[2086] | 1 | /* -*- C++ -*- |
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| 2 | * |
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| 3 | * This file is a part of LEMON, a generic C++ optimization library |
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| 4 | * |
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| 5 | * Copyright (C) 2003-2006 |
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| 6 | * Egervary Jeno Kombinatorikus Optimalizalasi Kutatocsoport |
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| 7 | * (Egervary Research Group on Combinatorial Optimization, EGRES). |
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| 8 | * |
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| 9 | * Permission to use, modify and distribute this software is granted |
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| 10 | * provided that this copyright notice appears in all copies. For |
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| 11 | * precise terms see the accompanying LICENSE file. |
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| 12 | * |
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| 13 | * This software is provided "AS IS" with no warranty of any kind, |
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| 14 | * express or implied, and with no claim as to its suitability for any |
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| 15 | * purpose. |
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| 16 | * |
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| 17 | */ |
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| 18 | |
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| 19 | #ifndef LEMON_BEZIER_H |
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| 20 | #define LEMON_BEZIER_H |
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| 21 | |
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| 22 | ///\ingroup misc |
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| 23 | ///\file |
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| 24 | ///\brief A simple class implementing polynomials. |
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| 25 | /// |
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| 26 | ///\author Alpar Juttner |
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| 27 | |
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| 28 | #include<vector> |
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| 29 | |
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| 30 | namespace lemon { |
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| 31 | |
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| 32 | /// \addtogroup misc |
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| 33 | /// @{ |
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| 34 | |
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| 35 | ///Simple polinomial class |
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| 36 | |
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| 37 | ///This class implements a polynomial where the coefficients are of |
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| 38 | ///type \c T. |
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| 39 | /// |
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| 40 | ///The coefficients are stored in an std::vector. |
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| 41 | template<class T> |
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| 42 | class Polynomial |
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| 43 | { |
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| 44 | std::vector<T> _coeff; |
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| 45 | public: |
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| 46 | ///Construct a polynomial of degree \c d. |
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| 47 | explicit Polynomial(int d=0) : _coeff(d+1) {} |
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| 48 | ///\e |
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| 49 | template<class U> Polynomial(const U &u) : _coeff(1,u) {} |
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| 50 | ///\e |
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| 51 | template<class U> Polynomial(const Polynomial<U> &u) : _coeff(u.deg()+1) |
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| 52 | { |
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| 53 | for(int i=0;i<(int)_coeff.size();i++) _coeff[i]=u[i]; |
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| 54 | } |
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| 55 | ///Query the degree of the polynomial. |
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| 56 | |
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| 57 | ///Query the degree of the polynomial. |
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| 58 | ///\warning This number differs from real degree of the polinomial if |
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| 59 | ///the coefficient of highest degree is 0. |
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| 60 | int deg() const { return _coeff.size()-1; } |
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| 61 | ///Set the degree of the polynomial. |
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| 62 | |
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| 63 | ///Set the degree of the polynomial. In fact it resizes the |
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| 64 | ///coefficient vector. |
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| 65 | void deg(int d) { _coeff.resize(d+1);} |
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| 66 | |
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| 67 | ///Returns (as a reference) the coefficient of degree \c d. |
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| 68 | typename std::vector<T>::reference operator[](int d) { return _coeff[d]; } |
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| 69 | ///Returns (as a const reference) the coefficient of degree \c d. |
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| 70 | typename std::vector<T>::const_reference |
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| 71 | operator[](int d) const {return _coeff[d];} |
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| 72 | |
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| 73 | ///Substitute the value u into the polinomial. |
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| 74 | |
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| 75 | ///Substitute the value u into the polinomial. |
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| 76 | ///The calculation will be done using type \c R. |
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| 77 | ///The following examples shows the usage of the template parameter \c R. |
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| 78 | ///\code |
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[2207] | 79 | /// Polynomial<dim2::Point<double> > line(1); |
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| 80 | /// line[0]=dim2::Point<double>(12,25); |
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| 81 | /// line[1]=dim2::Point<double>(2,7); |
