templatevalueanalysation.h

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/***************************************************************************
 *   Copyright (C) 2005-2009 by Robot Group Leipzig                        *
 *    martius@informatik.uni-leipzig.de                                    *
 *    fhesse@informatik.uni-leipzig.de                                     *
 *    der@informatik.uni-leipzig.de                                        *
 *    guettler@informatik.uni-leipzig.de                                   *
 *    jhoffmann@informatik.uni-leipzig.de                                  *
 *    joergweide84@aol.com (robot12)                                       *
 *                                                                         *
 *   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 for more details.                          *
 *                                                                         *
 *   You should have received a copy of the GNU General Public License     *
 *   along with this program; if not, write to the                         *
 *   Free Software Foundation, Inc.,                                       *
 *   59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.             *
 ***************************************************************************
 *                                                                         *
 *   This template class is for statistical calculations.                  *
 *                                                                         *
 *   $Log: templatevalueanalysation.h,v $
 *   Revision 1.3  2009/07/21 08:47:33  robot12
 *   add some comments
 *
 *   Revision 1.2  2009/06/29 12:38:16  robot12
 *   add the templatevalueanalysation for calculating some statistical values. Is a new part of the statistictools.
 *
 *
 ***************************************************************************/

#ifndef TEMPLATEVALUEANALYSATION_H_
#define TEMPLATEVALUEANALYSATION_H_

//macros
#define ANALYSATION_CONTEXT TemplateValueAnalysation<type,zero,lower,higher,doubleDiv,doubleMul,add,sub,mul,div>
#define DOUBLE_ANALYSATION_CONTEXT TemplateValueAnalysation<double,defaultZero>

//includes
#include <vector>
#include <list>

/**
 * default function for "lower as" operation.
 * @param a operator a
 * @param b operator b
 * @return (bool) true if a lower than b
 */
template
<class type>
bool defaultLower(const type& a, const type& b) {
        if(a<b)
                return true;

        return false;
}

/**
 * default function for divide by a double value.
 * @param a operator a
 * @param b (double) the double value
 * @return the result of the division
 */
template
<class type>
type defaultDoubleDiv(const type& a, const double& b) {
        return a/b;
}

/**
 * default function for mul. with a double value.
 * @param a operator a
 * @param b (double) the double value
 * @return the result of the mul.
 */
template
<class type>
type defaultDoubleMul(const type& a, const double& b) {
        return a*b;
}

/**
 * default function for "higher than" operation.
 * @param a operator a
 * @param b operator b
 * @return (bool) true if a higher than b
 */
template
<class type>
bool defaultHigher(const type& a,const type& b) {
        if(a>b)
                return true;

        return false;
}

/**
 * default function for add two values
 * @param a operator a
 * @param b operator b
 * @return the result of the add.
 */
template
<class type>
type defaultAdd(const type& a, const type& b) {
        return a+b;
}

/**
 * default function for sub. two values
 * @param a operator a
 * @param b operator b
 * @return the result of the sub.
 */
template
<class type>
type defaultSub(const type& a, const type& b) {
        return a-b;
}

/**
 * default function for mul. of two values
 * @param a operator a
 * @param b operator b
 * @return the result of the mul.
 */
template
<class type>
type defaultMul(const type& a, const type& b) {
        return a*b;
}

/**
 * default function for div. of two values
 * @param a operator a
 * @param b operator b
 * @return the result of the div.
 */
template
<class type>
type defaultDiv(const type& a, const type& b) {
        return a/b;
}

/**
 * default function for zero double value
 * @return (double) 0.0
 */
double defaultZero();

