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 Polynomial<ElemType> PolynomialType;    
    typedef int ExponentType;
    typedef ElemType CoefficientType;
    typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
    typedef typename PolynomialPairMap::iterator iterator;
    typedef typename PolynomialPairMap::const_iterator const_iterator;

    Polynomial() {}
    Polynomial(ElemType v) {setCoefficient(0, v);}
    /** 
     * 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(typename 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();
    }

    PolynomialType& operator += (const PolynomialType& p) {
        typename Polynomial<ElemType>::const_iterator i;

        for (i =  p.begin(); i  != p.end(); ++i) {
          this->addCoefficient(i->first, i->second);
        }

        return *this;        
    }

    PolynomialType& operator -= (const PolynomialType& p) {
        typename Polynomial<ElemType>::const_iterator i;
        for (i =  p.begin(); i  != p.end(); ++i) {
          this->addCoefficient(i->first, -i->second);
        }        
    }

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

    return *this;
    }

   
  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;
  }

  template<typename ElemType>
  Polynomial<ElemType> operator *(const Polynomial<ElemType>& p, const ElemType v) {
    typename Polynomial<ElemType>::const_iterator i;
    Polynomial<ElemType> result;
    
    for (i = p.begin(); i !=p.end(); ++i) {
        result.addCoefficient( i->first , i->second * v);
    }

    return result;
  }

  template<typename ElemType>
  Polynomial<ElemType> operator *( const ElemType v, const Polynomial<ElemType>& p) {
    typename Polynomial<ElemType>::const_iterator i;
    Polynomial<ElemType> result;
    
    for (i = p.begin(); i !=p.end(); ++i) {
        result.addCoefficient( i->first , i->second * v);
    }

