src/math/Polynomial.hpp

/*
 * Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
 * 
 * Contact: oopse@oopse.org
 * 
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU Lesser General Public License
 * as published by the Free Software Foundation; either version 2.1
 * of the License, or (at your option) any later version.
 * All we ask is that proper credit is given for our work, which includes
 * - but is not limited to - adding the above copyright notice to the beginning
 * of your source code files, and to any copyright notice that you may distribute
 * with programs based on this work.
 * 
 * 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 Lesser General Public License for more details.
 * 
 * You should have received a copy of the GNU Lesser 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.
 *
 */

/**
 * @file Polynomial.hpp
 * @author    teng lin
 * @date  11/16/2004
 * @version 1.0
 */ 

#ifndef MATH_POLYNOMIAL_HPP
#define MATH_POLYNOMIAL_HPP

#include <list>
#include <utility>

namespace oopse {

template<typename ElemType> pow(ElemType x, int N) {
    ElemType result(1);

    for (int i = 0; i < N; ++i) {
        result *= x;
    }

    return result;
}

/**
 * @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
 * A generic Polynomial class
 */
template<typename ElemType>
class Polynomial {

    public:
        
        typedef int ExponentType;
        typedef ElemType CoefficientType;
        typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
        typedef PolynomialPairMap::iterator PolynomialIterator;

        /** 
         * Calculates the value of this Polynomial evaluated at the given x value.
         * @return The value of this Polynomial evaluates at the given x value
         * @param x the value of the independent variable for this Polynomial function
         */
        ElemType evaluate(const ElemType& x) {
            ElemType result;
            double exponent;
            double coefficient;
            
            for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent) * coefficient;
            }

            return result;
        }

        /**
         * Returns the first derivative of this polynomial.
         * @return the first derivative of this polynomial
         * @param x
         */
        ElemType evaluateDerivative(const ElemType& x) {
            ElemType result;
            double exponent;
            double coefficient;
            
            for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
                exponent = i->first;
                coefficient = i->second;
                result  += pow(x, exponent - 1) * coefficient * exponent;
            }

            return result;
        }

        /**
         * Set the coefficent of the specified exponent, if the coefficient is already there, it
         * will be overwritten.
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void setCoefficient(int exponent, const ElemType& coefficient) {
            polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
        }

        /**
         * Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
         * new coefficient to the old one, otherwise,  just call setCoefficent
         * @param exponent exponent of a term in this Polynomial 
         * @param coefficient multiplier of a term in this Polynomial 
         */
        
        void addCoefficient(int exponent, const ElemType& coefficient) {
            PolynomialIterator i = find(exponent);

            if (i != end()) {
                i->second += coefficient;
            } else {
                setCoefficient(exponent, coefficient);
            }
        }


        /**
         * Returns the coefficient associated with the given power for this Polynomial.
         * @return the coefficient associated with the given power for this Polynomial
         * @exponent exponent of any term in this Polynomial
         */
        ElemType getCoefficient(ExponentType exponent) {
            PolynomialIterator i = find(exponent);

            if (i != end()) {
                return i->second;
            } else {
                return ElemType(0);
            }
        }

        PolynomialIterator begin() {
            return polyPairMap_.begin();
        }
        
        PolynomialIterator end() {
            return polyPairMap_.end();
        }

        PolynomialIterator find(ExponentType exponent) {
            return polyPairMap_.find();
        }

        size_t size() {
            return polyPairMap_.size();
        }
        
    private:
        
        PolynomialPairMap polyPairMap_;
};


/**
 * Generates and returns the product of two given Polynomials.
 * @return A Polynomial containing the product of the two given Polynomial parameters
 */
template<typename ElemType>
Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;
    typename Polynomial<ElemType>::PolynomialIterator k;
    Polynomial<ElemType> p;
    int exponent;
    int coefficient;
    
    for (i = p1.begin(); i !=p1.end(); ++i) {
        for (j = p1.begin(); j !=p1.end(); ++j) {
            exponent = i->first + j->first;            
            coefficient = i->second * j->second;
            k = p->find(exponent);

            if (k != p.end()) {
                p[exponent] = coefficient;
            } else {
                k->second += coefficient;
            }
        }
    }
}

/**
 * Generates and returns the sum of two given Polynomials.
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        j = p.find(i->first);
        if (j == p.end()) {
            p[j] = i->second;
        } else {
            j->second += i->second;
        }
    }

    return p;

}

/**
 * Generates and returns the difference of two given Polynomials. 
 * @return
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 */
template<typename ElemType>
Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
    Polynomial<ElemType> p(p1);