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[2086] | 82 | /// ... |
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[2207] | 83 | /// dim2::Point<double> d = line.subst<dim2::Point<double> >(23.2); |
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[2086] | 84 | ///\endcode |
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| 85 | /// |
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| 86 | ///\code |
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| 87 | /// Polynomial<double> p; |
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| 88 | /// Polynomial<double> q; |
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| 89 | /// ... |
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| 90 | /// Polynomial<double> s = p.subst<Polynomial<double> >(q); |
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| 91 | ///\endcode |
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| 92 | template<class R,class U> |
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| 93 | R subst(const U &u) const |
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| 94 | { |
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| 95 | typename std::vector<T>::const_reverse_iterator i=_coeff.rbegin(); |
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| 96 | R v=*i; |
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| 97 | for(++i;i!=_coeff.rend();++i) v=v*u+*i; |
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| 98 | return v; |
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| 99 | } |
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| 100 | ///Substitute the value u into the polinomial. |
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| 101 | |
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| 102 | ///Substitute the value u into the polinomial. |
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| 103 | ///The calculation will be done using type \c T |
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| 104 | ///(i.e. using the type of the coefficients.) |
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| 105 | template<class U> |
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| 106 | T operator()(const U &u) const |
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| 107 | { |
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| 108 | return subst<T>(u); |
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| 109 | } |
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| 110 | |
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| 111 | ///Derivate the polynomial (in place) |
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| 112 | Polynomial &derivateMyself() |
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| 113 | { |
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| 114 | for(int i=1;i<(int)_coeff.size();i++) _coeff[i-1]=i*_coeff[i]; |
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| 115 | _coeff.pop_back(); |
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| 116 | return *this; |
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| 117 | } |
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| 118 | |
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| 119 | ///Return the derivate of the polynomial |
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| 120 | Polynomial derivate() const |
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| 121 | { |
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| 122 | Polynomial tmp(deg()-1); |
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| 123 | for(int i=1;i<(int)_coeff.size();i++) tmp[i-1]=i*_coeff[i]; |
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| 124 | return tmp; |
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| 125 | } |
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| 126 | |
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| 127 | ///Integrate the polynomial (in place) |
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| 128 | Polynomial &integrateMyself() |
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| 129 | { |
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| 130 | _coeff.push_back(T()); |
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[2199] | 131 | for(int i=_coeff.size()-1;i>0;i--) _coeff[i]=_coeff[i-1]/i; |
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[2086] | 132 | _coeff[0]=0; |
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| 133 | return *this; |
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| 134 | } |
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| 135 | |
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| 136 | ///Return the integrate of the polynomial |
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| 137 | Polynomial integrate() const |
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| 138 | { |
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| 139 | Polynomial tmp(deg()+1); |
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| 140 | tmp[0]=0; |
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| 141 | for(int i=0;i<(int)_coeff.size();i++) tmp[i+1]=_coeff[i]/(i+1); |
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| 142 | return tmp; |
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| 143 | } |
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| 144 | |
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| 145 | ///\e |
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| 146 | template<class U> |
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| 147 | Polynomial &operator+=(const Polynomial<U> &p) |
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| 148 | { |
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| 149 | if(p.deg()>deg()) _coeff.resize(p.deg()+1); |
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| 150 | for(int i=0;i<=(int)std::min(deg(),p.deg());i++) |
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| 151 | _coeff[i]+=p[i]; |
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| 152 | return *this; |
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| 153 | } |
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| 154 | ///\e |
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| 155 | template<class U> |
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| 156 | Polynomial &operator-=(const Polynomial<U> &p) |
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| 157 | { |
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| 158 | if(p.deg()>deg()) _coeff.resize(p.deg()+1); |
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| 159 | for(int i=0;i<=std::min(deg(),p.deg());i++) _coeff[i]-=p[i]; |
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| 160 | return *this; |
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| 161 | } |
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| 162 | ///\e |
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| 163 | template<class U> |
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| 164 | Polynomial &operator+=(const U &u) |
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| 165 | { |
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| 166 | _coeff[0]+=u; |
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| 167 | return *this; |
