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vcglib/vcg/math/histogram.h

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/****************************************************************************
* VCGLib o o *
* Visual and Computer Graphics Library o o *
* _ O _ *
* Copyright(C) 2004 \/)\/ *
* Visual Computing Lab /\/| *
* ISTI - Italian National Research Council | *
* \ *
* All rights reserved. *
* *
* This program is free software; you can redistribute it and/or modify *
* it under the terms of the GNU General Public License as published by *
* the Free Software Foundation; either version 2 of the License, or *
* (at your option) any later version. *
* *
* This program is distributed in the hope that it will be useful, *
* but WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the *
* GNU General Public License (http://www.gnu.org/licenses/gpl.txt) *
* for more details. *
* *
****************************************************************************/
#ifndef __VCG_HISTOGRAM
#define __VCG_HISTOGRAM
#include <vector>
#include <algorithm>
#include <assert.h>
#include <string>
#include <limits>
#include <vcg/math/base.h>
#include <stdio.h>
namespace vcg {
template <class ScalarType>
class Distribution
{
private:
std::vector<ScalarType> vec;
bool dirty;
double valSum;
double sqrdValSum;
double avg;
double sqrdAvg;
double rms;
double min_v;
double max_v;
public:
Distribution() { Clear(); }
void Clear()
{
vec.clear();
dirty=true;
min_v = std::numeric_limits<float>::max();
max_v = -std::numeric_limits<float>::max();
}
void Add(const ScalarType v)
{
vec.push_back(v);
dirty=true;
if(v<min_v) min_v=v;
if(v>max_v) max_v=v;
}
ScalarType Min() const { return min_v; }
ScalarType Max() const { return max_v; }
ScalarType Cnt() const { return ScalarType(vec.size()); }
ScalarType Sum(){ DirtyCheck(); return valSum; }
ScalarType Avg(){ DirtyCheck(); return avg;}
//! Returns the Root Mean Square of the data.
ScalarType RMS(){ DirtyCheck(); return rms;}
//! \brief Returns the variance of the data.
/// the average of the squares less the square of the average.
ScalarType Variance(){ DirtyCheck(); return sqrdAvg - avg*avg ;}
//! Returns the standard deviation of the data.
ScalarType StandardDeviation(){ DirtyCheck(); return sqrt( Variance() );}
void DirtyCheck()
{
if(!dirty) return;
std::sort(vec.begin(),vec.end());
valSum=0;
sqrdValSum=0;
typename std::vector<ScalarType>::iterator vi;
for(vi=vec.begin();vi!=vec.end();++vi)
{
valSum += double(*vi);
sqrdValSum += double(*vi)*double(*vi);
}
avg = valSum/double(vec.size());
sqrdAvg = sqrdValSum/double(vec.size());
rms = math::Sqrt(sqrdAvg);
dirty=false;
}
ScalarType Percentile(ScalarType perc)
{
assert(!vec.empty());
assert(perc>=0 && perc<=1);
DirtyCheck();
int index = vec.size() *perc -1;
if(index< 0 ) index = 0;
return vec[index];
}
};
/**
* Histogram.
*
* This class implements a single-value histogram.
*/
template <class ScalarType>
class Histogram
{
// public data members
protected:
std::vector <ScalarType> H; //! Counters for bins.
std::vector <ScalarType> R; //! Range for bins.
ScalarType minv; //! Minimum value.
ScalarType maxv; //! Maximum value.
ScalarType minElem; //! Minimum value.
ScalarType maxElem; //! Maximum value.
int n; //! Number of vaild intervals stored between minv and maxv.
/// incrementally updated values
ScalarType cnt; //! Number of accumulated samples.
ScalarType sum; //! Average.
ScalarType rms; //! Root mean square.
/**
* Returns the index of the bin which contains a given value.
*/
int BinIndex(ScalarType val) ;
// public methods
public:
/**
* Set the histogram values.
