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root/OpenMD/trunk/src/math/Polynomial.hpp
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Comparing trunk/src/math/Polynomial.hpp (file contents):
Revision 385 by tim, Tue Mar 1 20:10:14 2005 UTC vs.
Revision 507 by gezelter, Fri Apr 15 22:04:00 2005 UTC

# Line 1 | Line 1
1 < /*
1 > /*
2   * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3   *
4   * The University of Notre Dame grants you ("Licensee") a
# Line 56 | Line 56 | namespace oopse {
56  
57   namespace oopse {
58  
59 < template<typename ElemType> ElemType pow(ElemType x, int N) {
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;
63 >      result *= x;
64      }
65  
66      return result;
67 < }
67 >  }
68  
69 < /**
70 < * @class Polynomial Polynomial.hpp "math/Polynomial.hpp"
71 < * A generic Polynomial class
72 < */
73 < template<typename ElemType>
74 < class Polynomial {
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:
76 >  public:
77          
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 <         * Calculates the value of this Polynomial evaluated at the given x value.
85 <         * @return The value of this Polynomial evaluates at the given x value
86 <         * @param x the value of the independent variable for this Polynomial function
87 <         */
88 <        ElemType evaluate(const ElemType& x) {
89 <            ElemType result = ElemType();
90 <            ExponentType exponent;
91 <            CoefficientType coefficient;
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 >     * Calculates the value of this Polynomial evaluated at the given x value.
85 >     * @return The value of this Polynomial evaluates at the given x value
86 >     * @param x the value of the independent variable for this Polynomial function
87 >     */
88 >    ElemType evaluate(const ElemType& x) {
89 >      ElemType result = ElemType();
90 >      ExponentType exponent;
91 >      CoefficientType coefficient;
92              
93 <            for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
94 <                exponent = i->first;
95 <                coefficient = i->second;
96 <                result  += pow(x, exponent) * coefficient;
97 <            }
93 >      for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
94 >        exponent = i->first;
95 >        coefficient = i->second;
96 >        result  += pow(x, exponent) * coefficient;
97 >      }
98  
99 <            return result;
100 <        }
99 >      return result;
100 >    }
101  
102 <        /**
103 <         * Returns the first derivative of this polynomial.
104 <         * @return the first derivative of this polynomial
105 <         * @param x
106 <         */
107 <        ElemType evaluateDerivative(const ElemType& x) {
108 <            ElemType result = ElemType();
109 <            ExponentType exponent;
110 <            CoefficientType coefficient;
102 >    /**
103 >     * Returns the first derivative of this polynomial.
104 >     * @return the first derivative of this polynomial
105 >     * @param x
106 >     */
107 >    ElemType evaluateDerivative(const ElemType& x) {
108 >      ElemType result = ElemType();
109 >      ExponentType exponent;
110 >      CoefficientType coefficient;
111              
112 <            for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
113 <                exponent = i->first;
114 <                coefficient = i->second;
115 <                result  += pow(x, exponent - 1) * coefficient * exponent;
116 <            }
112 >      for (iterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) {
113 >        exponent = i->first;
114 >        coefficient = i->second;
115 >        result  += pow(x, exponent - 1) * coefficient * exponent;
116 >      }
117  
118 <            return result;
119 <        }
118 >      return result;
119 >    }
120  
121 <        /**
122 <         * Set the coefficent of the specified exponent, if the coefficient is already there, it
123 <         * will be overwritten.
124 <         * @param exponent exponent of a term in this Polynomial
125 <         * @param coefficient multiplier of a term in this Polynomial
126 <         */
121 >    /**
122 >     * Set the coefficent of the specified exponent, if the coefficient is already there, it
123 >     * will be overwritten.
