233 lines
7.3 KiB
C++
233 lines
7.3 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2010 Manuel Yguel <manuel.yguel@gmail.com>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <unsupported/Eigen/Polynomials>
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#include <iostream>
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#include <algorithm>
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using namespace std;
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namespace Eigen {
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namespace internal {
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template<int Size>
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struct increment_if_fixed_size
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{
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enum {
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ret = (Size == Dynamic) ? Dynamic : Size+1
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};
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};
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}
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}
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template<typename PolynomialType>
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PolynomialType polyder(const PolynomialType& p)
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{
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typedef typename PolynomialType::Scalar Scalar;
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PolynomialType res(p.size());
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for(Index i=1; i<p.size(); ++i)
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res[i-1] = p[i]*Scalar(i);
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res[p.size()-1] = 0.;
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return res;
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}
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template<int Deg, typename POLYNOMIAL, typename SOLVER>
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bool aux_evalSolver( const POLYNOMIAL& pols, SOLVER& psolve )
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{
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typedef typename POLYNOMIAL::Scalar Scalar;
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typedef typename POLYNOMIAL::RealScalar RealScalar;
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typedef typename SOLVER::RootsType RootsType;
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typedef Matrix<RealScalar,Deg,1> EvalRootsType;
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const Index deg = pols.size()-1;
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// Test template constructor from coefficient vector
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SOLVER solve_constr (pols);
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psolve.compute( pols );
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const RootsType& roots( psolve.roots() );
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EvalRootsType evr( deg );
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POLYNOMIAL pols_der = polyder(pols);
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EvalRootsType der( deg );
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for( int i=0; i<roots.size(); ++i ){
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evr[i] = std::abs( poly_eval( pols, roots[i] ) );
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der[i] = numext::maxi(RealScalar(1.), std::abs( poly_eval( pols_der, roots[i] ) ));
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}
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// we need to divide by the magnitude of the derivative because
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// with a high derivative is very small error in the value of the root
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// yiels a very large error in the polynomial evaluation.
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bool evalToZero = (evr.cwiseQuotient(der)).isZero( test_precision<Scalar>() );
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if( !evalToZero )
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{
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cerr << "WRONG root: " << endl;
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cerr << "Polynomial: " << pols.transpose() << endl;
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cerr << "Roots found: " << roots.transpose() << endl;
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cerr << "Abs value of the polynomial at the roots: " << evr.transpose() << endl;
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cerr << endl;
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}
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std::vector<RealScalar> rootModuli( roots.size() );
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Map< EvalRootsType > aux( &rootModuli[0], roots.size() );
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aux = roots.array().abs();
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std::sort( rootModuli.begin(), rootModuli.end() );
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bool distinctModuli=true;
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for( size_t i=1; i<rootModuli.size() && distinctModuli; ++i )
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{
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if( internal::isApprox( rootModuli[i], rootModuli[i-1] ) ){
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distinctModuli = false; }
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}
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VERIFY( evalToZero || !distinctModuli );
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return distinctModuli;
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}
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template<int Deg, typename POLYNOMIAL>
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void evalSolver( const POLYNOMIAL& pols )
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{
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typedef typename POLYNOMIAL::Scalar Scalar;
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typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
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PolynomialSolverType psolve;
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aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve );
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}
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template< int Deg, typename POLYNOMIAL, typename ROOTS, typename REAL_ROOTS >
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void evalSolverSugarFunction( const POLYNOMIAL& pols, const ROOTS& roots, const REAL_ROOTS& real_roots )
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{
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using std::sqrt;
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typedef typename POLYNOMIAL::Scalar Scalar;
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typedef typename POLYNOMIAL::RealScalar RealScalar;
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typedef PolynomialSolver<Scalar, Deg > PolynomialSolverType;
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PolynomialSolverType psolve;
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if( aux_evalSolver<Deg, POLYNOMIAL, PolynomialSolverType>( pols, psolve ) )
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{
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//It is supposed that
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// 1) the roots found are correct
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// 2) the roots have distinct moduli
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//Test realRoots
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std::vector< RealScalar > calc_realRoots;