*
* This method is used to correctly initialize the bins of the histogram.
* n is the number of valid intervals between minv and maxv.
* for a more robust working, the Histogram class stores also the two out of range intervals (-inf, minv] and [maxv, +inf)
* Each bin is left closed (eg it contains the value
* The \a gamma parameter is applied to modify the distribution of the ranges of the bins. Default uniform distibution.
*
*/
void SetRange(ScalarType _minv, ScalarType _maxv, int _n,ScalarType gamma=1.0 );
ScalarType MinV() {return minv;} //! Minimum value.
ScalarType MaxV() {return maxv;} //! Maximum value.
ScalarType Sum() {return sum;} //! Total sum of inserted values.
ScalarType Cnt() {return cnt;}
ScalarType MinElem() {return minElem;} //! Minimum element added to the histogram. It could be < or > than MinV;.
ScalarType MaxElem() {return maxElem;} //! Maximum element added to the histogram. It could be < or > than MinV;..
/**
* Add a new value to the histogram.
*
* The statistics related to the histogram data (average, RMS, etc.) are
* also updated.
*/
void Add(ScalarType v, ScalarType increment=ScalarType(1.0));
ScalarType MaxCount() const;
int BinNum() const {return n;}
ScalarType BinCount(ScalarType v);
ScalarType BinCountInd(int index) {return H[index];}
ScalarType BinCount(ScalarType v, ScalarType width);
ScalarType BinLowerBound(int index) {return R[index];}
ScalarType BinUpperBound(int index) {return R[index+1];}
ScalarType RangeCount(ScalarType rangeMin, ScalarType rangeMax);
ScalarType BinWidth(ScalarType v);
/**
* Returns the value corresponding to a given percentile of the data.
*
* The percentile range between 0 and 1.
*/
ScalarType Percentile(ScalarType frac) const;
//! Returns the average of the data.
ScalarType Avg(){ return sum/cnt;}
//! Returns the Root Mean Square of the data.
ScalarType RMS(){ return sqrt(rms/double(cnt));}
//! Returns the variance of the data.
ScalarType Variance(){ return fabs(rms/cnt-Avg()*Avg());}
//! Returns the standard deviation of the data.
ScalarType StandardDeviation(){ return sqrt(Variance());}
//! Dump the histogram to a file.
void FileWrite(const std::string &filename);
//! Reset histogram data.
void Clear();
};
template <class ScalarType>
void Histogram<ScalarType>::Clear()
{
H.clear();
R.clear();
cnt=0;
sum=0;
rms=0;
n=0;
minv=0;
maxv=1;
minElem = std::numeric_limits<ScalarType>::max();
maxElem = -std::numeric_limits<ScalarType>::max();
}
/*
Note that the histogram holds <n> valid bins plus two semi-infinite bins.
R[0] = -inf
R[1] = minv
R[n+1] = maxv
R[n+2] = +inf
Eg. SetRange(0, 10, 5) asks for 5 intervals covering the 0..10 range
H[0] H[1] H[2] H[3] H[4] H[5] H[6]
-inf 0 2 4 6 8 10 +inf
R[0] R[1] R[2] R[3] R[4] R[5] R[6] R[7]
*/
template <class ScalarType>
void Histogram<ScalarType>::SetRange(ScalarType _minv, ScalarType _maxv, int _n, ScalarType gamma)
{
// reset data
Clear();
minv=_minv;maxv=_maxv;n=_n;
H.resize(n+2);
fill(H.begin(),H.end(),0);
R.resize(n+3);
R[0] = - std::numeric_limits< ScalarType >::max();
R[n+2] = std::numeric_limits< ScalarType >::max();
double delta=(maxv-minv);
if(gamma==1)
{
for(int i=0; i<=n; ++i)
R[i+1] = minv + delta*ScalarType(i)/n;
}
else
{
for(int i=0; i<=n; ++i)
R[i+1] = minv + delta*pow(ScalarType(i)/n,gamma);
}
}
template <class ScalarType>
int Histogram<ScalarType>::BinIndex(ScalarType val)
{
// lower_bound returns the furthermost iterator i in [first, last) such that, for every iterator j in [first, i), *j < value.
