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, 8 months ago) by tim
File size:	8370 byte(s)
Log Message:	more types stuff and Chebyshev Polynomial
#	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	* Set the coefficent of the specified exponent, if the coefficient is already there, it
105	* will be overwritten.
106	* @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	}
113
114	/**
115	* 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	* 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
140	if (i != end()) {
141	return i->second;
142	} else {
143	return ElemType(0);
144	}
145	}
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
159	size_t size() {
160	return polyPairMap_.size();
161	}
162
163	private:
164
165	PolynomialPairMap polyPairMap_;
166	};
167
168
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	for (j = p1.begin(); j !=p1.end(); ++j) {
184	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	} //end namespace oopse
277	#endif //MATH_POLYNOMIAL_HPP