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| 168 | } |
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| 169 | ///\e |
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| 170 | template<class U> |
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| 171 | Polynomial &operator-=(const U &u) |
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| 172 | { |
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| 173 | _coeff[0]+=u; |
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| 174 | return *this; |
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| 175 | } |
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| 176 | ///\e |
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| 177 | template<class U> |
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| 178 | Polynomial &operator*=(const U &u) |
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| 179 | { |
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| 180 | for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i) |
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| 181 | *i*=u; |
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| 182 | return *this; |
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| 183 | } |
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| 184 | ///\e |
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| 185 | template<class U> |
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| 186 | Polynomial &operator/=(const U &u) |
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| 187 | { |
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| 188 | for(typename std::vector<T>::iterator i=_coeff.begin();i!=_coeff.end();++i) |
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| 189 | *i/=u; |
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| 190 | return *this; |
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| 191 | } |
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| 192 | |
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| 193 | }; |
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| 194 | |
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| 195 | ///Equality comparison |
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| 196 | |
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| 197 | ///\relates Polynomial |
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| 198 | ///\warning Two polynomials are defined to be unequal if their degrees differ, |
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| 199 | ///even if the non-zero coefficients are the same. |
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| 200 | template<class U,class V> |
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| 201 | bool operator==(const Polynomial<U> &u,const Polynomial<V> &v) |
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| 202 | { |
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| 203 | if(u.deg()!=v.deg()) return false; |
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| 204 | for(int i=0;i<=u.deg();i++) if(u[i]!=v[i]) return false; |
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| 205 | return true; |
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| 206 | } |
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| 207 | |
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| 208 | ///Non-equality comparison |
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| 209 | |
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| 210 | ///\relates Polynomial |
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| 211 | ///\warning Two polynomials are defined to be unequal if their degrees differ, |
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| 212 | ///even if the non-zero coefficients are the same. |
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| 213 | template<class U,class V> |
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| 214 | bool operator!=(const Polynomial<U> &u,const Polynomial<V> &v) |
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| 215 | { |
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| 216 | return !(u==v); |
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| 217 | } |
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| 218 | |
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| 219 | ///\e |
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| 220 | |
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| 221 | ///\relates Polynomial |
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| 222 | /// |
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| 223 | template<class U,class V> |
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| 224 | Polynomial<U> operator+(const Polynomial<U> &u,const Polynomial<V> &v) |
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| 225 | { |
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| 226 | Polynomial<U> tmp=u; |
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| 227 | tmp+=v; |
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| 228 | return tmp; |
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| 229 | } |
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| 230 | |
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| 231 | ///\e |
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| 232 | |
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| 233 | ///\relates Polynomial |
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| 234 | /// |
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| 235 | template<class U,class V> |
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| 236 | Polynomial<U> operator-(const Polynomial<U> &u,const Polynomial<V> &v) |
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| 237 | { |
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| 238 | Polynomial<U> tmp=u; |
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| 239 | tmp-=v; |
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| 240 | return tmp; |
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| 241 | } |
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| 242 | |
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| 243 | ///\e |
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| 244 | |
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| 245 | ///\relates Polynomial |
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| 246 | /// |
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| 247 | template<class U,class V> |
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| 248 | Polynomial<U> operator*(const Polynomial<U> &u,const Polynomial<V> &v) |
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| 249 | { |
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| 250 | Polynomial<U> tmp(u.deg()+v.deg()); |
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| 251 | for(int i=0;i<=v.deg();i++) |
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| 252 | for(int j=0;j<=u.deg();j++) |
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| 253 | tmp[i+j]+=v[i]*u[j]; |
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| 254 | return tmp; |
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| 255 | } |
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| 256 | ///\e |