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psolve.realRoots( calc_realRoots, test_precision<RealScalar>());
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VERIFY_IS_EQUAL( calc_realRoots.size() , (size_t)real_roots.size() );
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const RealScalar psPrec = sqrt( test_precision<RealScalar>() );
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for( size_t i=0; i<calc_realRoots.size(); ++i )
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{
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bool found = false;
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for( size_t j=0; j<calc_realRoots.size()&& !found; ++j )
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{
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if( internal::isApprox( calc_realRoots[i], real_roots[j], psPrec ) ){
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found = true; }
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}
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VERIFY( found );
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}
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//Test greatestRoot
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VERIFY( internal::isApprox( roots.array().abs().maxCoeff(),
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abs( psolve.greatestRoot() ), psPrec ) );
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//Test smallestRoot
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VERIFY( internal::isApprox( roots.array().abs().minCoeff(),
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abs( psolve.smallestRoot() ), psPrec ) );
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bool hasRealRoot;
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//Test absGreatestRealRoot
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RealScalar r = psolve.absGreatestRealRoot( hasRealRoot );
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VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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if( hasRealRoot ){
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VERIFY( internal::isApprox( real_roots.array().abs().maxCoeff(), abs(r), psPrec ) ); }
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//Test absSmallestRealRoot
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r = psolve.absSmallestRealRoot( hasRealRoot );
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VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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if( hasRealRoot ){
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VERIFY( internal::isApprox( real_roots.array().abs().minCoeff(), abs( r ), psPrec ) ); }
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//Test greatestRealRoot
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r = psolve.greatestRealRoot( hasRealRoot );
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VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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if( hasRealRoot ){
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VERIFY( internal::isApprox( real_roots.array().maxCoeff(), r, psPrec ) ); }
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//Test smallestRealRoot
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r = psolve.smallestRealRoot( hasRealRoot );
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VERIFY( hasRealRoot == (real_roots.size() > 0 ) );
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if( hasRealRoot ){
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VERIFY( internal::isApprox( real_roots.array().minCoeff(), r, psPrec ) ); }
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}
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}
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template<typename _Scalar, int _Deg>
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void polynomialsolver(int deg)
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{
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typedef typename NumTraits<_Scalar>::Real RealScalar;
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typedef internal::increment_if_fixed_size<_Deg> Dim;
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typedef Matrix<_Scalar,Dim::ret,1> PolynomialType;
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typedef Matrix<_Scalar,_Deg,1> EvalRootsType;
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typedef Matrix<RealScalar,_Deg,1> RealRootsType;
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cout << "Standard cases" << endl;
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PolynomialType pols = PolynomialType::Random(deg+1);
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evalSolver<_Deg,PolynomialType>( pols );
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cout << "Hard cases" << endl;
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_Scalar multipleRoot = internal::random<_Scalar>();
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EvalRootsType allRoots = EvalRootsType::Constant(deg,multipleRoot);
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roots_to_monicPolynomial( allRoots, pols );
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evalSolver<_Deg,PolynomialType>( pols );
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cout << "Test sugar" << endl;
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RealRootsType realRoots = RealRootsType::Random(deg);
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roots_to_monicPolynomial( realRoots, pols );
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evalSolverSugarFunction<_Deg>(
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pols,
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realRoots.template cast <std::complex<RealScalar> >().eval(),
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realRoots );
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}
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EIGEN_DECLARE_TEST(polynomialsolver)
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{
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for(int i = 0; i < g_repeat; i++)
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{
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CALL_SUBTEST_1( (polynomialsolver<float,1>(1)) );
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CALL_SUBTEST_2( (polynomialsolver<double,2>(2)) );
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CALL_SUBTEST_3( (polynomialsolver<double,3>(3)) );
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CALL_SUBTEST_4( (polynomialsolver<float,4>(4)) );
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CALL_SUBTEST_5( (polynomialsolver<double,5>(5)) );
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CALL_SUBTEST_6( (polynomialsolver<float,6>(6)) );
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CALL_SUBTEST_7( (polynomialsolver<float,7>(7)) );
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CALL_SUBTEST_8( (polynomialsolver<double,8>(8)) );
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CALL_SUBTEST_9( (polynomialsolver<float,Dynamic>(
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internal::random<int>(9,13)
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)) );
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CALL_SUBTEST_10((polynomialsolver<double,Dynamic>(
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internal::random<int>(9,13)
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)) );
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CALL_SUBTEST_11((polynomialsolver<float,Dynamic>(1)) );
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CALL_SUBTEST_12((polynomialsolver<std::complex<double>,Dynamic>(internal::random<int>(2,13))) );
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}
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}
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