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);
        }        
        return *this;
    }

    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:	877
Committed:	Wed Feb 1 17:26:43 2006 UTC (19 years, 9 months ago) by gezelter
File size:	10186 byte(s)
Log Message:	Fixing some compile-time warnings and bugs for icc 9.1 on Mac OS X
#	User	Rev	Content
1	gezelter	507	/*
2	gezelter	246	* 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	507	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	gezelter	246	ElemType result(1);
61
62			for (int i = 0; i < N; ++i) {
63	gezelter	507	result *= x;
64	gezelter	246	}
65
66			return result;
67	gezelter	507	}
68	gezelter	246
69	gezelter	507	/**
70			* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71			* A generic Polynomial class
72			*/
73			template<typename ElemType>
74			class Polynomial {
75	gezelter	246
76	gezelter	507	public:
77	tim	749	typedef Polynomial<ElemType> PolynomialType;
78	gezelter	507	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	749
84			Polynomial() {}
85			Polynomial(ElemType v) {setCoefficient(0, v);}
86	gezelter	507	/**
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	246
96	gezelter	507	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	246
102	gezelter	507	return result;
103			}
104	gezelter	246
105	gezelter	507	/**
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	246
115	gezelter	507	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	246
121	gezelter	507	return result;
122			}
123	gezelter	246
124	gezelter	507	/**
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	246
131	gezelter	507	void setCoefficient(int exponent, const ElemType& coefficient) {
132			polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
133			}
134	gezelter	246
135	gezelter	507	/**
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	246
142	gezelter	507	void addCoefficient(int exponent, const ElemType& coefficient) {
143			iterator i = polyPairMap_.find(exponent);
144	gezelter	246
145	gezelter	507	if (i != end()) {
146			i->second += coefficient;
147			} else {
148			setCoefficient(exponent, coefficient);
149			}
150			}
151	gezelter	246
152
153	gezelter	507	/**
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	246
161	gezelter	507	if (i != end()) {
162			return i->second;
163			} else {
164			return ElemType(0);
165			}
166			}
167	gezelter	246
168	gezelter	507	iterator begin() {
169			return polyPairMap_.begin();
170			}
171	gezelter	246
172	gezelter	507	const_iterator begin() const{
173			return polyPairMap_.begin();
174			}
175	gezelter	246
176	gezelter	507	iterator end() {
177			return polyPairMap_.end();
178			}
179	gezelter	246
180	gezelter	507	const_iterator end() const{
181			return polyPairMap_.end();
182			}
183	gezelter	246
184	gezelter	507	iterator find(ExponentType exponent) {
185			return polyPairMap_.find(exponent);
186			}
187	gezelter	246
188	gezelter	507	size_t size() {
189			return polyPairMap_.size();
190			}
191	tim	749
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	gezelter	877	return *this;
208	tim	749	}
209
210			PolynomialType& operator *= (const PolynomialType& p) {
211			typename Polynomial<ElemType>::const_iterator i;
212			typename Polynomial<ElemType>::const_iterator j;
213
214			for (i = this->begin(); i !=this->end(); ++i) {
215			for (j = p.begin(); j !=p.end(); ++j) {
216			this->addCoefficient( i->first + j->first, i->second * j->second);
217			}
218			}
219
220			return *this;
221			}
222
223
224	gezelter	507	private:
225	gezelter	246
226	gezelter	507	PolynomialPairMap polyPairMap_;
227			};
228	gezelter	246
229
230	gezelter	507	/**
231			* Generates and returns the product of two given Polynomials.
232			* @return A Polynomial containing the product of the two given Polynomial parameters
233			*/
234			template<typename ElemType>
235			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
236	gezelter	246	typename Polynomial<ElemType>::const_iterator i;
237			typename Polynomial<ElemType>::const_iterator j;
238			Polynomial<ElemType> p;
239
240			for (i = p1.begin(); i !=p1.end(); ++i) {
241	gezelter	507	for (j = p2.begin(); j !=p2.end(); ++j) {
242			p.addCoefficient( i->first + j->first, i->second * j->second);
243			}
244	gezelter	246	}
245
246			return p;
247	gezelter	507	}
248	gezelter	246
249	tim	876	template<typename ElemType>
250			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p, const ElemType v) {
251			typename Polynomial<ElemType>::const_iterator i;
252			Polynomial<ElemType> result;
253
254			for (i = p.begin(); i !=p.end(); ++i) {
255			result.addCoefficient( i->first , i->second * v);
256			}
257
258			return result;
259			}
260
261			template<typename ElemType>
262			Polynomial<ElemType> operator *( const ElemType v, const Polynomial<ElemType>& p) {
263			typename Polynomial<ElemType>::const_iterator i;
264			Polynomial<ElemType> result;
265
266			for (i = p.begin(); i !=p.end(); ++i) {
267			result.addCoefficient( i->first , i->second * v);
268			}
269
270			return result;
271			}
272
273	gezelter	507	/**
274			* Generates and returns the sum of two given Polynomials.
275			* @param p1 the first polynomial
276			* @param p2 the second polynomial
277			*/
278			template<typename ElemType>
279			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
280	gezelter	246	Polynomial<ElemType> p(p1);
281
282			typename Polynomial<ElemType>::const_iterator i;
283
284			for (i = p2.begin(); i != p2.end(); ++i) {
285	gezelter	507	p.addCoefficient(i->first, i->second);
286	gezelter	246	}
287
288			return p;
289
290	gezelter	507	}
291	gezelter	246
292	gezelter	507	/**
293			* Generates and returns the difference of two given Polynomials.
294			* @return
295			* @param p1 the first polynomial
296			* @param p2 the second polynomial
297			*/
298			template<typename ElemType>
299			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
300	gezelter	246	Polynomial<ElemType> p(p1);
301
302			typename Polynomial<ElemType>::const_iterator i;
303
304			for (i = p2.begin(); i != p2.end(); ++i) {
305	gezelter	507	p.addCoefficient(i->first, -i->second);
306	gezelter	246	}
307
308			return p;
309
310	gezelter	507	}
311	gezelter	246
312	gezelter	507	/**
313			* Tests if two polynomial have the same exponents
314			* @return true if these all of the exponents in these Polynomial are identical
315			* @param p1 the first polynomial
316			* @param p2 the second polynomial
317			* @note this function does not compare the coefficient
318			*/
319			template<typename ElemType>
320			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
321	gezelter	246
322			typename Polynomial<ElemType>::const_iterator i;
323			typename Polynomial<ElemType>::const_iterator j;
324
325			if (p1.size() != p2.size() ) {
326	gezelter	507	return false;
327	gezelter	246	}
328
329			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
330	gezelter	507	if (i->first != j->first) {
331			return false;
332			}
333	gezelter	246	}
334
335			return true;
336	gezelter	507	}
337	gezelter	246
338	gezelter	507	typedef Polynomial<double> DoublePolynomial;
339	gezelter	246
340			} //end namespace oopse
341			#endif //MATH_POLYNOMIAL_HPP