vcglib/vcg/math/histogram.h

/****************************************************************************
* 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.                                                         *
*                                                                           *
****************************************************************************/
/****************************************************************************
  History

$Log: not supported by cvs2svn $
Revision 1.18  2008/03/05 11:21:49  cignoni
Heavily refactored the whole structure.
Some interfaces have been changed. Be careful.

Revision 1.17  2008/02/29 12:15:06  cignoni
added maxcount

Revision 1.16  2006/11/28 21:29:21  cignoni
Re added typedef Histogramf and Histogramd

Revision 1.15  2006/11/28 09:47:42  corsini
add documentation
fix typo

Revision 1.14  2006/05/04 00:09:53  cignoni
minor change: removed unused vars

Revision 1.13  2006/03/29 09:25:47  zifnab1974
extra includes necessary for compilation of meshlab on AMD 64 with gcc 3.4.5

Revision 1.12  2006/01/12 13:12:54  callieri
in FileWrite, added file closing after finishing

Revision 1.11  2005/09/16 11:51:23  cignoni
removed signed/unsigned warning

Revision 1.10  2005/06/17 00:54:55  cignoni
Corrected small bug in SetRange (H was resized to n instead of n+1)

Revision 1.9  2005/06/14 14:27:00  ganovelli
added include of algorithm

Revision 1.8  2005/06/10 14:59:39  cignoni
Added include assert.h and cast to ScalarType for a pow in SetRange() function.

Revision 1.7  2005/06/09 14:19:55  cignoni
Added typedef Histogramf and Histogramd

Revision 1.6  2005/06/07 09:37:33  ponchio
Added fabs() to variance, which can sometime be negative in case
of rounding errors (and sqrt chokes on it).

Revision 1.5  2005/06/07 07:44:08  cignoni
Added Percentile and removed small bug in Add

Revision 1.4  2005/04/04 10:48:35  cignoni
Added missing functions Avg, rms etc, now fully (almost) functional

Revision 1.3  2005/03/14 09:23:40  cignoni
Added missing include<vector>

Revision 1.2  2004/08/25 15:15:26  ganovelli
minor changes to comply gcc compiler (typename's and stuff)

Revision 1.1  2004/06/24 09:12:28  cignoni
Initial Release


****************************************************************************/

#ifndef __VCG_HISTOGRAM
#define __VCG_HISTOGRAM

#include <vector>
#include <algorithm>
#include <assert.h>
#include <string>
#include <limits>


namespace vcg {

/**
 * Histogram.
 *
 * This class implements a single-value histogram.
 */
template <class ScalarType> 
class Histogram 
{

// public data members
private:

	std::vector <int> H; 	//! Counters for bins.
  std::vector <ScalarType> R; 	//! Range for bins.
	ScalarType minv; 	//! Minimum value.
	ScalarType maxv;	//! Maximum value.
	int n;	//! Number of vaild intervals stored between minv and maxv.


  /// incrementally updated values
	int cnt;	//! Number of accumulated samples.
	ScalarType avg;	//! 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;}; 	//! Minimum value.

  

	/** 
	 * Add a new value to the histogram.
	 *
	 * The statistics related to the histogram data (average, RMS, etc.) are 
	 * also updated.
	 */
	void Add(ScalarType v);

  int MaxCount() const;
	int BinCount(ScalarType v);
	int BinCount(ScalarType v, ScalarType width);
	int 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 avg/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;
	avg=0;
	rms=0;
	n=0;
	minv=0;
	maxv=1;
}

/*
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)
{
	int pos=BinIndex(v);
  if(pos>=0 && pos<=n)
	{
		++H[pos];
		++cnt;
		avg+=v;
		rms += v*v;
	}
}

template <class ScalarType> 
int Histogram<ScalarType>::BinCount(ScalarType v) 
{
	return H[BinIndex(v)];
}

template <class ScalarType> 
int Histogram<ScalarType>::BinCount(ScalarType v, ScalarType width) 
{
	return RangeCount(v-width/2.0,v+width/2.0);
}

template <class ScalarType> 
int Histogram<ScalarType>::RangeCount(ScalarType rangeMin, ScalarType rangeMax) 
{
	int firstBin=BinIndex(rangeMin);
	int lastBin=BinIndex (rangeMax);
	int 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> 
int 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;
	int 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 */