/**
 * This template class give you some methods to calculate some statistical values like average, min, max, upper quartil,
 * lower quartil and many more.
 *
 * All functions are implemented in the header because by generating the library it isn't known which type are later used.
 * And a later compiling needs the implementation two!
 */
template
<class type,                                                                                                                    //data type of the calculation
type zero(void),                                                                                                                //gives the zero of this data type back
bool lower(const type&, const type&)=defaultLower<type>,                                //test if one element of the type lower than the other
bool higher(const type&, const type&)=defaultHigher<type>,                      //test if one element of the type higher than the other
type doubleDiv(const type&, const double&)=defaultDoubleDiv<type>,      //divide a element of the type by a double value
type doubleMul(const type&, const double&)=defaultDoubleMul<type>,      //mul. a element of the type by a double value
type add(const type&, const type&)=defaultAdd<type>,                                    //add two elements of type
type sub(const type&, const type&)=defaultSub<type>,                                    //sub two elements of type
type mul(const type&, const type&)=defaultMul<type>,                                    //mul two elements of type
type div(const type&, const type&)=defaultDiv<type> >                           //div two elements of type
class TemplateValueAnalysation {
public:
        /**
         * constructor
         * Needs a set of values for which the statistical values will calculate.
         * @param values (vector<type>& the set)
         */
        TemplateValueAnalysation(std::vector<type>& values) : m_vector(values), m_list(), m_listCreated(false) {}

        /**
         * default destructor
         */
        ~TemplateValueAnalysation() {}

        /**
         * this function calculate the average of the giving set
         *
         * It used zero, add and doubleDiv to calculate the average.
         * @return the average
         */
        type getAvg() {
                type avg=zero();                                                                                                                                                //by begin the average is zero
                __gnu_cxx::__normal_iterator<type*,std::vector<type,std::allocator<type> > > iter;

                for(iter = m_vector.begin(); iter != m_vector.end(); iter++) {
                        avg = add(avg,(*iter));                                                                                                                         //for all elements in the set add it to the average.
                                                                                                                                                                                                //So we become the sum. of all elements in the set.
                }

                if(m_vector.size()!=0)
                        avg = doubleDiv(avg,m_vector.size());                                                                                           //now devide the sum by the count of elements in the set.

                return avg;                                                                                                                                                             //return the result
        }

        /**
         * this function search the min. value in the set
         *
         * For this it use lower
         * @return the minimum
         */
        type getMin() {
                type min = m_vector[0];                 //the lowest element is at begin the first element
                __gnu_cxx::__normal_iterator<type*,std::vector<type,std::allocator<type> > > iter = m_vector.begin();

                for(iter++; iter != m_vector.end(); iter++) {
                        if(lower((*iter),min))          //if a element lower than min, so reset the min to the lower value.
                                min=(*iter);
                }

                return min;                                             //return the lowest element
        }

        /**
         * this function search the max. value in the set
         *
         * For this it use lower
         * @return the minimum
         */
        type getMax() {
                type max = m_vector[0];                 //the highest element is at begin the first element
                __gnu_cxx::__normal_iterator<type*,std::vector<type,std::allocator<type> > > iter = m_vector.begin();

                for(iter++; iter != m_vector.end(); iter++) {
                        if(lower(max,(*iter)))          //if a element higher than max, so reset the max to the higher value.
                                max=(*iter);
                }

                return max;                                             //return the lowest element
        }

        /**
         * this function calculate the range of all values. For this he search the mibn and max and calculate from this values.
         *
         * use sub
         * @return the range of the values in the set
         */
        type getRange() {
                type dMax = getMax();                   //become max
                type dMin = getMin();                   //become min

                return sub(dMax,dMin);                  //range=max-min
        }

        /**
         * this function search the median of the giving set of values.
         *
         * use add and doubleMul
         * @return the median
         */
        type getMedian() {
                type median;
                int x;
                int num = m_vector.size()/2;
                std::_List_iterator<TYPE_SAVE> iter;

                if(!m_listCreated)
                        sort();                                                         //sort the set. to define the middle

                iter = m_list.begin();                                  //go to the middle
                for(x=0;x<num;x++) iter++;

                if(m_vector.size() % 2 == 0) {                  //if the real middle between two values add this values and calculate the arithmetical middle.
                        median = (*iter->pointer);
                        iter--;
                        median = add(median,(*iter->pointer));
                        median = doubleMul(median,0.5);
                }

                else {
                        median = (*iter->pointer);                      //else gives the middle back
                }

                return median;
        }

        /**
         * this function calculate the under quartil
         *
         * use add and doubleMul
         * @return the under quartil
         */
        type getQuartil1() {
                type q;
                int x;
                int num = m_vector.size()/4;
                std::_List_iterator<TYPE_SAVE> iter;

                if(!m_listCreated)
                        sort();                                                         //sort the set.

