[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <unsupported/Eigen/Polynomials>
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| 12 | #include <iostream>
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| 13 | #include <algorithm>
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| 14 |
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| 15 | using namespace std;
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| 16 |
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| 17 | namespace Eigen {
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| 18 | namespace internal {
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| 19 | template<int Size>
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| 20 | struct increment_if_fixed_size
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| 21 | {
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| 22 | enum {
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| 23 | ret = (Size == Dynamic) ? Dynamic : Size+1
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| 24 | };
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| 25 | };
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| 26 | }
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| 27 | }
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| 28 |
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| 29 |
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| 30 | template<int Deg, typename POLYNOMIAL, typename SOLVER>
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| 31 | bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve )
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| 32 | {
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| 33 | typedef typename POLYNOMIAL::Index Index;
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| 34 | typedef typename POLYNOMIAL::Scalar Scalar;
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| 35 |
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| 36 | typedef typename SOLVER::RootsType RootsType;
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| 37 | typedef Matrix<Scalar,Deg,1> EvalRootsType;
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| 38 |
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| 39 | const Index deg = pols.size()-1;
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| 40 |
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| 41 | psolve.compute( pols );
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| 42 | const RootsType& roots( psolve.roots() );
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| 43 | EvalRootsType evr( deg );
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| 44 | for( int i=0; i<roots.size(); ++i ){
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| 45 | evr[i] = std::abs( poly_eval( pols, roots[i] ) ); }
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| 46 |
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| 47 | bool evalToZero = evr.isZero( test_precision<Scalar>() );
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| 48 | if( !evalToZero )
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| 49 | {
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| 50 | cerr << "WRONG root: " << endl;
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| 51 | cerr << "Polynomial: " << pols.transpose() << endl;
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| 52 | cerr << "Roots found: " << roots.transpose() << endl;
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| 53 | cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl;
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| 54 | cerr << endl;
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| 55 | }
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| 56 |
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| 57 | std::vector<Scalar> rootModuli( roots.size() );
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| 58 | Map< EvalRootsType > aux( &rootModuli[0], roots.size() );
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| 59 | aux = roots.array().abs();
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| 60 | std::sort( rootModuli.begin(), rootModuli.end() );
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| 61 | bool distinctModuli=true;
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| 62 | for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i )
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| 63 | {
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| 64 | if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){
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| 65 | distinctModuli = false; }
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| 66 | }
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| 67 | VERIFY( evalToZero || !distinctModuli );
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| 68 |
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| 69 | return distinctModuli;
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| 70 | }
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| 71 |
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| 72 |
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| 73 |
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| 74 |
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| 75 |
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| 76 |
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| 77 |
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| 78 | template<int Deg, typename POLYNOMIAL>
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| 79 | void evalSolver( const POLYNOMIAL& pols )
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| 80 | {
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| 81 | typedef typename POLYNOMIAL::Scalar Scalar;
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| 82 |
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| 83 | typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
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| 84 |
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| 85 | PolynomialSolverType psolve;
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| 86 | aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve );
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| 87 | }
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| 88 |
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| 89 |
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| 90 |
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| 91 |
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| 92 | template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >
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| 93 | void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )
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| 94 | {
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| 95 | using std::sqrt;
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| 96 | typedef typename POLYNOMIAL::Scalar Scalar;
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| 97 |
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| 98 | typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
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| 99 |
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| 100 | PolynomialSolverType psolve;
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| 101 | if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) )
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| 102 | {
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| 103 | //It is supposed that
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| 104 | // 1) the roots found are correct
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| 105 | // 2) the roots have distinct moduli
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| 106 |
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| 107 | typedef typename REAL_ROOTS::Scalar Real;
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| 108 |
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| 109 | //Test realRoots
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| 110 | std::vector< Real > calc_realRoots;
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| 111 | psolve.realRoots( calc_realRoots );
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| 112 | VERIFY( calc_realRoots.size() == (size_t)real_roots.size() );
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| 113 |
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| 114 | const Scalar psPrec = sqrt( test_precision<Scalar>() );
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| 115 |
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| 116 | for( size_t i=0; i<calc_realRoots.size(); ++i )