    return result;
  }
  
  /**
   * 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:	2576
Committed:	Mon Jan 30 22:25:27 2006 UTC (18 years, 5 months ago) by tim
File size:	10164 byte(s)
Log Message:	Adding :LegendrePolynomial
#	User	Rev	Content
1	gezelter	2204	/*
2	gezelter	1930	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3			*
4			* 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			*/
41
42			/**
43			* @file Polynomial.hpp
44			* @author teng lin
45			* @date 11/16/2004
46			* @version 1.0
47			*/
48
49			#ifndef MATH_POLYNOMIAL_HPP
50			#define MATH_POLYNOMIAL_HPP
51
52			#include <iostream>
53			#include <list>
54			#include <map>
55			#include <utility>
56
57			namespace oopse {
58
59	gezelter	2204	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	gezelter	1930	ElemType result(1);
61
62			for (int i = 0; i < N; ++i) {
63	gezelter	2204	result *= x;
64	gezelter	1930	}
65
66			return result;
67	gezelter	2204	}
68	gezelter	1930
69	gezelter	2204	/**
70			* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71			* A generic Polynomial class
72			*/
73			template<typename ElemType>
74			class Polynomial {
75	gezelter	1930
76	gezelter	2204	public:
77	tim	2448	typedef Polynomial<ElemType> PolynomialType;
78	gezelter	2204	typedef int ExponentType;
79			typedef ElemType CoefficientType;
80			typedef std::map<ExponentType, CoefficientType> PolynomialPairMap;
81			typedef typename PolynomialPairMap::iterator iterator;
82			typedef typename PolynomialPairMap::const_iterator const_iterator;
83	tim	2448
84			Polynomial() {}
85			Polynomial(ElemType v) {setCoefficient(0, v);}
86	gezelter	2204	/**
87			* Calculates the value of this Polynomial evaluated at the given x value.
88			* @return The value of this Polynomial evaluates at the given x value
89			* @param x the value of the independent variable for this Polynomial function
90			*/
91			ElemType evaluate(const ElemType& x) {
92			ElemType result = ElemType();
93			ExponentType exponent;
94			CoefficientType coefficient;
95	gezelter	1930
96	gezelter	2204	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
97			exponent = i->first;
98			coefficient = i->second;
99			result += pow(x, exponent) * coefficient;
100			}
101	gezelter	1930
102	gezelter	2204	return result;
103			}
104	gezelter	1930
105	gezelter	2204	/**
106			* Returns the first derivative of this polynomial.
107			* @return the first derivative of this polynomial
108			* @param x
109			*/
110			ElemType evaluateDerivative(const ElemType& x) {
111			ElemType result = ElemType();
112			ExponentType exponent;
113			CoefficientType coefficient;
114	gezelter	1930
115	gezelter	2204	for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
116			exponent = i->first;
117			coefficient = i->second;
118			result += pow(x, exponent - 1) * coefficient * exponent;
119			}
120	gezelter	1930
121	gezelter	2204	return result;
122			}
123	gezelter	1930
124	gezelter	2204	/**
125			* Set the coefficent of the specified exponent, if the coefficient is already there, it
126			* will be overwritten.
127			* @param exponent exponent of a term in this Polynomial
128			* @param coefficient multiplier of a term in this Polynomial
129			*/
130	gezelter	1930
131	gezelter	2204	void setCoefficient(int exponent, const ElemType& coefficient) {
132			polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
133			}
134	gezelter	1930
135	gezelter	2204	/**
136			* Set the coefficent of the specified exponent. If the coefficient is already there, just add the
137			* new coefficient to the old one, otherwise, just call setCoefficent
138			* @param exponent exponent of a term in this Polynomial
139			* @param coefficient multiplier of a term in this Polynomial
140			*/
141	gezelter	1930
142	gezelter	2204	void addCoefficient(int exponent, const ElemType& coefficient) {
143			iterator i = polyPairMap_.find(exponent);
144	gezelter	1930
145	gezelter	2204	if (i != end()) {
146			i->second += coefficient;
147			} else {
148			setCoefficient(exponent, coefficient);
149			}
150			}
151	gezelter	1930
152
153	gezelter	2204	/**
154			* Returns the coefficient associated with the given power for this Polynomial.
155			* @return the coefficient associated with the given power for this Polynomial
156			* @exponent exponent of any term in this Polynomial
157			*/
158			ElemType getCoefficient(ExponentType exponent) {
159			iterator i = polyPairMap_.find(exponent);
160	gezelter	1930
161	gezelter	2204	if (i != end()) {
162			return i->second;
163			} else {
164			return ElemType(0);
165			}
166			}
167	gezelter	1930
168	gezelter	2204	iterator begin() {
169			return polyPairMap_.begin();
170			}
171	gezelter	1930
172	gezelter	2204	const_iterator begin() const{
173			return polyPairMap_.begin();
174			}
175	gezelter	1930
176	gezelter	2204	iterator end() {
177			return polyPairMap_.end();
178			}
179	gezelter	1930