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| 257 | |
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| 258 | ///\relates Polynomial |
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| 259 | /// |
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| 260 | template<class U,class V> |
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| 261 | Polynomial<U> operator+(const Polynomial<U> &u,const V &v) |
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| 262 | { |
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| 263 | Polynomial<U> tmp=u; |
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| 264 | tmp+=v; |
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| 265 | return tmp; |
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| 266 | } |
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| 267 | ///\e |
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| 268 | |
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| 269 | ///\relates Polynomial |
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| 270 | /// |
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| 271 | template<class U,class V> |
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| 272 | Polynomial<U> operator+(const V &v,const Polynomial<U> &u) |
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| 273 | { |
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| 274 | Polynomial<U> tmp=u; |
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| 275 | tmp+=v; |
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| 276 | return tmp; |
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| 277 | } |
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| 278 | ///\e |
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| 279 | |
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| 280 | ///\relates Polynomial |
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| 281 | /// |
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| 282 | template<class U,class V> |
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| 283 | Polynomial<U> operator-(const Polynomial<U> &u,const V &v) |
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| 284 | { |
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| 285 | Polynomial<U> tmp=u; |
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| 286 | tmp-=v; |
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| 287 | return tmp; |
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| 288 | } |
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| 289 | ///\e |
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| 290 | |
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| 291 | ///\relates Polynomial |
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| 292 | /// |
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| 293 | template<class U> |
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| 294 | Polynomial<U> operator-(const Polynomial<U> &u) |
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| 295 | { |
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| 296 | Polynomial<U> tmp(u.deg()); |
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| 297 | for(int i=0;i<=u.deg();i++) tmp[i]=-u[i]; |
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| 298 | return tmp; |
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| 299 | } |
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| 300 | ///\e |
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| 301 | |
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| 302 | ///\relates Polynomial |
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| 303 | /// |
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| 304 | template<class U,class V> |
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| 305 | Polynomial<U> operator-(const V &v,const Polynomial<U> &u) |
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| 306 | { |
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| 307 | Polynomial<U> tmp=-u; |
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| 308 | tmp+=v; |
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| 309 | return tmp; |
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| 310 | } |
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| 311 | ///\e |
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| 312 | |
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| 313 | ///\relates Polynomial |
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| 314 | /// |
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| 315 | template<class U,class V> |
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| 316 | Polynomial<U> operator*(const Polynomial<U> &u,const V &v) |
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| 317 | { |
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| 318 | Polynomial<U> tmp=u; |
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| 319 | tmp*=v; |
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| 320 | return tmp; |
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| 321 | } |
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| 322 | ///\e |
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| 323 | |
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| 324 | ///\relates Polynomial |
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| 325 | /// |
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| 326 | template<class U,class V> |
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| 327 | Polynomial<U> operator*(const V &v,const Polynomial<U> &u) |
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| 328 | { |
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| 329 | Polynomial<U> tmp=u; |
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| 330 | tmp*=v; |
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| 331 | return tmp; |
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| 332 | } |
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| 333 | ///\e |
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| 334 | |
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| 335 | ///\relates Polynomial |
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| 336 | /// |
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| 337 | template<class U,class V> |
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| 338 | Polynomial<U> operator/(const Polynomial<U> &u,const V &v) |
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| 339 | { |
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| 340 | Polynomial<U> tmp=u; |
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| 341 | tmp/=v; |
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| 342 | return tmp; |
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| 343 | } |
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| 344 | |
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| 345 | /// @} |
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| 346 | |
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| 347 | } //END OF NAMESPACE LEMON |
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| 348 | |
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| 349 | #endif // LEMON_POLYNOMIAL_H |
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