1 | /*
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2 | * vmg - a versatile multigrid solver
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3 | * Copyright (C) 2012 Institute for Numerical Simulation, University of Bonn
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4 | *
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5 | * vmg is free software: you can redistribute it and/or modify
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6 | * it under the terms of the GNU General Public License as published by
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7 | * the Free Software Foundation, either version 3 of the License, or
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8 | * (at your option) any later version.
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9 | *
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10 | * vmg is distributed in the hope that it will be useful,
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11 | * but WITHOUT ANY WARRANTY; without even the implied warranty of
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12 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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13 | * GNU General Public License for more details.
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14 | *
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15 | * You should have received a copy of the GNU General Public License
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16 | * along with this program. If not, see <http://www.gnu.org/licenses/>.
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17 | */
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18 |
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19 | /**
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20 | * @file givens.hpp
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21 | * @author Julian Iseringhausen <isering@ins.uni-bonn.de>
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22 | * @date Mon Apr 18 13:10:15 2011
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23 | *
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24 | * @brief Solves system of linear equations using Givens rotations.
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25 | * Compare to Meister, Numerik lineare Gleichungssysteme.
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26 | *
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27 | */
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28 |
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29 | #ifndef GIVENS_HPP_
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30 | #define GIVENS_HPP_
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31 |
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32 | #include <cfloat>
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33 |
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34 | #include "solver/solver.hpp"
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35 |
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36 | namespace VMG
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37 | {
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38 |
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39 | template<class T>
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40 | class Givens : public T
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41 | {
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42 | public:
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43 | Givens(bool register_ = true) :
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44 | T(register_)
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45 | {}
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46 |
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47 | Givens(int size, bool register_ = true) :
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48 | T(size, register_)
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49 | {}
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50 |
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51 | protected:
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52 | void Compute();
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53 | };
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54 |
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55 | template<class T>
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56 | void Givens<T>::Compute()
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57 | {
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58 | int n = this->Size();
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59 | vmg_float c,s,t;
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60 |
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61 | for (int i=0; i<n-1; i++)
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62 | for (int j=i+1; j<n; j++)
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63 | if (fabs(this->Mat(j,i)) > DBL_EPSILON) {
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64 |
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65 | t = 1.0 / sqrt(this->Mat(i,i)*this->Mat(i,i) + this->Mat(j,i)*this->Mat(j,i));
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66 | s = t * this->Mat(j,i);
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67 | c = t * this->Mat(i,i);
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68 |
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69 | for (int k=i; k<n; k++) {
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70 |
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71 | t = c * this->Mat(i,k) + s * this->Mat(j,k);
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72 |
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73 | if (k != i)
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74 | this->Mat(j,k) = c * this->Mat(j,k) - s * this->Mat(i,k);
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75 |
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76 | this->Mat(i,k) = t;
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77 |
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78 | }
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79 |
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80 | t = c * this->Rhs(i) + s * this->Rhs(j);
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81 |
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82 | this->Rhs(j) = c * this->Rhs(j) - s * this->Rhs(i);
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83 |
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84 | this->Rhs(i) = t;
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85 |
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86 | this->Mat(j,i) = 0.0;
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87 |
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88 | }
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89 |
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90 | for (int i=n-1; i>=0; i--) {
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91 |
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92 | for (int j=i+1; j<n; j++)
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93 | this->Rhs(i) -= this->Mat(i,j) * this->Sol(j);
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94 |
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95 | this->Sol(i) = this->Rhs(i) / this->Mat(i,i);
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96 |
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97 | }
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98 | }
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99 |
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100 | }
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101 |
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102 | #endif /* GIVENS_HPP_ */
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