Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 1 | // This file is part of Eigen, a lightweight C++ template library |
| 2 | // for linear algebra. |
| 3 | // |
| 4 | // Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com> |
| 5 | // |
| 6 | // This Source Code Form is subject to the terms of the Mozilla |
| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed |
| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. |
| 9 | |
| 10 | #include "main.h" |
| 11 | #include <unsupported/Eigen/Polynomials> |
| 12 | #include <iostream> |
| 13 | #include <algorithm> |
| 14 | |
| 15 | using namespace std; |
| 16 | |
| 17 | namespace Eigen { |
| 18 | namespace internal { |
| 19 | template<int Size> |
| 20 | struct increment_if_fixed_size |
| 21 | { |
| 22 | enum { |
| 23 | ret = (Size == Dynamic) ? Dynamic : Size+1 |
| 24 | }; |
| 25 | }; |
| 26 | } |
| 27 | } |
| 28 | |
| 29 | |
| 30 | template<int Deg, typename POLYNOMIAL, typename SOLVER> |
| 31 | bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve ) |
| 32 | { |
| 33 | typedef typename POLYNOMIAL::Index Index; |
| 34 | typedef typename POLYNOMIAL::Scalar Scalar; |
| 35 | |
| 36 | typedef typename SOLVER::RootsType RootsType; |
| 37 | typedef Matrix<Scalar,Deg,1> EvalRootsType; |
| 38 | |
| 39 | const Index deg = pols.size()-1; |
| 40 | |
| 41 | psolve.compute( pols ); |
| 42 | const RootsType& roots( psolve.roots() ); |
| 43 | EvalRootsType evr( deg ); |
| 44 | for( int i=0; i<roots.size(); ++i ){ |
| 45 | evr[i] = std::abs( poly_eval( pols, roots[i] ) ); } |
| 46 | |
| 47 | bool evalToZero = evr.isZero( test_precision<Scalar>() ); |
| 48 | if( !evalToZero ) |
| 49 | { |
| 50 | cerr << "WRONG root: " << endl; |
| 51 | cerr << "Polynomial: " << pols.transpose() << endl; |
| 52 | cerr << "Roots found: " << roots.transpose() << endl; |
| 53 | cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl; |
| 54 | cerr << endl; |
| 55 | } |
| 56 | |
| 57 | std::vector<Scalar> rootModuli( roots.size() ); |
| 58 | Map< EvalRootsType > aux( &rootModuli[0], roots.size() ); |
| 59 | aux = roots.array().abs(); |
| 60 | std::sort( rootModuli.begin(), rootModuli.end() ); |
| 61 | bool distinctModuli=true; |
| 62 | for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i ) |
| 63 | { |
| 64 | if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){ |
| 65 | distinctModuli = false; } |
| 66 | } |
| 67 | VERIFY( evalToZero || !distinctModuli ); |
| 68 | |
| 69 | return distinctModuli; |
| 70 | } |
| 71 | |
| 72 | |
| 73 | |
| 74 | |
| 75 | |
| 76 | |
| 77 | |
| 78 | template<int Deg, typename POLYNOMIAL> |
| 79 | void evalSolver( const POLYNOMIAL& pols ) |
| 80 | { |
| 81 | typedef typename POLYNOMIAL::Scalar Scalar; |
| 82 | |
| 83 | typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; |
| 84 | |
| 85 | PolynomialSolverType psolve; |
| 86 | aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ); |
| 87 | } |
| 88 | |
| 89 | |
| 90 | |
| 91 | |
| 92 | template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS > |
| 93 | void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots ) |
| 94 | { |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 95 | using std::sqrt; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 96 | typedef typename POLYNOMIAL::Scalar Scalar; |
| 97 | |
| 98 | typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; |
| 99 | |
| 100 | PolynomialSolverType psolve; |
| 101 | if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) ) |
| 102 | { |
| 103 | //It is supposed that |
| 104 | // 1) the roots found are correct |
| 105 | // 2) the roots have distinct moduli |
| 106 | |
| 107 | typedef typename POLYNOMIAL::Scalar Scalar; |
| 108 | typedef typename REAL_ROOTS::Scalar Real; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 109 | typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType; |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 110 | |
| 111 | //Test realRoots |
| 112 | std::vector< Real > calc_realRoots; |
| 113 | psolve.realRoots( calc_realRoots ); |
| 114 | VERIFY( calc_realRoots.size() == (size_t)real_roots.size() ); |
| 115 | |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 116 | const Scalar psPrec = sqrt( test_precision<Scalar>() ); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 117 | |
