src/math/Polynomial.hpp

 /*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Acknowledgement of the program authors must be made in any
 *    publication of scientific results based in part on use of the
 *    program.  An acceptable form of acknowledgement is citation of
 *    the article in which the program was described (Matthew
 *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
 *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
 *    Parallel Simulation Engine for Molecular Dynamics,"
 *    J. Comput. Chem. 26, pp. 252-271 (2005))
 *
 * 2. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 3. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 */
 
/**
 * @file Polynomial.hpp
 * @author    teng lin
 * @date  11/16/2004
 * @version 1.0
 */ 

#ifndef MATH_POLYNOMIAL_HPP
#define MATH_POLYNOMIAL_HPP

#include <iostream>
#include <list>
#include <map>
#include <utility>

namespace oopse {

template<typename ElemType> 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 typename PolynomialPairMap::iterator iterator;
        typedef typename PolynomialPairMap::const_iterator const_iterator;
        /** 
         * 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 = ElemType();
            ExponentType exponent;
            CoefficientType coefficient;
            
            for (iterator 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 = ElemType();
            ExponentType exponent;
            CoefficientType coefficient;
            
            for (iterator 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) {
            iterator i = polyPairMap_.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) {
            iterator i = polyPairMap_.find(exponent);

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

        iterator begin() {
            return polyPairMap_.begin();
        }

        const_iterator begin() const{
            return polyPairMap_.begin();
        }
        
        iterator end() {
            return polyPairMap_.end();
        }

        const_iterator end() const{
            return polyPairMap_.end();
        }

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

        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>::const_iterator i;
    typename Polynomial<ElemType>::const_iterator j;
    Polynomial<ElemType> p;
    
    for (i = p1.begin(); i !=p1.end(); ++i) {
        for (j = p2.begin(); j !=p2.end(); ++j) {
            p.addCoefficient( i->first + j->first, i->second * j->second);
        }
    }

    return p;
}

/**
 * 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>::const_iterator i;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        p.addCoefficient(i->first, 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>::const_iterator i;

