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 <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:	1856
Committed:	Mon Dec 6 04:49:53 2004 UTC (19 years, 7 months ago) by tim
File size:	8037 byte(s)
Log Message:	fix a bug in Exclude List
#	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 <iostream>
37	#include <list>
38	#include <map>
39	#include <utility>
40
41	namespace oopse {
42
43	template<typename ElemType> ElemType pow(ElemType x, int N) {
44	ElemType result(1);
45
46	for (int i = 0; i < N; ++i) {
47	result *= x;
48	}
49
50	return result;
51	}
52
53	/**
54	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
55	* A generic Polynomial class
56	*/
57	template<typename ElemType>
58	class Polynomial {
59
60	public:
61
62	typedef int ExponentType;
63	typedef ElemType CoefficientType;
64	typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
65	typedef typename PolynomialPairMap::iterator iterator;
66	typedef typename PolynomialPairMap::const_iterator const_iterator;
67	/**
68	* Calculates the value of this Polynomial evaluated at the given x value.
69	* @return The value of this Polynomial evaluates at the given x value
70	* @param x the value of the independent variable for this Polynomial function
71	*/
72	ElemType evaluate(const ElemType& x) {
73	ElemType result = ElemType();
74	ExponentType exponent;
75	CoefficientType coefficient;
76
77	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
78	exponent = i->first;
79	coefficient = i->second;
80	result += pow(x, exponent) * coefficient;
81	}
82
83	return result;
84	}
85
86	/**
87	* Returns the first derivative of this polynomial.
88	* @return the first derivative of this polynomial
89	* @param x
90	*/
91	ElemType evaluateDerivative(const ElemType& x) {
92	ElemType result = ElemType();
93	ExponentType exponent;
94	CoefficientType coefficient;
95
96	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
97	exponent = i->first;
98	coefficient = i->second;
99	result += pow(x, exponent - 1) * coefficient * exponent;
100	}
101
102	return result;
103	}
104
105	/**
106	* Set the coefficent of the specified exponent, if the coefficient is already there, it
107	* will be overwritten.
108	* @param exponent exponent of a term in this Polynomial
109	* @param coefficient multiplier of a term in this Polynomial
110	*/
111
112	void setCoefficient(int exponent, const ElemType& coefficient) {
113	polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient));
114	}
115
116	/**
117	* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
118	* new coefficient to the old one, otherwise, just call setCoefficent
119	* @param exponent exponent of a term in this Polynomial
120	* @param coefficient multiplier of a term in this Polynomial
121	*/
122
123	void addCoefficient(int exponent, const ElemType& coefficient) {
124	iterator i = polyPairMap_.find(exponent);
125
126	if (i != end()) {
127	i->second += coefficient;
128	} else {
129	setCoefficient(exponent, coefficient);
130	}
131	}
132
133
134	/**
135	* Returns the coefficient associated with the given power for this Polynomial.
136	* @return the coefficient associated with the given power for this Polynomial
137	* @exponent exponent of any term in this Polynomial
138	*/
139	ElemType getCoefficient(ExponentType exponent) {
140	iterator i = polyPairMap_.find(exponent);
141
142	if (i != end()) {
143	return i->second;
144	} else {
145	return ElemType(0);
146	}
147	}
148
149	iterator begin() {
150	return polyPairMap_.begin();
151	}
152
153	const_iterator begin() const{
154	return polyPairMap_.begin();
155	}
156
157	iterator end() {
158	return polyPairMap_.end();
159	}
160
161	const_iterator end() const{
162	return polyPairMap_.end();
163	}
164
165	iterator find(ExponentType exponent) {
166	return polyPairMap_.find(exponent);
167	}
168
169	size_t size() {
170	return polyPairMap_.size();
171	}
172
173	private:
174
175	PolynomialPairMap polyPairMap_;
176	};
177
178
179	/**
180	* Generates and returns the product of two given Polynomials.
181	* @return A Polynomial containing the product of the two given Polynomial parameters
182	*/
183	template<typename ElemType>
184	Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
185	typename Polynomial<ElemType>::const_iterator i;
186	typename Polynomial<ElemType>::const_iterator j;
187	Polynomial<ElemType> p;
188
189	for (i = p1.begin(); i !=p1.end(); ++i) {
190	for (j = p2.begin(); j !=p2.end(); ++j) {
191	p.addCoefficient( i->first + j->first, i->second * j->second);
192	}
193	}
194
195	return p;
196	}
197
198	/**
199	* Generates and returns the sum of two given Polynomials.
200	* @param p1 the first polynomial
201	* @param p2 the second polynomial
202	*/
203	template<typename ElemType>
204	Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
205	Polynomial<ElemType> p(p1);
206
207	typename Polynomial<ElemType>::const_iterator i;
208
209	for (i = p2.begin(); i != p2.end(); ++i) {
210	p.addCoefficient(i->first, i->second);
211	}
212
213	return p;
214
215	}
216
217	/**
218	* Generates and returns the difference of two given Polynomials.
219	* @return
220	* @param p1 the first polynomial
221	* @param p2 the second polynomial
222	*/
223	template<typename ElemType>
224	Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
225	Polynomial<ElemType> p(p1);
226
227	typename Polynomial<ElemType>::const_iterator i;
228
229	for (i = p2.begin(); i != p2.end(); ++i) {
230	p.addCoefficient(i->first, -i->second);
231	}
232
233	return p;
234
235	}
236
237	/**
238	* Tests if two polynomial have the same exponents
239	* @return true if these all of the exponents in these Polynomial are identical
240	* @param p1 the first polynomial
241	* @param p2 the second polynomial
242	* @note this function does not compare the coefficient
243	*/
244	template<typename ElemType>
245	bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
246
247	typename Polynomial<ElemType>::const_iterator i;
248	typename Polynomial<ElemType>::const_iterator j;
249
250	if (p1.size() != p2.size() ) {
251	return false;
252	}
253
254	for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
255	if (i->first != j->first) {
256	return false;
257	}
258	}
259
260	return true;
261	}
262
263	typedef Polynomial<double> DoublePolynomial;
264
265	} //end namespace oopse
266	#endif //MATH_POLYNOMIAL_HPP