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