                iter = m_list.begin();                                  //go to the under quartil
                for(x=0;x<num;x++) iter++;

                if(m_vector.size() % 4 == 0) {                  //if the real under quartil between two values add this values and calculate the arithmetical middle.
                        q = (*iter->pointer);
                        iter--;
                        q = add(q,(*iter->pointer));
                        q = doubleMul(q,0.5);
                }
                else {                                                                  //else return the quartil
                        q = (*iter->pointer);
                }

                return q;
        }

        /**
         * this function calculate the upper quartil.
         *
         * use add and doubleMul
         * @return the upper quartil
         */
        type getQuartil3() {
                type q;
                int x;
                int num = m_vector.size()*3/4;
                std::_List_iterator<TYPE_SAVE> iter;

                if(!m_listCreated)
                        sort();                                                         //sort the set.

                iter = m_list.begin();
                for(x=0;x<num;x++) iter++;                              //go to the upper quartil

                if(m_vector.size() % 4 == 0) {                  //if the real upper quartil between two values add this values and calculate the arithmetical middle.
                        q = (*iter->pointer);
                        iter--;
                        q = add(q,(*iter->pointer));
                        q = doubleMul(q,0.5);
                }
                else {                                                                  //else return the quartil
                        q = (*iter->pointer);
                }

                return q;
        }

        /**
         * this function calculate the range between the upper and under quartil. This range is called inter-quartil-range.
         *
         * use sub
         * @return the IQR
         */
        type getIQR() {
                type q1 = getQuartil1();                        //calculate the under quartil
                type q3 = getQuartil3();                        //calculate the upper quartil

                return sub(q3,q1);                                      //IQR = Q3 - Q1
        }

        /**
         * this function calculate the whisker distance
         *
         * use doubleMul
         * @param factor (double) the factor for this distance
         * @return the result
         */
        type getWhisker(double factor) {
                type dIqr = getIQR();                   //calculate the IQR

                return doubleMul(dIqr,factor);  //WHISKER distance is factor*IQR
        }

        /**
         * this function search the lowest value in the set which is from under quartil inside the whisker distance
         *
         * use sub, lower and zero
         * @param factor (double) this factor is for calculating the whisker distance.
         * @return the lowest value inside
         */
        type getWhisker1(double factor) {
                type dW = getWhisker(factor);                           //calculate the whisker distance
                type dQ1 = getQuartil1();                                       //calculate the under quartil
                                                                                                        //TODO for optimization: getWhisker use getIQR and this calculate Q1 so it will be calculate two times!!!
                type dBorder = sub(dQ1,dW);                                     //where is the border for the lowest value
                std::_List_iterator<TYPE_SAVE> iter = m_list.begin();

                while(lower((*iter->pointer),dBorder) && iter!=m_list.end()) {          //search
                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                if(iter==m_list.end())          // ERROR
                        return zero();

                return (*iter->pointer);
        }

        /**
         * this function search the highest value in the set which is from the upper quartil inside the whisker distance
         *
         * use add and lower
         * @param factor (double) this factor is for calculating the whisker distance.
         * @return the highest value inside
         */
        type getWhisker3(double factor) {
                type dW = getWhisker(factor);                           //calculate the whisker distance
                type dQ3 = getQuartil3();                                       //calculate the upper quartil
                                                                                                        //TODO for optimization: getWhisker use getIQR and this calculate Q3 so it will be calculate two times!!!
                type dBorder = add(dQ3,dW);                                     //where is the border for the lowest value
                std::_List_iterator<TYPE_SAVE> iter = m_list.begin();

                while(lower((*iter->pointer),dBorder) && iter!=m_list.end()) {          //search
                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                if(iter!=m_list.begin())
                        iter--;

