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>
#include "config.h"
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_[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) {

      if (this != &p)  // protect against invalid self-assignment
      {
        typename Polynomial<ElemType>::const_iterator i;

        polyPairMap_.clear();  // clear out the old map
      
        for (i =  p.begin(); i != p.end(); ++i) {
          this->setCoefficient(i->first, i->second);
        }
      }
      // by convention, always return *this
      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;
        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;
    Polynomial<ElemType> p2(*this);
   
    polyPairMap_.clear();  // clear out old map
    for (i = p2.begin(); i !=p2.end(); ++i) {
      for (j = p.begin(); j !=p.end(); ++j) {
        this->addCoefficient( i->first + j->first, i->second * j->second);
      }
    }
    return *this;
    }

    //PolynomialType& operator *= (const ElemType v)
    PolynomialType& operator *= (const ElemType v) {
    typename Polynomial<ElemType>::const_iterator i;
    //Polynomial<ElemType> result;

    for (i = this->begin(); i != this->end(); ++i) {
        this->setCoefficient( i->first, i->second*v);
    }

    return *this;
    }

    PolynomialType& operator += (const ElemType v) {    
    this->addCoefficient( 0, v);
    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.setCoefficient( 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.setCoefficient( 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 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<RealType> DoublePolynomial;

} //end namespace oopse
#endif //MATH_POLYNOMIAL_HPP
Revision:	1290
Committed:	Wed Sep 10 19:51:45 2008 UTC (16 years, 7 months ago) by cli2
Original Path:	*trunk/src/math/Polynomial.hpp*
File size:	11114 byte(s)
Log Message:	Inversion fixes and amber mostly working
#	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	tim	963	#include "config.h"
57	gezelter	246	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	cli2	1290	polyPairMap_[exponent] = coefficient;
133	gezelter	507	}
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	gezelter	507	/**
153			* Returns the coefficient associated with the given power for this Polynomial.
154			* @return the coefficient associated with the given power for this Polynomial
155			* @exponent exponent of any term in this Polynomial
156			*/
157			ElemType getCoefficient(ExponentType exponent) {
158			iterator i = polyPairMap_.find(exponent);
159	gezelter	246
160	gezelter	507	if (i != end()) {
161			return i->second;
162			} else {
163			return ElemType(0);
164			}
165			}
166	gezelter	246
167	gezelter	507	iterator begin() {
168			return polyPairMap_.begin();
169			}
170	gezelter	246
171	gezelter	507	const_iterator begin() const{
172			return polyPairMap_.begin();
173			}
174	gezelter	246
175	gezelter	507	iterator end() {
176			return polyPairMap_.end();
177			}
178	gezelter	246
179	gezelter	507	const_iterator end() const{
180			return polyPairMap_.end();
181			}
182	gezelter	246
183	gezelter	507	iterator find(ExponentType exponent) {
184			return polyPairMap_.find(exponent);
185			}
186	gezelter	246
187	gezelter	507	size_t size() {
188			return polyPairMap_.size();
189			}
190	tim	749
191	cpuglis	1230	PolynomialType& operator = (const PolynomialType& p) {
192
193			if (this != &p) // protect against invalid self-assignment
194			{
195			typename Polynomial<ElemType>::const_iterator i;
196
197			polyPairMap_.clear(); // clear out the old map
198
199			for (i = p.begin(); i != p.end(); ++i) {
200			this->setCoefficient(i->first, i->second);
201			}
202			}
203			// by convention, always return *this
204			return *this;
205			}
206
207	tim	749	PolynomialType& operator += (const PolynomialType& p) {
208			typename Polynomial<ElemType>::const_iterator i;
209
210			for (i = p.begin(); i != p.end(); ++i) {
211			this->addCoefficient(i->first, i->second);
212			}
213
214			return *this;
215			}
216
217			PolynomialType& operator -= (const PolynomialType& p) {
218			typename Polynomial<ElemType>::const_iterator i;
219			for (i = p.begin(); i != p.end(); ++i) {
220			this->addCoefficient(i->first, -i->second);
221			}
222	gezelter	877	return *this;
223	tim	749	}
224
225			PolynomialType& operator *= (const PolynomialType& p) {
226			typename Polynomial<ElemType>::const_iterator i;
227			typename Polynomial<ElemType>::const_iterator j;
228	cli2	1290	Polynomial<ElemType> p2(*this);