    for (i =  p2.begin(); i  != p2.end(); ++i) {
        p.addCoefficient(i->first, -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>::const_iterator i;
    typename Polynomial<ElemType>::const_iterator 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:	1927
Committed:	Wed Jan 12 17:14:35 2005 UTC (20 years, 6 months ago) by tim
File size:	8967 byte(s)
Log Message:	change license
#	User	Rev	Content
1	tim	1927	/*
2			* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	1744	*
4	tim	1927	* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
6			* redistribute this software in source and binary code form, provided
7			* that the following conditions are met:
8			*
9			* 1. Acknowledgement of the program authors must be made in any
10			* publication of scientific results based in part on use of the
11			* program. An acceptable form of acknowledgement is citation of
12			* the article in which the program was described (Matthew
13			* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14			* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15			* Parallel Simulation Engine for Molecular Dynamics,"
16			* J. Comput. Chem. 26, pp. 252-271 (2005))
17			*
18			* 2. Redistributions of source code must retain the above copyright
19			* notice, this list of conditions and the following disclaimer.
20			*
21			* 3. Redistributions in binary form must reproduce the above copyright
22			* notice, this list of conditions and the following disclaimer in the
23			* documentation and/or other materials provided with the
24			* distribution.
25			*
26			* This software is provided "AS IS," without a warranty of any
27			* kind. All express or implied conditions, representations and
28			* warranties, including any implied warranty of merchantability,
29			* fitness for a particular purpose or non-infringement, are hereby
30			* excluded. The University of Notre Dame and its licensors shall not
31			* be liable for any damages suffered by licensee as a result of
32			* using, modifying or distributing the software or its
33			* derivatives. In no event will the University of Notre Dame or its
34			* licensors be liable for any lost revenue, profit or data, or for
35			* direct, indirect, special, consequential, incidental or punitive
36			* damages, however caused and regardless of the theory of liability,
37			* arising out of the use of or inability to use software, even if the
38			* University of Notre Dame has been advised of the possibility of
39			* such damages.
40	tim	1744	*/
41	tim	1927
42	tim	1744	/**
43			* @file Polynomial.hpp
44	tim	1746	* @author teng lin
45			* @date 11/16/2004
46	tim	1744	* @version 1.0
47			*/
48
49			#ifndef MATH_POLYNOMIAL_HPP
50			#define MATH_POLYNOMIAL_HPP
51
52	tim	1796	#include <iostream>
53	tim	1744	#include <list>
54	tim	1796	#include <map>
55	tim	1744	#include <utility>
56
57			namespace oopse {
58
59	tim	1796	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	tim	1744	ElemType result(1);
61
62			for (int i = 0; i < N; ++i) {
63			result *= x;
64			}
65
66			return result;
67			}
68
69	tim	1746	/**
70			* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71			* A generic Polynomial class
72			*/
73	tim	1744	template<typename ElemType>
74			class Polynomial {
75
76			public:
77
78			typedef int ExponentType;
79	tim	1746	typedef ElemType CoefficientType;
80			typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
81	tim	1856	typedef typename PolynomialPairMap::iterator iterator;
82			typedef typename PolynomialPairMap::const_iterator const_iterator;
83	tim	1744	/**
84	tim	1746	* Calculates the value of this Polynomial evaluated at the given x value.
85			* @return The value of this Polynomial evaluates at the given x value
86			* @param x the value of the independent variable for this Polynomial function
87	tim	1744	*/
88			ElemType evaluate(const ElemType& x) {
89	tim	1796	ElemType result = ElemType();
90	tim	1856	ExponentType exponent;
91			CoefficientType coefficient;
92	tim	1744
93	tim	1796	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
94	tim	1744	exponent = i->first;
95	tim	1746	coefficient = i->second;
96			result += pow(x, exponent) * coefficient;
97	tim	1744	}
98
99			return result;
100			}
101
102	tim	1746	/**
103			* Returns the first derivative of this polynomial.
104			* @return the first derivative of this polynomial
105			* @param x
106			*/
107			ElemType evaluateDerivative(const ElemType& x) {
108	tim	1796	ElemType result = ElemType();
109	tim	1856	ExponentType exponent;
110			CoefficientType coefficient;
111	tim	1744
112	tim	1796	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
113	tim	1744	exponent = i->first;
114	tim	1746	coefficient = i->second;
115			result += pow(x, exponent - 1) * coefficient * exponent;
116	tim	1744	}
117
118			return result;
119			}
120
121	tim	1746	/**
122	tim	1747	* Set the coefficent of the specified exponent, if the coefficient is already there, it
123			* will be overwritten.
124	tim	1746	* @param exponent exponent of a term in this Polynomial
125			* @param coefficient multiplier of a term in this Polynomial
126			*/
127
128			void setCoefficient(int exponent, const ElemType& coefficient) {
129			polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
130	tim	1744	}
131
132	tim	1746	/**
133	tim	1747	* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
134			* new coefficient to the old one, otherwise, just call setCoefficent
135			* @param exponent exponent of a term in this Polynomial
136			* @param coefficient multiplier of a term in this Polynomial
137			*/
138
139			void addCoefficient(int exponent, const ElemType& coefficient) {
140	tim	1796	iterator i = polyPairMap_.find(exponent);
141	tim	1747
142			if (i != end()) {
143			i->second += coefficient;
144			} else {
145			setCoefficient(exponent, coefficient);
146			}
147			}
148
149
150			/**
151	tim	1746	* Returns the coefficient associated with the given power for this Polynomial.
152			* @return the coefficient associated with the given power for this Polynomial
153			* @exponent exponent of any term in this Polynomial
154			*/
155			ElemType getCoefficient(ExponentType exponent) {
156	tim	1796	iterator i = polyPairMap_.find(exponent);
157	tim	1744
158	tim	1746	if (i != end()) {
159			return i->second;
160			} else {
161			return ElemType(0);
162			}
163	tim	1744	}
164
165	tim	1796	iterator begin() {
166	tim	1744	return polyPairMap_.begin();
167			}
168	tim	1796
169			const_iterator begin() const{
170			return polyPairMap_.begin();
171			}
172	tim	1744
173	tim	1796	iterator end() {
174	tim	1744	return polyPairMap_.end();
175			}
176
177	tim	1796	const_iterator end() const{
178			return polyPairMap_.end();
179	tim	1744	}
180	tim	1746
181	tim	1796	iterator find(ExponentType exponent) {
182			return polyPairMap_.find(exponent);
183			}
184
185	tim	1746	size_t size() {
186			return polyPairMap_.size();
187			}
188
189	tim	1744	private:
190
191			PolynomialPairMap polyPairMap_;
192			};
193
194	tim	1746
195			/**
196			* Generates and returns the product of two given Polynomials.
197			* @return A Polynomial containing the product of the two given Polynomial parameters
198			*/
199			template<typename ElemType>
200			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
201	tim	1796	typename Polynomial<ElemType>::const_iterator i;
202			typename Polynomial<ElemType>::const_iterator j;
203	tim	1746	Polynomial<ElemType> p;
204
205			for (i = p1.begin(); i !=p1.end(); ++i) {
206	tim	1796	for (j = p2.begin(); j !=p2.end(); ++j) {
207			p.addCoefficient( i->first + j->first, i->second * j->second);
208	tim	1746	}
209			}
210	tim	1796
211			return p;
212	tim	1746	}
213
214			/**
215			* Generates and returns the sum of two given Polynomials.
216			* @param p1 the first polynomial
217			* @param p2 the second polynomial
218			*/
219			template<typename ElemType>
220			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
221			Polynomial<ElemType> p(p1);
222
223	tim	1796	typename Polynomial<ElemType>::const_iterator i;
224	tim	1746
225			for (i = p2.begin(); i != p2.end(); ++i) {
226	tim	1796	p.addCoefficient(i->first, i->second);
227	tim	1746	}
228
229			return p;
230
231			}
232
233			/**
234			* Generates and returns the difference of two given Polynomials.
235			* @return
236			* @param p1 the first polynomial
237			* @param p2 the second polynomial
238			*/
239			template<typename ElemType>
240			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
241			Polynomial<ElemType> p(p1);
242
243	tim	1796	typename Polynomial<ElemType>::const_iterator i;
244	tim	1746
245			for (i = p2.begin(); i != p2.end(); ++i) {
246	tim	1796	p.addCoefficient(i->first, -i->second);
247	tim	1746	}
248
249			return p;
250
251			}
252
253			/**
254			* Tests if two polynomial have the same exponents
255			* @return true if these all of the exponents in these Polynomial are identical
256			* @param p1 the first polynomial
257			* @param p2 the second polynomial
258			* @note this function does not compare the coefficient
259			*/
260			template<typename ElemType>
261			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
262
263	tim	1796	typename Polynomial<ElemType>::const_iterator i;
264			typename Polynomial<ElemType>::const_iterator j;
265	tim	1746
266	tim	1851	if (p1.size() != p2.size() ) {
267	tim	1746	return false;
268			}
269
270			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
271			if (i->first != j->first) {
272			return false;
273			}
274			}
275
276			return true;
277			}
278
279			typedef Polynomial<double> DoublePolynomial;
280
281	tim	1744	} //end namespace oopse
282			#endif //MATH_POLYNOMIAL_HPP