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;
        }

        /**
         * @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));
        }

        /**
         * 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.begjn(); 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:	1746
Committed:	Wed Nov 17 06:37:56 2004 UTC (19 years, 8 months ago) by tim
File size:	7585 byte(s)
Log Message:	add PolynomialBondType, PolynomialBendType, PolynomialTorsionType, HarmonicBendType and CharmmTorsionType. Need to refine the design and add document for them
#	Content
1	/*
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	* @author teng lin
29	* @date 11/16/2004
30	* @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	template<typename ElemType> pow(ElemType x, int N) {
42	ElemType result(1);
43
44	for (int i = 0; i < N; ++i) {
45	result *= x;
46	}
47
48	return result;
49	}
50
51	/**
52	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
53	* A generic Polynomial class
54	*/
55	template<typename ElemType>
56	class Polynomial {
57
58	public:
59
60	typedef int ExponentType;
61	typedef ElemType CoefficientType;
62	typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
63	typedef PolynomialPairMap::iterator PolynomialIterator;
64
65	/**
66	* 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	*/
70	ElemType evaluate(const ElemType& x) {
71	ElemType result;
72	double exponent;
73	double coefficient;
74
75	for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
76	exponent = i->first;
77	coefficient = i->second;
78	result += pow(x, exponent) * coefficient;
79	}
80
81	return result;
82	}
83
84	/**
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	ElemType result;
91	double exponent;
92	double coefficient;
93
94	for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
95	exponent = i->first;
96	coefficient = i->second;
97	result += pow(x, exponent - 1) * coefficient * exponent;
98	}
99
100	return result;
101	}
102
103	/**
104	* @param exponent exponent of a term in this Polynomial
105	* @param coefficient multiplier of a term in this Polynomial
106	*/
107
108	void setCoefficient(int exponent, const ElemType& coefficient) {
109	polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
110	}
111
112	/**
113	* Returns the coefficient associated with the given power for this Polynomial.
114	* @return the coefficient associated with the given power for this Polynomial
115	* @exponent exponent of any term in this Polynomial
116	*/
117	ElemType getCoefficient(ExponentType exponent) {
118	PolynomialIterator i = find(exponent);
119
120	if (i != end()) {
121	return i->second;
122	} else {
123	return ElemType(0);
124	}
125	}
126
127	PolynomialIterator begin() {
128	return polyPairMap_.begin();
129	}
130
131	PolynomialIterator end() {
132	return polyPairMap_.end();
133	}
134
135	PolynomialIterator find(ExponentType exponent) {
136	return polyPairMap_.find();
137	}
138
139	size_t size() {
140	return polyPairMap_.size();
141	}
142
143	private:
144
145	PolynomialPairMap polyPairMap_;
146	};
147
148
149	/**
150	* Generates and returns the product of two given Polynomials.
151	* @return A Polynomial containing the product of the two given Polynomial parameters
152	*/
153	template<typename ElemType>
154	Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
155	typename Polynomial<ElemType>::PolynomialIterator i;
156	typename Polynomial<ElemType>::PolynomialIterator j;
157	typename Polynomial<ElemType>::PolynomialIterator k;
158	Polynomial<ElemType> p;
159	int exponent;
160	int coefficient;
161
162	for (i = p1.begin(); i !=p1.end(); ++i) {
163	for (j = p1.begjn(); j !=p1.end(); ++j) {
164	exponent = i->first + j->first;
165	coefficient = i->second * j->second;
166	k = p->find(exponent);
167
168	if (k != p.end()) {
169	p[exponent] = coefficient;
170	} else {
171	k->second += coefficient;
172	}
173	}
174	}
175	}
176
177	/**
178	* Generates and returns the sum of two given Polynomials.
179	* @param p1 the first polynomial
180	* @param p2 the second polynomial
181	*/
182	template<typename ElemType>
183	Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
184	Polynomial<ElemType> p(p1);
185
186	typename Polynomial<ElemType>::PolynomialIterator i;
187	typename Polynomial<ElemType>::PolynomialIterator j;
188
189	for (i = p2.begin(); i != p2.end(); ++i) {
190	j = p.find(i->first);
191	if (j == p.end()) {
192	p[j] = i->second;
193	} else {
194	j->second += i->second;
195	}
196	}
197
198	return p;
199
200	}
201
202	/**
203	* Generates and returns the difference of two given Polynomials.
204	* @return
205	* @param p1 the first polynomial
206	* @param p2 the second polynomial
207	*/
208	template<typename ElemType>
209	Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
210	Polynomial<ElemType> p(p1);
211
212	typename Polynomial<ElemType>::PolynomialIterator i;
213	typename Polynomial<ElemType>::PolynomialIterator j;
214
215	for (i = p2.begin(); i != p2.end(); ++i) {
216	j = p.find(i->first);
217	if (j == p.end()) {
218	p[j] = -i->second;
219	} else {
220	j->second -= i->second;
221	}
222	}
223
224	return p;
225
226	}
227
228	/**
229	* Tests if two polynomial have the same exponents
230	* @return true if these all of the exponents in these Polynomial are identical
231	* @param p1 the first polynomial
232	* @param p2 the second polynomial
233	* @note this function does not compare the coefficient
234	*/
235	template<typename ElemType>
236	bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
237
238	typename Polynomial<ElemType>::PolynomialIterator i;
239	typename Polynomial<ElemType>::PolynomialIterator j;
240
241	if (p1.size() !== p2.size() ) {
242	return false;
243	}
244
245	for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
246	if (i->first != j->first) {
247	return false;
248	}
249	}
250
251	return true;
252	}
253
254	typedef Polynomial<double> DoublePolynomial;
255
256	} //end namespace oopse
257	#endif //MATH_POLYNOMIAL_HPP