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        j = p.find(i->first);
        if (j == p.end()) {
            p[j] = -i->second;
        } else {
            j->second -= i->second;
        }
    }

    return p;

}

/**
 * Tests if two polynomial have the same exponents
 * @return true if these all of the exponents in these Polynomial are identical
 * @param p1 the first polynomial
 * @param p2 the second polynomial
 * @note this function does not compare the coefficient
 */
template<typename ElemType>
bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {

    typename Polynomial<ElemType>::PolynomialIterator i;
    typename Polynomial<ElemType>::PolynomialIterator j;

    if (p1.size() !== p2.size() ) {
        return false;
    }
    
    for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
        if (i->first != j->first) {
            return false;
        }
    }

    return true;
}

typedef Polynomial<double> DoublePolynomial;

} //end namespace oopse
#endif //MATH_POLYNOMIAL_HPP
Revision:	1747
Committed:	Wed Nov 17 18:58:49 2004 UTC (19 years, 7 months ago) by tim
File size:	8370 byte(s)
Log Message:	more types stuff and Chebyshev Polynomial
#	User	Rev	Content
1	tim	1744	/*
2			* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project
3			*
4			* Contact: oopse@oopse.org
5			*
6			* This program is free software; you can redistribute it and/or
7			* modify it under the terms of the GNU Lesser General Public License
8			* as published by the Free Software Foundation; either version 2.1
9			* of the License, or (at your option) any later version.
10			* All we ask is that proper credit is given for our work, which includes
11			* - but is not limited to - adding the above copyright notice to the beginning
12			* of your source code files, and to any copyright notice that you may distribute
13			* with programs based on this work.
14			*
15			* This program is distributed in the hope that it will be useful,
16			* but WITHOUT ANY WARRANTY; without even the implied warranty of
17			* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
18			* GNU Lesser General Public License for more details.
19			*
20			* You should have received a copy of the GNU Lesser General Public License
21			* along with this program; if not, write to the Free Software
22			* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
23			*
24			*/
25
26			/**
27			* @file Polynomial.hpp
28	tim	1746	* @author teng lin
29			* @date 11/16/2004
30	tim	1744	* @version 1.0
31			*/
32
33			#ifndef MATH_POLYNOMIAL_HPP
34			#define MATH_POLYNOMIAL_HPP
35
36			#include <list>
37			#include <utility>
38
39			namespace oopse {
40
41	tim	1746	template<typename ElemType> pow(ElemType x, int N) {
42	tim	1744	ElemType result(1);
43
44			for (int i = 0; i < N; ++i) {
45			result *= x;
46			}
47
48			return result;
49			}
50
51	tim	1746	/**
52			* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
53			* A generic Polynomial class
54			*/
55	tim	1744	template<typename ElemType>
56			class Polynomial {
57
58			public:
59
60			typedef int ExponentType;
61	tim	1746	typedef ElemType CoefficientType;
62			typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
63	tim	1744	typedef PolynomialPairMap::iterator PolynomialIterator;
64
65			/**
66	tim	1746	* Calculates the value of this Polynomial evaluated at the given x value.
67			* @return The value of this Polynomial evaluates at the given x value
68			* @param x the value of the independent variable for this Polynomial function
69	tim	1744	*/
70			ElemType evaluate(const ElemType& x) {
71			ElemType result;
72			double exponent;
73	tim	1746	double coefficient;
74	tim	1744
75			for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
76			exponent = i->first;
77	tim	1746	coefficient = i->second;
78			result += pow(x, exponent) * coefficient;
79	tim	1744	}
80
81			return result;
82			}
83
84	tim	1746	/**
85			* Returns the first derivative of this polynomial.
86			* @return the first derivative of this polynomial
87			* @param x
88			*/
89			ElemType evaluateDerivative(const ElemType& x) {
90	tim	1744	ElemType result;
91			double exponent;
92	tim	1746	double coefficient;
93	tim	1744
94			for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
95			exponent = i->first;
96	tim	1746	coefficient = i->second;
97			result += pow(x, exponent - 1) * coefficient * exponent;
98	tim	1744	}
99
100			return result;
101			}
102
103	tim	1746	/**
104	tim	1747	* Set the coefficent of the specified exponent, if the coefficient is already there, it
105			* will be overwritten.
106	tim	1746	* @param exponent exponent of a term in this Polynomial
107			* @param coefficient multiplier of a term in this Polynomial
108			*/