// E.g. An iterator pointing to the first element "not less than" val, or end() if every element is less than val.
typename std::vector<ScalarType>::iterator it = lower_bound(R.begin(),R.end(),val);
assert(it!=R.begin());
assert(it!=R.end());
assert((*it)>=val);
int pos = it-R.begin();
assert(pos >=1);
pos -= 1;
assert (R[pos] < val);
assert ( val <= R[pos+1] );
return pos;
}
/*
H[0] H[1] H[2] H[3] H[4] H[5] H[6]
-inf 0 2 4 6 8 10 +inf
R[0] R[1] R[2] R[3] R[4] R[5] R[6] R[7]
asking for 3.14 lower bound will return an iterator pointing to R[3]==4; and will increase H[2]
asking for 4 lower bound will return an iterator pointing to R[3]==4; and will increase H[2]
*/
template <class ScalarType>
void Histogram<ScalarType>::Add(ScalarType v, ScalarType increment)
{
int pos=BinIndex(v);
if(v<minElem) minElem=v;
if(v>maxElem) maxElem=v;
assert((pos>=0)&&(pos<=n+1));
H[pos]+=increment;
cnt+=increment;
sum+=v*increment;
rms += (v*v)*increment;
}
template <class ScalarType>
ScalarType Histogram<ScalarType>::BinCount(ScalarType v)
{
return H[BinIndex(v)];
}
template <class ScalarType>
ScalarType Histogram<ScalarType>::BinCount(ScalarType v, ScalarType width)
{
return RangeCount(v-width/2.0,v+width/2.0);
}
template <class ScalarType>
ScalarType Histogram<ScalarType>::RangeCount(ScalarType rangeMin, ScalarType rangeMax)
{
int firstBin=BinIndex(rangeMin);
int lastBin=BinIndex (rangeMax);
ScalarType sum=0;
for(int i=firstBin; i<=lastBin;++i)
sum+=H[i];
return sum;
}
template <class ScalarType>
ScalarType Histogram<ScalarType>::BinWidth(ScalarType v)
{
int pos=BinIndex(v);
return R[pos+1]-R[pos];
}
template <class ScalarType>
void Histogram<ScalarType>::FileWrite(const std::string &filename)
{
FILE *fp;
fp=fopen(filename.c_str(),"w");
for(unsigned int i=0; i<H.size(); i++)
fprintf (fp,"%12.8lf , %12.8lf \n",R[i],double(H[i])/cnt);
fclose(fp);
}
template <class ScalarType>
ScalarType Histogram<ScalarType>::MaxCount() const
{
return *(std::max_element(H.begin(),H.end()));
}
// Return the scalar value <r> such that there are <frac> samples <= <r>.
// E.g. Percentile(0.0) will return R[1] e.g. min value
// E.g. Percentile(1.0) will return R[n+1] e.g max value
template <class ScalarType>
ScalarType Histogram<ScalarType>::Percentile(ScalarType frac) const
{
if(H.size()==0 && R.size()==0)
return 0;
// check percentile range
assert(frac >= 0 && frac <= 1);
ScalarType sum=0,partsum=0;
size_t i;
// useless summation just to be sure
for(i=0;i<H.size();i++) sum+=H[i];
assert(sum==cnt);
sum*=frac;
for(i=0; i<H.size(); i++)
{
partsum+=H[i];
if(partsum>=sum) break;
}
assert(i<H.size());
return R[i+1];
}
typedef Histogram<double> Histogramd ;
typedef Histogram<float> Histogramf ;
} // end namespace (vcg)
#endif /* __VCG_HISTOGRAM */
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