124 >     * @param exponent exponent of a term in this Polynomial
125 >     * @param coefficient multiplier of a term in this Polynomial
126 >     */
127          
128 <        void setCoefficient(int exponent, const ElemType& coefficient) {
129 <            polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
130 <        }
128 >    void setCoefficient(int exponent, const ElemType& coefficient) {
129 >      polyPairMap_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
130 >    }
131  
132 <        /**
133 <         * Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
134 <         * new coefficient to the old one, otherwise,  just call setCoefficent
135 <         * @param exponent exponent of a term in this Polynomial
136 <         * @param coefficient multiplier of a term in this Polynomial
137 <         */
132 >    /**
133 >     * Set the coefficent of the specified exponent. If the coefficient is already there,  just add the
134 >     * new coefficient to the old one, otherwise,  just call setCoefficent
135 >     * @param exponent exponent of a term in this Polynomial
136 >     * @param coefficient multiplier of a term in this Polynomial
137 >     */
138          
139 <        void addCoefficient(int exponent, const ElemType& coefficient) {
140 <            iterator i = polyPairMap_.find(exponent);
139 >    void addCoefficient(int exponent, const ElemType& coefficient) {
140 >      iterator i = polyPairMap_.find(exponent);
141  
142 <            if (i != end()) {
143 <                i->second += coefficient;
144 <            } else {
145 <                setCoefficient(exponent, coefficient);
146 <            }
147 <        }
142 >      if (i != end()) {
143 >        i->second += coefficient;
144 >      } else {
145 >        setCoefficient(exponent, coefficient);
146 >      }
147 >    }
148  
149  
150 <        /**
151 <         * Returns the coefficient associated with the given power for this Polynomial.
152 <         * @return the coefficient associated with the given power for this Polynomial
153 <         * @exponent exponent of any term in this Polynomial
154 <         */
155 <        ElemType getCoefficient(ExponentType exponent) {
156 <            iterator i = polyPairMap_.find(exponent);
157 <
158 <            if (i != end()) {
159 <                return i->second;
160 <            } else {
161 <                return ElemType(0);
162 <            }
163 <        }
164 <
165 <        iterator begin() {
166 <            return polyPairMap_.begin();
167 <        }
150 >    /**
151 >     * Returns the coefficient associated with the given power for this Polynomial.
152 >     * @return the coefficient associated with the given power for this Polynomial
153 >     * @exponent exponent of any term in this Polynomial
154 >     */
155 >    ElemType getCoefficient(ExponentType exponent) {
156 >      iterator i = polyPairMap_.find(exponent);
157  
158 <        const_iterator begin() const{
159 <            return polyPairMap_.begin();
160 <        }
158 >      if (i != end()) {
159 >        return i->second;
160 >      } else {
161 >        return ElemType(0);
162 >      }
163 >    }
164 >
165 >    iterator begin() {
166 >      return polyPairMap_.begin();
167 >    }
168 >
169 >    const_iterator begin() const{
170 >      return polyPairMap_.begin();
171 >    }
172          
173 <        iterator end() {
174 <            return polyPairMap_.end();
175 <        }
173 >    iterator end() {
174 >      return polyPairMap_.end();
175 >    }
176  
177 <        const_iterator end() const{
178 <            return polyPairMap_.end();
179 <        }
177 >    const_iterator end() const{
178 >      return polyPairMap_.end();
179 >    }
180  
181 <        iterator find(ExponentType exponent) {
182 <            return polyPairMap_.find(exponent);
183 <        }
181 >    iterator find(ExponentType exponent) {
182 >      return polyPairMap_.find(exponent);
183 >    }
184  
185 <        size_t size() {
186 <            return polyPairMap_.size();
187 <        }
185 >    size_t size() {
186 >      return polyPairMap_.size();
187 >    }
188          
189 <    private:
189 >  private:
190          
191 <        PolynomialPairMap polyPairMap_;
192 < };
191 >    PolynomialPairMap polyPairMap_;
192 >  };
193  
194  
195 < /**
196 < * Generates and returns the product of two given Polynomials.
