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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 876 by tim, Mon Jan 30 22:25:27 2006 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:
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;
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 <            }
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 <        }
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;
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 <            }
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 <        }
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 <         */
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_.insert(typename PolynomialPairMap::value_type(exponent, coefficient));
133 <        }
131 >    void setCoefficient(int exponent, const ElemType& coefficient) {
132 >      polyPairMap_.insert(typename PolynomialPairMap::value_type(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 <         */
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);
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 <        }
145 >      if (i != end()) {
146 >        i->second += coefficient;
147 >      } else {
148 >        setCoefficient(exponent, coefficient);
149 >      }
150 >    }
151  
152  
153 <        /**
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);
153 >    /**
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  
161 <            if (i != end()) {
162 <                return i->second;
163 <            } else {
164 <                return ElemType(0);
165 <            }
166 <        }
161 >      if (i != end()) {
162 >        return i->second;
163 >      } else {
164 >        return ElemType(0);
165 >      }
166 >    }
167  
168 <        iterator begin() {
169 <            return polyPairMap_.begin();
170 <        }
168 >    iterator begin() {
169 >      return polyPairMap_.begin();
170 >    }
171  
172 <        const_iterator begin() const{
173 <            return polyPairMap_.begin();
174 <        }
175 <        
176 <        iterator end() {
177 <            return polyPairMap_.end();
178 <        }
172 >    const_iterator begin() const{
173 >      return polyPairMap_.begin();
174 >    }
175 >        
176 >    iterator end() {
177 >      return polyPairMap_.end();
178 >    }
179  
180 <        const_iterator end() const{
181 <            return polyPairMap_.end();
182 <        }
180 >    const_iterator end() const{
181 >      return polyPairMap_.end();
182 >    }
183  
184 <        iterator find(ExponentType exponent) {
185 <            return polyPairMap_.find(exponent);
186 <        }
184 >    iterator find(ExponentType exponent) {
185 >      return polyPairMap_.find(exponent);
186 >    }
187  
188 <        size_t size() {
189 <            return polyPairMap_.size();
188 >    size_t size() {
189 >      return polyPairMap_.size();
190 >    }
191 >
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 +  private:
224          
225 <    private:
226 <        
191 <        PolynomialPairMap polyPairMap_;
192 < };
225 >    PolynomialPairMap polyPairMap_;
226 >  };
227  
228  
229 < /**
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) {
229 >  /**
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      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 <        for (j = p2.begin(); j !=p2.end(); ++j) {
241 <            p.addCoefficient( i->first + j->first, i->second * j->second);
242 <        }
240 >      for (j = p2.begin(); j !=p2.end(); ++j) {
241 >        p.addCoefficient( i->first + j->first, i->second * j->second);
242 >      }
243      }
244  
245      return p;
246 < }
246 >  }
247  
248 < /**
249 < * Generates and returns the sum of two given Polynomials.
250 < * @param p1 the first polynomial
251 < * @param p2 the second polynomial
252 < */
253 < template<typename ElemType>
254 < Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) {
248 >  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 >  /**
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      Polynomial<ElemType> p(p1);
280  
281      typename Polynomial<ElemType>::const_iterator i;
282  
283      for (i =  p2.begin(); i  != p2.end(); ++i) {
284 <        p.addCoefficient(i->first, i->second);
284 >      p.addCoefficient(i->first, i->second);
285      }
286  
287      return p;
288  
289 < }
289 >  }
290  
291 < /**
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) {
291 >  /**
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      Polynomial<ElemType> p(p1);
300  
301      typename Polynomial<ElemType>::const_iterator i;
302  
303      for (i =  p2.begin(); i  != p2.end(); ++i) {
304 <        p.addCoefficient(i->first, -i->second);
304 >      p.addCoefficient(i->first, -i->second);
305      }
306  
307      return p;
308  
309 < }
309 >  }
310  
311 < /**
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) {
311 >  /**
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  
321      typename Polynomial<ElemType>::const_iterator i;
322      typename Polynomial<ElemType>::const_iterator j;
323  
324      if (p1.size() != p2.size() ) {
325 <        return false;
325 >      return false;
326      }
327      
328      for (i =  p1.begin(), j = p2.begin(); i  != p1.end() && j != p2.end(); ++i, ++j) {
329 <        if (i->first != j->first) {
330 <            return false;
331 <        }
329 >      if (i->first != j->first) {
330 >        return false;
331 >      }
332      }
333  
334      return true;
335 < }
335 >  }
336  
337 < typedef Polynomial<double> DoublePolynomial;
337 >  typedef Polynomial<double> DoublePolynomial;
338  
339   } //end namespace oopse
340   #endif //MATH_POLYNOMIAL_HPP

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