| 118 | for( size_t i=0; i<calc_realRoots.size(); ++i ) |
| 119 | { |
| 120 | bool found = false; |
| 121 | for( size_t j=0; j<calc_realRoots.size()&& !found; ++j ) |
| 122 | { |
| 123 | if( internal::isApprox( calc_realRoots[i], real_roots[j] ), psPrec ){ |
| 124 | found = true; } |
| 125 | } |
| 126 | VERIFY( found ); |
| 127 | } |
| 128 | |
| 129 | //Test greatestRoot |
| 130 | VERIFY( internal::isApprox( roots.array().abs().maxCoeff(), |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 131 | abs( psolve.greatestRoot() ), psPrec ) ); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 132 | |
| 133 | //Test smallestRoot |
| 134 | VERIFY( internal::isApprox( roots.array().abs().minCoeff(), |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 135 | abs( psolve.smallestRoot() ), psPrec ) ); |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 136 | |
| 137 | bool hasRealRoot; |
| 138 | //Test absGreatestRealRoot |
| 139 | Real r = psolve.absGreatestRealRoot( hasRealRoot ); |
| 140 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); |
| 141 | if( hasRealRoot ){ |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 142 | VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) ); } |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 143 | |
| 144 | //Test absSmallestRealRoot |
| 145 | r = psolve.absSmallestRealRoot( hasRealRoot ); |
| 146 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); |
| 147 | if( hasRealRoot ){ |
Carlos Hernandez | 7faaa9f | 2014-08-05 17:53:32 -0700 | [diff] [blame] | 148 | VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); } |
Narayan Kamath | c981c48 | 2012-11-02 10:59:05 +0000 | [diff] [blame] | 149 | |
| 150 | //Test greatestRealRoot |
| 151 | r = psolve.greatestRealRoot( hasRealRoot ); |
| 152 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); |
| 153 | if( hasRealRoot ){ |
| 154 | VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); } |
| 155 | |
| 156 | //Test smallestRealRoot |
| 157 | r = psolve.smallestRealRoot( hasRealRoot ); |
| 158 | VERIFY( hasRealRoot == (real_roots.size() > 0 ) ); |
| 159 | if( hasRealRoot ){ |
| 160 | VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); } |
| 161 | } |
| 162 | } |
| 163 | |
| 164 | |
| 165 | template<typename _Scalar, int _Deg> |
| 166 | void polynomialsolver(int deg) |
| 167 | { |
| 168 | typedef internal::increment_if_fixed_size<_Deg> Dim; |
| 169 | typedef Matrix<_Scalar,Dim::ret,1> PolynomialType; |
| 170 | typedef Matrix<_Scalar,_Deg,1> EvalRootsType; |
| 171 | |
| 172 | cout << "Standard cases" << endl; |
| 173 | PolynomialType pols = PolynomialType::Random(deg+1); |
| 174 | evalSolver<_Deg,PolynomialType>( pols ); |
| 175 | |
| 176 | cout << "Hard cases" << endl; |
| 177 | _Scalar multipleRoot = internal::random<_Scalar>(); |
| 178 | EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot); |
| 179 | roots_to_monicPolynomial( allRoots, pols ); |
| 180 | evalSolver<_Deg,PolynomialType>( pols ); |
| 181 | |
| 182 | cout << "Test sugar" << endl; |
| 183 | EvalRootsType realRoots = EvalRootsType::Random(deg); |
| 184 | roots_to_monicPolynomial( realRoots, pols ); |
| 185 | evalSolverSugarFunction<_Deg>( |
| 186 | pols, |
| 187 | realRoots.template cast < |
| 188 | std::complex< |
| 189 | typename NumTraits<_Scalar>::Real |
| 190 | > |
| 191 | >(), |
| 192 | realRoots ); |
| 193 | } |
| 194 | |
| 195 | void test_polynomialsolver() |
| 196 | { |
| 197 | for(int i = 0; i < g_repeat; i++) |
| 198 | { |
| 199 | CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) ); |
| 200 | CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) ); |
| 201 | CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) ); |
| 202 | CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) ); |
| 203 | CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) ); |
| 204 | CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) ); |
| 205 | CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) ); |
| 206 | CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) ); |
| 207 | |
| 208 | CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>( |
| 209 | internal::random<int>(9,13) |
| 210 | )) ); |
| 211 | CALL_SUBTEST_10((polynomialsolver<double,Dynamic>( |
| 212 | internal::random<int>(9,13) |
| 213 | )) ); |
| 214 | } |
| 215 | } |