197 < * @return A Polynomial containing the product of the two given Polynomial parameters
198 < */
199 < template<typename ElemType>
200 < Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
195 >  /**
196 >   * Generates and returns the product of two given Polynomials.
197 >   * @return A Polynomial containing the product of the two given Polynomial parameters
198 >   */
199 >  template<typename ElemType>
200 >  Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
201      typename Polynomial<ElemType>::const_iterator i;
202      typename Polynomial<ElemType>::const_iterator j;
203      Polynomial<ElemType> p;
204      
205      for (i = p1.begin(); i !=p1.end(); ++i) {
206 <        for (j = p2.begin(); j !=p2.end(); ++j) {
207 <            p.addCoefficient( i->first + j->first, i->second * j->second);
208 <        }
206 >      for (j = p2.begin(); j !=p2.end(); ++j) {
207 >        p.addCoefficient( i->first + j->first, i->second * j->second);
208 >      }
209      }
210  
211      return p;
212 < }
212 >  }
213  
214 < /**
215 < * Generates and returns the sum of two given Polynomials.
216 < * @param p1 the first polynomial
217 < * @param p2 the second polynomial
218 < */
219 < template<typename ElemType>
220 < Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
214 >  /**
215 >   * Generates and returns the sum of two given Polynomials.
216 >   * @param p1 the first polynomial
217 >   * @param p2 the second polynomial
218 >   */
219 >  template<typename ElemType>
220 >  Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
221      Polynomial<ElemType> p(p1);
222  
223      typename Polynomial<ElemType>::const_iterator i;
224  
225      for (i =  p2.begin(); i  != p2.end(); ++i) {
226 <        p.addCoefficient(i->first, i->second);
226 >      p.addCoefficient(i->first, i->second);
227      }
228  
229      return p;
230  
231 < }
231 >  }
232  
233 < /**
234 < * Generates and returns the difference of two given Polynomials.
235 < * @return
236 < * @param p1 the first polynomial
237 < * @param p2 the second polynomial
238 < */
239 < template<typename ElemType>
240 < Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
233 >  /**
234 >   * Generates and returns the difference of two given Polynomials.
235 >   * @return
236 >   * @param p1 the first polynomial
237 >   * @param p2 the second polynomial
238 >   */
239 >  template<typename ElemType>
240 >  Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
241      Polynomial<ElemType> p(p1);
242  
243      typename Polynomial<ElemType>::const_iterator i;
244  
245      for (i =  p2.begin(); i  != p2.end(); ++i) {
246 <        p.addCoefficient(i->first, -i->second);
246 >      p.addCoefficient(i->first, -i->second);
247      }
248  
249      return p;
250  
251 < }
251 >  }
252  
253 < /**
254 < * Tests if two polynomial have the same exponents
255 < * @return true if these all of the exponents in these Polynomial are identical
256 < * @param p1 the first polynomial
257 < * @param p2 the second polynomial
258 < * @note this function does not compare the coefficient
259 < */
260 < template<typename ElemType>
261 < bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
253 >  /**
254 >   * Tests if two polynomial have the same exponents
255 >   * @return true if these all of the exponents in these Polynomial are identical
256 >   * @param p1 the first polynomial
257 >   * @param p2 the second polynomial
258 >   * @note this function does not compare the coefficient
259 >   */
260 >  template<typename ElemType>
261 >  bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
262  
263      typename Polynomial<ElemType>::const_iterator i;
264      typename Polynomial<ElemType>::const_iterator j;
265  
266      if (p1.size() != p2.size() ) {
267 <        return false;
267 >      return false;
268      }
269      
270      for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
271 <        if (i->first != j->first) {
272 <            return false;
273 <        }
271 >      if (i->first != j->first) {
272 >        return false;
273 >      }
274      }
275  
276      return true;
277 < }
277 >  }
278  
279 < typedef Polynomial<double> DoublePolynomial;
279 >  typedef Polynomial<double> DoublePolynomial;
280  
281   } //end namespace oopse
282   #endif //MATH_POLYNOMIAL_HPP

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