                return (*iter->pointer);
        }

        /**
         * this function give you the number of elements in the giving set, which aren't in the whisker distance
         *
         * use lower and higher
         * @param factor (double) this factor is for calculating the whisker distance
         * @return (int) the number of extreme values in the set
         */
        unsigned int getNumExtrems(double factor) {
                unsigned int result = 0;
                type dW1 = getWhisker1(factor);                                                         //find W1
                type dW3 = getWhisker3(factor);                                                         //find W3
                std::_List_iterator<TYPE_SAVE> iter = m_list.begin();

                while(lower((*iter->pointer),dW1) && iter!=m_list.end()) {      //count all elements which are lower than W1
                        iter++;
                        if(iter==m_list.end())
                                break;
                        result++;
                }

                while(!higher((*iter->pointer),dW3) && iter!=m_list.end()) {    //go from W1 to W3
                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                while(iter!=m_list.end()) {                                                                     //count all element which are higher than W3
                        iter++;
                        result++;
                }

                return result;
        }

        /**
         * this function gives one extreme value back
         *
         * use lower, higher and zero
         * @param factor (double) the factor for the whisker distance
         * @param i (unsigned int) the index of the searched extreme value
         * @return the founded extreme value
         */
        type getExtrem(double factor, unsigned int i) {
                type dW1 = getWhisker1(factor);                                                 //find W1
                type dW3 = getWhisker3(factor);                                                 //find W3
                std::_List_iterator<TYPE_SAVE> iter = m_list.begin();

                while(lower((*iter->pointer),dW1) && iter!=m_list.end()) {                      //search in lower area
                        i--;

                        if(i==0)
                                return (*iter->pointer);

                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                while(!higher((*iter->pointer),dW3) && iter!=m_list.end()) {            //go from W1 to W3
                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                while(iter!=m_list.end()) {                                                                                     //search in upper area
                        i--;

                        if(i==0)
                                return (*iter->pointer);

                        iter++;
                }

                return zero();          //not found                                                                             //if not found return zero
        }

        /**
         * this function search the value which is next to zero.
         *
         * use zero, sub and lower
         * @return the best value
         */
        type getBest(void) {
                type z = zero();                                                                                        //test value is zero
                type* l;
                type* h;

                if(!m_listCreated)
                        sort();                                                                                                 //sort the list

                std::_List_iterator<TYPE_SAVE> iter = m_list.begin();

                while(lower((*iter->pointer),z) && iter!=m_list.end()) {        //search the element which is as first higher than zero
                        iter++;
                        if(iter==m_list.end())
                                break;
                }

                if(iter!=m_list.end())
                        //return (*iter->pointer);
                        h = iter->pointer;

                else {
                        iter--;
                        //return (*iter->pointer);
                        h = iter->pointer;
                }

                while(!lower((*iter->pointer),z) && iter!= m_list.begin()) {    //search the element which is as first lower than zero
                        iter--;
                        if(iter==m_list.begin())
                                break;
                }

                l = iter->pointer;

                if(lower(sub(*h,z),sub(z,*l)))          //test which is next to zero
                        return *h;
                else
                        return *l;
        }

protected:

        /**
         * help structur for sorting the set.
         * define the lower than operator
         */
        struct TYPE_SAVE {
                TYPE_SAVE(type& a) : pointer(&a) {}

                type* pointer;

                bool operator<(const TYPE_SAVE& other) {
                        return lower((*pointer),(*other.pointer));
                }
        };

        /**
         * this vector save the giving set.
         */
        std::vector<type>& m_vector;

        /**
         * this list saves the sorted set
         */
        std::list<TYPE_SAVE> m_list;

        /**
         * this variable remember if the sorted list is created
         */
        bool m_listCreated;

        /**
         * this function create the sorted list
         */
        void sort(void) {
                __gnu_cxx::__normal_iterator<type*,std::vector<type,std::allocator<type> > > iter;

                for(iter = m_vector.begin(); iter != m_vector.end(); iter++) {                  //fill the sorted list with elements of the help structur
                        m_list.push_back(TYPE_SAVE((*iter)));
                }

                m_list.sort();                          //sort the list
                m_listCreated = true;           //remember that it is created.
        }
};

#endif /* TEMPLATEVALUEANALYSATION_H_ */

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