Line data Source code
1 : /*
2 : * Copyright (c) 2010-2015: G-CSC, Goethe University Frankfurt
3 : * Author: Andreas Vogel
4 : *
5 : * This file is part of UG4.
6 : *
7 : * UG4 is free software: you can redistribute it and/or modify it under the
8 : * terms of the GNU Lesser General Public License version 3 (as published by the
9 : * Free Software Foundation) with the following additional attribution
10 : * requirements (according to LGPL/GPL v3 §7):
11 : *
12 : * (1) The following notice must be displayed in the Appropriate Legal Notices
13 : * of covered and combined works: "Based on UG4 (www.ug4.org/license)".
14 : *
15 : * (2) The following notice must be displayed at a prominent place in the
16 : * terminal output of covered works: "Based on UG4 (www.ug4.org/license)".
17 : *
18 : * (3) The following bibliography is recommended for citation and must be
19 : * preserved in all covered files:
20 : * "Reiter, S., Vogel, A., Heppner, I., Rupp, M., and Wittum, G. A massively
21 : * parallel geometric multigrid solver on hierarchically distributed grids.
22 : * Computing and visualization in science 16, 4 (2013), 151-164"
23 : * "Vogel, A., Reiter, S., Rupp, M., Nägel, A., and Wittum, G. UG4 -- a novel
24 : * flexible software system for simulating pde based models on high performance
25 : * computers. Computing and visualization in science 16, 4 (2013), 165-179"
26 : *
27 : * This program is distributed in the hope that it will be useful,
28 : * but WITHOUT ANY WARRANTY; without even the implied warranty of
29 : * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
30 : * GNU Lesser General Public License for more details.
31 : */
32 :
33 : #ifndef __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__
34 : #define __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__
35 :
36 : #include "common/math/ugmath.h"
37 : #include <vector>
38 :
39 : namespace ug{
40 :
41 : /// \addtogroup lib_discretization
42 : /// @{
43 :
44 : /** base class for one dimensional polynomials
45 : * This class is used to represent polynomials in one variable. For the
46 : * evaluation the horner scheme is used. Note that using this representation
47 : * the computation of higher order derivatives turns out easier than by
48 : * hard coded implementations.
49 : */
50 299 : class Polynomial1D
51 : {
52 : public:
53 : /// Constructor producing zero polynomial of degree 'degree'
54 : Polynomial1D(size_t degree = 0)
55 210 : : m_vCoeff(degree+1, 0.0)
56 10 : {}
57 :
58 : /// Constructor passing coefficients for the polynomial
59 112 : Polynomial1D(const std::vector<number>& a)
60 112 : : m_vCoeff(a)
61 : {
62 : // check that at least constant of polynomial set
63 112 : if(m_vCoeff.empty())
64 0 : m_vCoeff.resize(1, 0.0);
65 112 : };
66 :
67 : /** returns the degree of the polynomial.
68 : * This function returns the degree of the polynomial, i.e. the
69 : * highest coefficient stored. Note that no checking is performed if
70 : * the leading coefficient is zero.
71 : */
72 56 : size_t degree() const {return m_vCoeff.size() - 1;}
73 :
74 : /// evaluate the value of the polynom at x
75 : number value(const number x) const
76 : {
77 : // get degree of polynomial (is >= 0 by construction)
78 230202 : const size_t deg = m_vCoeff.size() - 1;
79 :
80 : // loop horner scheme
81 230202 : number val = m_vCoeff[deg];
82 476238 : for(size_t i = deg; i > 0; --i)
83 366474 : val = m_vCoeff[i-1] + val * x;
84 :
85 : // we're done
86 : return val;
87 : }
88 :
89 : /// returns the derivative of this polynomial as a polynomial
90 66 : Polynomial1D derivative() const
91 : {
92 : // if only constant present, return empty Polynomial
93 66 : if(degree() == 0)
94 : return Polynomial1D();
95 :
96 : // create empty polynomial of with correct size
97 : Polynomial1D tmpPol(degree() - 1);
98 :
99 : // differentiate
100 168 : for(size_t i = 0; i <= tmpPol.degree(); ++i)
101 112 : tmpPol.m_vCoeff[i] = (i+1) * m_vCoeff[i+1];
102 :
103 : // return derivative by copy
104 : return tmpPol;
105 : }
106 :
107 : /// multiply by a polynomial
108 112 : Polynomial1D& operator *=(const Polynomial1D& v)
109 : {
110 : // new size of polynomial
111 112 : size_t newDeg = degree() + v.degree();
112 :
113 : // create new coefficients
114 112 : std::vector<number> vNewCoeff(newDeg+1, 0.0);
115 :
116 : // multiply
117 299 : for(size_t i = 0; i <= degree(); ++i)
118 561 : for(size_t j = 0; j <= v.degree(); ++j)
119 374 : vNewCoeff[i+j] += m_vCoeff[i] * v.m_vCoeff[j];
120 :
121 : // Copy new coeffs
122 112 : m_vCoeff = vNewCoeff;
123 :
124 : // we're done
125 112 : return *this;
126 112 : }
127 :
128 : /// multiply by a scalar
129 : Polynomial1D& operator *=(number scale)
130 : {
131 : // multiply
132 244 : for(size_t i = 0; i <= degree(); ++i)
133 178 : m_vCoeff[i] *= scale;
134 :
135 : // we're done
136 : return *this;
137 : }
138 :
139 : // output
140 : friend std::ostream& operator<< (std::ostream& outStream, Polynomial1D& v);
141 :
142 : protected:
143 66 : void set_coefficients(const std::vector<number>& a)
144 : {
145 : // assign coefficients
146 66 : m_vCoeff = a;
147 :
148 : // check that at least constant of polynomial set
149 66 : if(m_vCoeff.empty())
150 0 : m_vCoeff.resize(1, 0.0);
151 66 : };
152 :
153 : private:
154 : // vector holding the coefficients of the polynom
155 : // An empty vector is the Polynomial p = 0;
156 : // else we have p(x) = sum_i m_vCoeff[i] *x^i
157 : std::vector<number> m_vCoeff;
158 : };
159 :
160 : inline std::ostream& operator<< (std::ostream& outStream, Polynomial1D& v)
161 : {
162 : for(size_t i = 0; i <= v.degree(); ++i)
163 : {
164 : outStream << v.m_vCoeff[i] << " *x^" << i;
165 : if(i != v.degree()) outStream << " + ";
166 : }
167 : return outStream;
168 : }
169 :
170 : /// @}
171 : } // end namespace ug
172 :
173 : #endif /* __H__UG__LIB_DISC__LOCAL_SHAPE_FUNCTION_SET__COMMON__POLYNOMIAL1D__ */
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