229
230			polyPairMap_.clear(); // clear out old map
231			for (i = p2.begin(); i !=p2.end(); ++i) {
232	tim	749	for (j = p.begin(); j !=p.end(); ++j) {
233			this->addCoefficient( i->first + j->first, i->second * j->second);
234			}
235			}
236	cli2	1290	return *this;
237			}
238	tim	749
239	cli2	1290	//PolynomialType& operator *= (const ElemType v)
240			PolynomialType& operator *= (const ElemType v) {
241			typename Polynomial<ElemType>::const_iterator i;
242			//Polynomial<ElemType> result;
243
244			for (i = this->begin(); i != this->end(); ++i) {
245			this->setCoefficient( i->first, i->second*v);
246			}
247
248	tim	749	return *this;
249			}
250
251	cli2	1290	PolynomialType& operator += (const ElemType v) {
252			this->addCoefficient( 0, v);
253			return *this;
254			}
255	tim	749
256	gezelter	507	private:
257	gezelter	246
258	gezelter	507	PolynomialPairMap polyPairMap_;
259			};
260	gezelter	246
261
262	gezelter	507	/**
263			* Generates and returns the product of two given Polynomials.
264			* @return A Polynomial containing the product of the two given Polynomial parameters
265			*/
266			template<typename ElemType>
267			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
268	gezelter	246	typename Polynomial<ElemType>::const_iterator i;
269			typename Polynomial<ElemType>::const_iterator j;
270			Polynomial<ElemType> p;
271
272			for (i = p1.begin(); i !=p1.end(); ++i) {
273	gezelter	507	for (j = p2.begin(); j !=p2.end(); ++j) {
274			p.addCoefficient( i->first + j->first, i->second * j->second);
275			}
276	gezelter	246	}
277
278			return p;
279	gezelter	507	}
280	gezelter	246
281	tim	876	template<typename ElemType>
282			Polynomial<ElemType> operator *(const Polynomial<ElemType>& p, const ElemType v) {
283			typename Polynomial<ElemType>::const_iterator i;
284			Polynomial<ElemType> result;
285
286			for (i = p.begin(); i !=p.end(); ++i) {
287	cli2	1290	result.setCoefficient( i->first , i->second * v);
288	tim	876	}
289
290			return result;
291			}
292
293			template<typename ElemType>
294			Polynomial<ElemType> operator *( const ElemType v, const Polynomial<ElemType>& p) {
295			typename Polynomial<ElemType>::const_iterator i;
296			Polynomial<ElemType> result;
297
298			for (i = p.begin(); i !=p.end(); ++i) {
299	cli2	1290	result.setCoefficient( i->first , i->second * v);
300	tim	876	}
301
302			return result;
303			}
304
305	gezelter	507	/**
306			* Generates and returns the sum of two given Polynomials.
307			* @param p1 the first polynomial
308			* @param p2 the second polynomial
309			*/
310			template<typename ElemType>
311			Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
312	gezelter	246	Polynomial<ElemType> p(p1);
313
314			typename Polynomial<ElemType>::const_iterator i;
315
316			for (i = p2.begin(); i != p2.end(); ++i) {
317	gezelter	507	p.addCoefficient(i->first, i->second);
318	gezelter	246	}
319
320			return p;
321
322	gezelter	507	}
323	gezelter	246
324	gezelter	507	/**
325			* Generates and returns the difference of two given Polynomials.
326			* @return
327			* @param p1 the first polynomial
328			* @param p2 the second polynomial
329			*/
330			template<typename ElemType>
331			Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
332	gezelter	246	Polynomial<ElemType> p(p1);
333
334			typename Polynomial<ElemType>::const_iterator i;
335
336			for (i = p2.begin(); i != p2.end(); ++i) {
337	gezelter	507	p.addCoefficient(i->first, -i->second);
338	gezelter	246	}
339
340			return p;
341
342	gezelter	507	}
343	gezelter	246
344	gezelter	507	/**
345			* Tests if two polynomial have the same exponents
346	tim	883	* @return true if all of the exponents in these Polynomial are identical
347	gezelter	507	* @param p1 the first polynomial
348			* @param p2 the second polynomial
349			* @note this function does not compare the coefficient
350			*/
351			template<typename ElemType>
352			bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
353	gezelter	246
354			typename Polynomial<ElemType>::const_iterator i;
355			typename Polynomial<ElemType>::const_iterator j;
356
357			if (p1.size() != p2.size() ) {
358	gezelter	507	return false;
359	gezelter	246	}
360
361			for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
362	gezelter	507	if (i->first != j->first) {
363			return false;
364			}
365	gezelter	246	}
366
367			return true;
368	gezelter	507	}
369	gezelter	246
370	tim	963	typedef Polynomial<RealType> DoublePolynomial;
371	gezelter	246
372			} //end namespace oopse
373			#endif //MATH_POLYNOMIAL_HPP