180	gezelter	2204	const_iterator end() const{
181			return polyPairMap_.end();
182			}
183	gezelter	1930
184	gezelter	2204	iterator find(ExponentType exponent) {
185			return polyPairMap_.find(exponent);
186			}
187	gezelter	1930
188	gezelter	2204	size_t size() {
189			return polyPairMap_.size();
190			}
191	tim	2448
192			PolynomialType& operator += (const PolynomialType& p) {
193			typename Polynomial<ElemType>::const_iterator i;
194
195			for (i = p.begin(); i != p.end(); ++i) {
196			this->addCoefficient(i->first, i->second);
197			}
198
199			return *this;
200			}
201
202			PolynomialType& operator -= (const PolynomialType& p) {
203			typename Polynomial<ElemType>::const_iterator i;
204			for (i = p.begin(); i != p.end(); ++i) {
205			this->addCoefficient(i->first, -i->second);
206			}
207			}
208
209			PolynomialType& operator *= (const PolynomialType& p) {
210			typename Polynomial<ElemType>::const_iterator i;
211			typename Polynomial<ElemType>::const_iterator j;
212
213			for (i = this->begin(); i !=this->end(); ++i) {
214			for (j = p.begin(); j !=p.end(); ++j) {
215			this->addCoefficient( i->first + j->first, i->second * j->second);
216			}
217			}
218
219			return *this;
220			}
221
222
223	gezelter	2204	private:
224	gezelter	1930
225	gezelter	2204	PolynomialPairMap polyPairMap_;
226			};
227	gezelter	1930
228
229	gezelter	2204	/**
230			* Generates and returns the product of two given Polynomials.
231			* @return A Polynomial containing the product of the two given Polynomial parameters
232			*/
233			template<typename ElemType>
234			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
235	gezelter	1930	typename Polynomial<ElemType>::const_iterator i;
236			typename Polynomial<ElemType>::const_iterator j;
237			Polynomial<ElemType> p;
238
239			for (i = p1.begin(); i !=p1.end(); ++i) {
240	gezelter	2204	for (j = p2.begin(); j !=p2.end(); ++j) {
241			p.addCoefficient( i->first + j->first, i->second * j->second);
242			}
243	gezelter	1930	}
244
245			return p;
246	gezelter	2204	}
247	gezelter	1930
248	tim	2576	template<typename ElemType>
249			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p, const ElemType v) {
250			typename Polynomial<ElemType>::const_iterator i;
251			Polynomial<ElemType> result;
252
253			for (i = p.begin(); i !=p.end(); ++i) {
254			result.addCoefficient( i->first , i->second * v);
255			}
256
257			return result;
258			}
259
260			template<typename ElemType>
261			Polynomial<ElemType> operator *( const ElemType v, const Polynomial<ElemType>& p) {
262			typename Polynomial<ElemType>::const_iterator i;
263			Polynomial<ElemType> result;
264
265			for (i = p.begin(); i !=p.end(); ++i) {
266			result.addCoefficient( i->first , i->second * v);
267			}
268
269			return result;
270			}
271
272	gezelter	2204	/**
273			* Generates and returns the sum of two given Polynomials.
274			* @param p1 the first polynomial
275			* @param p2 the second polynomial
276			*/
277			template<typename ElemType>
278			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
279	gezelter	1930	Polynomial<ElemType> p(p1);
280
281			typename Polynomial<ElemType>::const_iterator i;
282
283			for (i = p2.begin(); i != p2.end(); ++i) {
284	gezelter	2204	p.addCoefficient(i->first, i->second);
285	gezelter	1930	}
286
287			return p;
288
289	gezelter	2204	}
290	gezelter	1930
291	gezelter	2204	/**
292			* Generates and returns the difference of two given Polynomials.
293			* @return
294			* @param p1 the first polynomial
295			* @param p2 the second polynomial
296			*/
297			template<typename ElemType>
298			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
299	gezelter	1930	Polynomial<ElemType> p(p1);
300
301			typename Polynomial<ElemType>::const_iterator i;
302
303			for (i = p2.begin(); i != p2.end(); ++i) {
304	gezelter	2204	p.addCoefficient(i->first, -i->second);
305	gezelter	1930	}
306
307			return p;
308
309	gezelter	2204	}
310	gezelter	1930
311	gezelter	2204	/**
312			* Tests if two polynomial have the same exponents
313			* @return true if these all of the exponents in these Polynomial are identical
314			* @param p1 the first polynomial
315			* @param p2 the second polynomial
316			* @note this function does not compare the coefficient
317			*/
318			template<typename ElemType>
319			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
320	gezelter	1930
321			typename Polynomial<ElemType>::const_iterator i;
322			typename Polynomial<ElemType>::const_iterator j;
323
324			if (p1.size() != p2.size() ) {
325	gezelter	2204	return false;
326	gezelter	1930	}
327
328			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
329	gezelter	2204	if (i->first != j->first) {
330			return false;
331			}
332	gezelter	1930	}
333
334			return true;
335	gezelter	2204	}
336	gezelter	1930
337	gezelter	2204	typedef Polynomial<double> DoublePolynomial;
338	gezelter	1930
339			} //end namespace oopse
340			#endif //MATH_POLYNOMIAL_HPP