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/** |
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* @file Polynomial.hpp |
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* @author tlin |
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* @date 11/01/2004 |
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* @author teng lin |
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* @date 11/16/2004 |
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* @version 1.0 |
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*/ |
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namespace oopse { |
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template<typename ElemType, int N> pow(ElemType x) { |
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template<typename ElemType> pow(ElemType x, int N) { |
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ElemType result(1); |
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for (int i = 0; i < N; ++i) { |
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return result; |
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} |
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/** |
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* @class Polynomial Polynomial.hpp "math/Polynomial.hpp" |
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* A generic Polynomial class |
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*/ |
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template<typename ElemType> |
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class Polynomial { |
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public: |
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typedef int ExponentType; |
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typedef ElemType ConstantType; |
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typedef std::map<ExponentType, ConstantType> PolynomialPairMap; |
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typedef ElemType CoefficientType; |
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typedef std::map<ExponentType, CoefficientType> PolynomialPairMap; |
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typedef PolynomialPairMap::iterator PolynomialIterator; |
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Polynomial(); |
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template<U> Polynomial(const Polynomial<U>& p); |
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template<U> Polynomial& operator=(const Polynomial<U>& p); |
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/** |
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* |
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* Calculates the value of this Polynomial evaluated at the given x value. |
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* @return The value of this Polynomial evaluates at the given x value |
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* @param x the value of the independent variable for this Polynomial function |
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*/ |
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ElemType evaluate(const ElemType& x) { |
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ElemType result; |
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double exponent; |
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double constant; |
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double coefficient; |
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for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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constant = i->second; |
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result += pow<exponent>(x) * constant; |
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coefficient = i->second; |
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result += pow(x, exponent) * coefficient; |
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} |
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return result; |
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} |
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ElemType evaluateFirstDerivative(const ElemType& x) { |
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/** |
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* Returns the first derivative of this polynomial. |
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* @return the first derivative of this polynomial |
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* @param x |
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*/ |
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ElemType evaluateDerivative(const ElemType& x) { |
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ElemType result; |
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double exponent; |
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double constant; |
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double coefficient; |
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for (PolynomialIterator i = polyPairMap_.begin(); i != polyPairMap_.end(); ++i) { |
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exponent = i->first; |
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constant = i->second; |
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result += pow<exponent - 1>(x) * constant * exponent; |
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coefficient = i->second; |
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result += pow(x, exponent - 1) * coefficient * exponent; |
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} |
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return result; |
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} |
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void addPolynomialTerm(int exponent, const ElemType& constant) { |
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/** |
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* Set the coefficent of the specified exponent, if the coefficient is already there, it |
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* will be overwritten. |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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void setCoefficient(int exponent, const ElemType& coefficient) { |
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polyPairMap_.insert(PolynomialPairMap::value_type(exponent, coefficient)); |
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} |
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bool getConstant(ExponentType exponent, & constant) { |
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/** |
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* Set the coefficent of the specified exponent. If the coefficient is already there, just add the |
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* new coefficient to the old one, otherwise, just call setCoefficent |
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* @param exponent exponent of a term in this Polynomial |
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* @param coefficient multiplier of a term in this Polynomial |
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*/ |
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void addCoefficient(int exponent, const ElemType& coefficient) { |
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PolynomialIterator i = find(exponent); |
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if (i != end()) { |
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i->second += coefficient; |
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} else { |
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setCoefficient(exponent, coefficient); |
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} |
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} |
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/** |
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* Returns the coefficient associated with the given power for this Polynomial. |
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* @return the coefficient associated with the given power for this Polynomial |
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* @exponent exponent of any term in this Polynomial |
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*/ |
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ElemType getCoefficient(ExponentType exponent) { |
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PolynomialIterator i = find(exponent); |
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if (i != end()) { |
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return i->second; |
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} else { |
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return ElemType(0); |
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} |
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} |
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PolynomialIterator begin() { |
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return polyPairMap_.begin(); |
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} |
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PolynomialIterator find(ExponentType exponent) { |
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return polyPairMap_.find(); |
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} |
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size_t size() { |
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return polyPairMap_.size(); |
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} |
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private: |
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PolynomialPairMap polyPairMap_; |
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}; |
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/** |
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* Generates and returns the product of two given Polynomials. |
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* @return A Polynomial containing the product of the two given Polynomial parameters |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator *(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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typename Polynomial<ElemType>::PolynomialIterator i; |
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typename Polynomial<ElemType>::PolynomialIterator j; |
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typename Polynomial<ElemType>::PolynomialIterator k; |
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Polynomial<ElemType> p; |
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int exponent; |
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int coefficient; |
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|
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for (i = p1.begin(); i !=p1.end(); ++i) { |
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for (j = p1.begin(); j !=p1.end(); ++j) { |
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exponent = i->first + j->first; |
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coefficient = i->second * j->second; |
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k = p->find(exponent); |
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|
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if (k != p.end()) { |
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p[exponent] = coefficient; |
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} else { |
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k->second += coefficient; |
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} |
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} |
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} |
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} |
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/** |
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* Generates and returns the sum of two given Polynomials. |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator +(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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Polynomial<ElemType> p(p1); |
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typename Polynomial<ElemType>::PolynomialIterator i; |
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typename Polynomial<ElemType>::PolynomialIterator j; |
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for (i = p2.begin(); i != p2.end(); ++i) { |
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j = p.find(i->first); |
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if (j == p.end()) { |
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p[j] = i->second; |
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} else { |
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j->second += i->second; |
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} |
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} |
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return p; |
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|
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} |
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|
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/** |
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* Generates and returns the difference of two given Polynomials. |
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* @return |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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*/ |
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template<typename ElemType> |
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Polynomial<ElemType> operator -(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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Polynomial<ElemType> p(p1); |
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typename Polynomial<ElemType>::PolynomialIterator i; |
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typename Polynomial<ElemType>::PolynomialIterator j; |
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for (i = p2.begin(); i != p2.end(); ++i) { |
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j = p.find(i->first); |
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if (j == p.end()) { |
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p[j] = -i->second; |
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} else { |
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j->second -= i->second; |
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} |
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} |
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return p; |
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|
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} |
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|
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/** |
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* Tests if two polynomial have the same exponents |
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* @return true if these all of the exponents in these Polynomial are identical |
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* @param p1 the first polynomial |
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* @param p2 the second polynomial |
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* @note this function does not compare the coefficient |
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*/ |
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template<typename ElemType> |
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bool equal(const Polynomial<ElemType>& p1, const Polynomial<ElemType>& p2) { |
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|
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typename Polynomial<ElemType>::PolynomialIterator i; |
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typename Polynomial<ElemType>::PolynomialIterator j; |
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|
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if (p1.size() !== p2.size() ) { |
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return false; |
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} |
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|
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for (i = p1.begin(), j = p2.begin(); i != p1.end() && j != p2.end(); ++i, ++j) { |
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if (i->first != j->first) { |
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return false; |
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} |
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} |
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|
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return true; |
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} |
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|
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typedef Polynomial<double> DoublePolynomial; |
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|
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} //end namespace oopse |
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#endif //MATH_POLYNOMIAL_HPP |