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| 117 | {
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| 118 | bool found = false;
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| 119 | for( size_t j=0; j<calc_realRoots.size()&& !found; ++j )
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| 120 | {
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| 121 | if( internal::isApprox( calc_realRoots[i], real_roots[j] ), psPrec ){
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| 122 | found = true; }
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| 123 | }
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| 124 | VERIFY( found );
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| 125 | }
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| 126 |
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| 127 | //Test greatestRoot
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| 128 | VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),
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| 129 | abs( psolve.greatestRoot() ), psPrec ) );
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| 130 |
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| 131 | //Test smallestRoot
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| 132 | VERIFY( internal::isApprox( roots.array().abs().minCoeff(),
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| 133 | abs( psolve.smallestRoot() ), psPrec ) );
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| 134 |
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| 135 | bool hasRealRoot;
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| 136 | //Test absGreatestRealRoot
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| 137 | Real r = psolve.absGreatestRealRoot( hasRealRoot );
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| 138 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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| 139 | if( hasRealRoot ){
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| 140 | VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) ); }
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| 141 |
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| 142 | //Test absSmallestRealRoot
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| 143 | r = psolve.absSmallestRealRoot( hasRealRoot );
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| 144 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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| 145 | if( hasRealRoot ){
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| 146 | VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); }
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| 147 |
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| 148 | //Test greatestRealRoot
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| 149 | r = psolve.greatestRealRoot( hasRealRoot );
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| 150 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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| 151 | if( hasRealRoot ){
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| 152 | VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); }
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| 153 |
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| 154 | //Test smallestRealRoot
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| 155 | r = psolve.smallestRealRoot( hasRealRoot );
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| 156 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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| 157 | if( hasRealRoot ){
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| 158 | VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); }
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| 159 | }
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| 160 | }
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| 161 |
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| 162 |
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| 163 | template<typename _Scalar, int _Deg>
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| 164 | void polynomialsolver(int deg)
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| 165 | {
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| 166 | typedef internal::increment_if_fixed_size<_Deg> Dim;
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| 167 | typedef Matrix<_Scalar,Dim::ret,1> PolynomialType;
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| 168 | typedef Matrix<_Scalar,_Deg,1> EvalRootsType;
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| 169 |
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| 170 | cout << "Standard cases" << endl;
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| 171 | PolynomialType pols = PolynomialType::Random(deg+1);
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| 172 | evalSolver<_Deg,PolynomialType>( pols );
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| 173 |
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| 174 | cout << "Hard cases" << endl;
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| 175 | _Scalar multipleRoot = internal::random<_Scalar>();
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| 176 | EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot);
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| 177 | roots_to_monicPolynomial( allRoots, pols );
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| 178 | evalSolver<_Deg,PolynomialType>( pols );
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| 179 |
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| 180 | cout << "Test sugar" << endl;
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| 181 | EvalRootsType realRoots = EvalRootsType::Random(deg);
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| 182 | roots_to_monicPolynomial( realRoots, pols );
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| 183 | evalSolverSugarFunction<_Deg>(
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| 184 | pols,
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| 185 | realRoots.template cast <
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| 186 | std::complex<
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| 187 | typename NumTraits<_Scalar>::Real
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| 188 | >
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| 189 | >(),
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| 190 | realRoots );
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| 191 | }
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| 192 |
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| 193 | void test_polynomialsolver()
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| 194 | {
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| 195 | for(int i = 0; i < g_repeat; i++)
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| 196 | {
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| 197 | CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) );
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| 198 | CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) );
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| 199 | CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) );
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| 200 | CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) );
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| 201 | CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) );
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| 202 | CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) );
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| 203 | CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) );
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| 204 | CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) );
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| 205 |
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| 206 | CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>(
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| 207 | internal::random<int>(9,13)
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| 208 | )) );
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| 209 | CALL_SUBTEST_10((polynomialsolver<double,Dynamic>(
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| 210 | internal::random<int>(9,13)
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| 211 | )) );
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| 212 | }
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| 213 | }
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