109
110			void setCoefficient(int exponent, const ElemType& coefficient) {
111			polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
112	tim	1744	}
113
114	tim	1746	/**
115	tim	1747	* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
116			* new coefficient to the old one, otherwise, just call setCoefficent
117			* @param exponent exponent of a term in this Polynomial
118			* @param coefficient multiplier of a term in this Polynomial
119			*/
120
121			void addCoefficient(int exponent, const ElemType& coefficient) {
122			PolynomialIterator i = find(exponent);
123
124			if (i != end()) {
125			i->second += coefficient;
126			} else {
127			setCoefficient(exponent, coefficient);
128			}
129			}
130
131
132			/**
133	tim	1746	* Returns the coefficient associated with the given power for this Polynomial.
134			* @return the coefficient associated with the given power for this Polynomial
135			* @exponent exponent of any term in this Polynomial
136			*/
137			ElemType getCoefficient(ExponentType exponent) {
138			PolynomialIterator i = find(exponent);
139	tim	1744
140	tim	1746	if (i != end()) {
141			return i->second;
142			} else {
143			return ElemType(0);
144			}
145	tim	1744	}
146
147			PolynomialIterator begin() {
148			return polyPairMap_.begin();
149			}
150
151			PolynomialIterator end() {
152			return polyPairMap_.end();
153			}
154
155			PolynomialIterator find(ExponentType exponent) {
156			return polyPairMap_.find();
157			}
158	tim	1746
159			size_t size() {
160			return polyPairMap_.size();
161			}
162
163	tim	1744	private:
164
165			PolynomialPairMap polyPairMap_;
166			};
167
168	tim	1746
169			/**
170			* Generates and returns the product of two given Polynomials.
171			* @return A Polynomial containing the product of the two given Polynomial parameters
172			*/
173			template<typename ElemType>
174			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
175			typename Polynomial<ElemType>::PolynomialIterator i;
176			typename Polynomial<ElemType>::PolynomialIterator j;
177			typename Polynomial<ElemType>::PolynomialIterator k;
178			Polynomial<ElemType> p;
179			int exponent;
180			int coefficient;
181
182			for (i = p1.begin(); i !=p1.end(); ++i) {
183	tim	1747	for (j = p1.begin(); j !=p1.end(); ++j) {
184	tim	1746	exponent = i->first + j->first;
185			coefficient = i->second * j->second;
186			k = p->find(exponent);
187
188			if (k != p.end()) {
189			p[exponent] = coefficient;
190			} else {
191			k->second += coefficient;
192			}
193			}
194			}
195			}
196
197			/**
198			* Generates and returns the sum of two given Polynomials.
199			* @param p1 the first polynomial
200			* @param p2 the second polynomial
201			*/
202			template<typename ElemType>
203			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
204			Polynomial<ElemType> p(p1);
205
206			typename Polynomial<ElemType>::PolynomialIterator i;
207			typename Polynomial<ElemType>::PolynomialIterator j;
208
209			for (i = p2.begin(); i != p2.end(); ++i) {
210			j = p.find(i->first);
211			if (j == p.end()) {
212			p[j] = i->second;
213			} else {
214			j->second += i->second;
215			}
216			}
217
218			return p;
219
220			}
221
222			/**
223			* Generates and returns the difference of two given Polynomials.
224			* @return
225			* @param p1 the first polynomial
226			* @param p2 the second polynomial
227			*/
228			template<typename ElemType>
229			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
230			Polynomial<ElemType> p(p1);
231
232			typename Polynomial<ElemType>::PolynomialIterator i;
233			typename Polynomial<ElemType>::PolynomialIterator j;
234
235			for (i = p2.begin(); i != p2.end(); ++i) {
236			j = p.find(i->first);
237			if (j == p.end()) {
238			p[j] = -i->second;
239			} else {
240			j->second -= i->second;
241			}
242			}
243
244			return p;
245
246			}
247
248			/**
249			* Tests if two polynomial have the same exponents
250			* @return true if these all of the exponents in these Polynomial are identical
251			* @param p1 the first polynomial
252			* @param p2 the second polynomial
253			* @note this function does not compare the coefficient
254			*/
255			template<typename ElemType>
256			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
257
258			typename Polynomial<ElemType>::PolynomialIterator i;
259			typename Polynomial<ElemType>::PolynomialIterator j;
260
261			if (p1.size() !== p2.size() ) {
262			return false;
263			}
264
265			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
266			if (i->first != j->first) {
267			return false;
268			}
269			}
270
271			return true;
272			}
273
274			typedef Polynomial<double> DoublePolynomial;
275
276	tim	1744	} //end namespace oopse
277			#endif //MATH_POLYNOMIAL_HPP