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
File size:	11114 byte(s)
Log Message:	Inversion fixes and amber mostly working
#	Content
1	/*
2	* 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	#include "config.h"
57	namespace oopse {
58
59	template<typename ElemType> ElemType pow(ElemType x, int N) {
60	ElemType result(1);
61
62	for (int i = 0; i < N; ++i) {
63	result *= x;
64	}
65
66	return result;
67	}
68
69	/**
70	* @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71	* A generic Polynomial class
72	*/
73	template<typename ElemType>
74	class Polynomial {
75
76	public:
77	typedef Polynomial<ElemType> PolynomialType;
78	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
84	Polynomial() {}
85	Polynomial(ElemType v) {setCoefficient(0, v);}
86	/**
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
96	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
102	return result;
103	}
104
105	/**
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
115	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
121	return result;
122	}
123
124	/**
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
131	void setCoefficient(int exponent, const ElemType& coefficient) {
132	polyPairMap_[exponent] = coefficient;
133	}
134
135	/**
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
142	void addCoefficient(int exponent, const ElemType& coefficient) {
143	iterator i = polyPairMap_.find(exponent);
144
145	if (i != end()) {
146	i->second += coefficient;
147	} else {
148	setCoefficient(exponent, coefficient);
149	}
150	}
151
152	/**
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
160	if (i != end()) {
161	return i->second;
162	} else {
163	return ElemType(0);
164	}
165	}
166
167	iterator begin() {
168	return polyPairMap_.begin();
169	}
170
171	const_iterator begin() const{
172	return polyPairMap_.begin();
173	}
174
175	iterator end() {
176	return polyPairMap_.end();
177	}
178
179	const_iterator end() const{
180	return polyPairMap_.end();
181	}
182
183	iterator find(ExponentType exponent) {
184	return polyPairMap_.find(exponent);
185	}
186
187	size_t size() {
188	return polyPairMap_.size();
189	}
190
191	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	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	return *this;
223	}
224
225	PolynomialType& operator *= (const PolynomialType& p) {
226	typename Polynomial<ElemType>::const_iterator i;
227	typename Polynomial<ElemType>::const_iterator j;
228	Polynomial<ElemType> p2(*this);
229
230	polyPairMap_.clear(); // clear out old map
231	for (i = p2.begin(); i !=p2.end(); ++i) {
232	for (j = p.begin(); j !=p.end(); ++j) {
233	this->addCoefficient( i->first + j->first, i->second * j->second);
234	}
235	}
236	return *this;
237	}
238
239	//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	return *this;
249	}
250
251	PolynomialType& operator += (const ElemType v) {
252	this->addCoefficient( 0, v);
253	return *this;
254	}
255
256	private:
257
258	PolynomialPairMap polyPairMap_;
259	};
260
261
262	/**
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	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	for (j = p2.begin(); j !=p2.end(); ++j) {
274	p.addCoefficient( i->first + j->first, i->second * j->second);
275	}
276	}
277
278	return p;
279	}
280
281	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	result.setCoefficient( i->first , i->second * v);
288	}
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	result.setCoefficient( i->first , i->second * v);
300	}
301
302	return result;
303	}
304
305	/**
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	Polynomial<ElemType> p(p1);
313
314	typename Polynomial<ElemType>::const_iterator i;
315
316	for (i = p2.begin(); i != p2.end(); ++i) {
317	p.addCoefficient(i->first, i->second);
318	}
319
320	return p;
321
322	}
323
324	/**
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	Polynomial<ElemType> p(p1);
333
334	typename Polynomial<ElemType>::const_iterator i;
335
336	for (i = p2.begin(); i != p2.end(); ++i) {
337	p.addCoefficient(i->first, -i->second);
338	}
339
340	return p;
341
342	}
343
344	/**
345	* Tests if two polynomial have the same exponents
346	* @return true if all of the exponents in these Polynomial are identical
347	* @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
354	typename Polynomial<ElemType>::const_iterator i;
355	typename Polynomial<ElemType>::const_iterator j;
356
357	if (p1.size() != p2.size() ) {
358	return false;
359	}
360
361	for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) {
362	if (i->first != j->first) {
363	return false;
364	}
365	}
366
367	return true;
368	}
369
370	typedef Polynomial<RealType> DoublePolynomial;
371
372	} //end namespace oopse
373	#endif //MATH_POLYNOMIAL_HPP