(); i++ ) {
return Z;
}
- /// Returns maximum value of entries
- T maxVal() const {
+ /// Returns maximum value of all entries
+ T max() const {
T Z = *std::max_element( _p.begin(), _p.end() );
return Z;
}
- /// Returns minimum value of entries
- T minVal() const {
+ /// Returns minimum value of all entries
+ T min() const {
T Z = *std::min_element( _p.begin(), _p.end() );
return Z;
}
- /// Normalizes using the specified norm
- T normalize( NormType norm = NORMPROB ) {
+ /// Returns {arg,}maximum value
+ std::pair<size_t,T> argmax() const {
+ T max = _p[0];
+ size_t arg = 0;
+ for( size_t i = 1; i < size(); i++ ) {
+ if( _p[i] > max ) {
+ max = _p[i];
+ arg = i;
+ }
+ }
+ return std::make_pair(arg,max);
+ }
+
+ /// Normalizes vector using the specified norm
+ T normalize( NormType norm=NORMPROB ) {
T Z = 0.0;
if( norm == NORMPROB )
- Z = totalSum();
+ Z = sum();
else if( norm == NORMLINF )
Z = maxAbs();
-#ifdef DAI_DEBUG
- assert( Z != 0.0 );
-#endif
- *this /= Z;
+ if( Z == 0.0 )
+ DAI_THROW(NOT_NORMALIZABLE);
+ else
+ *this /= Z;
return Z;
}
/// Returns true if one or more entries are NaN
bool hasNaNs() const {
- return (std::find_if( _p.begin(), _p.end(), isnan ) != _p.end());
+ bool foundnan = false;
+ for( typename std::vector<T>::const_iterator x = _p.begin(); x != _p.end(); x++ )
+ if( isnan( *x ) ) {
+ foundnan = true;
+ break;
+ }
+ return foundnan;
}
/// Returns true if one or more entries are negative
return (std::find_if( _p.begin(), _p.end(), std::bind2nd( std::less<Real>(), 0.0 ) ) != _p.end());
}
- /// Returns true if one or more entries are non-positive (causes problems with logscale)
- bool hasNonPositives() const {
- return (std::find_if( _p.begin(), _p.end(), std::bind2nd( std::less_equal<Real>(), 0.0 ) ) != _p.end());
- }
-
- /// Returns entropy
+ /// Returns entropy of *this
Real entropy() const {
Real S = 0.0;
for( size_t i = 0; i < size(); i++ )
- S -= xlogx(_p[i]);
+ S -= (_p[i] == 0 ? 0 : _p[i] * std::log(_p[i]));
return S;
}
- /// Writes a TProb<T> to an output stream
- friend std::ostream& operator<< (std::ostream& os, const TProb<T>& P) {
- os << "[";
- std::copy( P._p.begin(), P._p.end(), std::ostream_iterator<T>(os, " ") );
- os << "]";
- return os;
+ /// Returns a random index, according to the (normalized) distribution described by *this
+ size_t draw() {
+ double x = rnd_uniform() * sum();
+ T s = 0;
+ for( size_t i = 0; i < size(); i++ ) {
+ s += _p[i];
+ if( s > x )
+ return i;
+ }
+ return( size() - 1 );
}
-
- private:
- /// Returns x*log(x), or 0 if x == 0
- Real xlogx( Real x ) const { return( x == 0.0 ? 0.0 : x * std::log(x)); }
};
-/// Returns TProb<T> containing the pointwise minimum of a and b (which should have equal size)
+/// Returns distance of p and q (sizes should be identical), measured using distance measure dt
+/** \relates TProb
+ */
+template<typename T> Real dist( const TProb<T> &p, const TProb<T> &q, typename TProb<T>::DistType dt ) {
+#ifdef DAI_DEBUG
+ assert( p.size() == q.size() );
+#endif
+ Real result = 0.0;
+ switch( dt ) {
+ case TProb<T>::DISTL1:
+ for( size_t i = 0; i < p.size(); i++ )
+ result += fabs((Real)p[i] - (Real)q[i]);
+ break;
+
+ case TProb<T>::DISTLINF:
+ for( size_t i = 0; i < p.size(); i++ ) {
+ Real z = fabs((Real)p[i] - (Real)q[i]);
+ if( z > result )
+ result = z;
+ }
+ break;
+
+ case TProb<T>::DISTTV:
+ for( size_t i = 0; i < p.size(); i++ )
+ result += fabs((Real)p[i] - (Real)q[i]);
+ result *= 0.5;
+ break;
+
+ case TProb<T>::DISTKL:
+ for( size_t i = 0; i < p.size(); i++ ) {
+ if( p[i] != 0.0 )
+ result += p[i] * (std::log(p[i]) - std::log(q[i]));
+ }
+ }
+ return result;
+}
+
+
+/// Writes a TProb<T> to an output stream
+/** \relates TProb
+ */
+template<typename T> std::ostream& operator<< (std::ostream& os, const TProb<T>& P) {
+ os << "[";
+ std::copy( P.p().begin(), P.p().end(), std::ostream_iterator<T>(os, " ") );
+ os << "]";
+ return os;
+}
+
+
+/// Returns the TProb<T> containing the pointwise minimum of a and b (which should have equal size)
+/** \relates TProb
+ */
template<typename T> TProb<T> min( const TProb<T> &a, const TProb<T> &b ) {
assert( a.size() == b.size() );
TProb<T> result( a.size() );
}
-/// Returns TProb<T> containing the pointwise maximum of a and b (which should have equal size)
+/// Returns the TProb<T> containing the pointwise maximum of a and b (which should have equal size)
+/** \relates TProb
+ */
template<typename T> TProb<T> max( const TProb<T> &a, const TProb<T> &b ) {
assert( a.size() == b.size() );
TProb<T> result( a.size() );
}
+/// Represents a vector with entries of type Real.
+typedef TProb<Real> Prob;
+
+
} // end of namespace dai
projects / libdai.git / blobdiff