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// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// 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 <limits>
#include <Eigen/Eigenvalues>
template<typename EigType,typename MatType>
void check_eigensolver_for_given_mat(const EigType &eig, const MatType& a)
{
typedef typename NumTraits<typename MatType::Scalar>::Real RealScalar;
typedef Matrix<RealScalar, MatType::RowsAtCompileTime, 1> RealVectorType;
typedef typename std::complex<RealScalar> Complex;
Index n = a.rows();
VERIFY_IS_EQUAL(eig.info(), Success);
VERIFY_IS_APPROX(a * eig.pseudoEigenvectors(), eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix());
VERIFY_IS_APPROX(a.template cast<Complex>() * eig.eigenvectors(),
eig.eigenvectors() * eig.eigenvalues().asDiagonal());
VERIFY_IS_APPROX(eig.eigenvectors().colwise().norm(), RealVectorType::Ones(n).transpose());
VERIFY_IS_APPROX(a.eigenvalues(), eig.eigenvalues());
}
template<typename MatrixType> void eigensolver(const MatrixType& m)
{
/* this test covers the following files:
EigenSolver.h
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef typename std::complex<RealScalar> Complex;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
EigenSolver<MatrixType> ei0(symmA);
VERIFY_IS_EQUAL(ei0.info(), Success);
VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
(ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
EigenSolver<MatrixType> ei1(a);
CALL_SUBTEST( check_eigensolver_for_given_mat(ei1,a) );
EigenSolver<MatrixType> ei2;
ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
VERIFY_IS_EQUAL(ei2.info(), Success);
VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
if (rows > 2) {
ei2.setMaxIterations(1).compute(a);
VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
}
EigenSolver<MatrixType> eiNoEivecs(a, false);
VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
if (rows > 2 && rows < 20)
{
// Test matrix with NaN
a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
EigenSolver<MatrixType> eiNaN(a);
VERIFY_IS_NOT_EQUAL(eiNaN.info(), Success);
}
// regression test for bug 1098
{
EigenSolver<MatrixType> eig(a.adjoint() * a);
eig.compute(a.adjoint() * a);
}
// regression test for bug 478
{
a.setZero();
EigenSolver<MatrixType> ei3(a);
VERIFY_IS_EQUAL(ei3.info(), Success);
VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1));
VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity());
}
}
template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
{
EigenSolver<MatrixType> eig;
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
VERIFY_RAISES_ASSERT(eig.eigenvalues());
MatrixType a = MatrixType::Random(m.rows(),m.cols());
eig.compute(a, false);
VERIFY_RAISES_ASSERT(eig.eigenvectors());
VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
}
template<typename CoeffType>
Matrix<typename CoeffType::Scalar,Dynamic,Dynamic>
make_companion(const CoeffType& coeffs)
{
Index n = coeffs.size()-1;
Matrix<typename CoeffType::Scalar,Dynamic,Dynamic> res(n,n);
res.setZero();
res.row(0) = -coeffs.tail(n) / coeffs(0);
res.diagonal(-1).setOnes();
return res;
}
template<int>
void eigensolver_generic_extra()
{
{
// regression test for bug 793
MatrixXd a(3,3);
a << 0, 0, 1,
1, 1, 1,
1, 1e+200, 1;
Eigen::EigenSolver<MatrixXd> eig(a);
double scale = 1e-200; // scale to avoid overflow during the comparisons
VERIFY_IS_APPROX(a * eig.pseudoEigenvectors()*scale, eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()*scale);
VERIFY_IS_APPROX(a * eig.eigenvectors()*scale, eig.eigenvectors() * eig.eigenvalues().asDiagonal()*scale);
}
{
// check a case where all eigenvalues are null.
MatrixXd a(2,2);
a << 1, 1,
-1, -1;
Eigen::EigenSolver<MatrixXd> eig(a);
VERIFY_IS_APPROX(eig.pseudoEigenvectors().squaredNorm(), 2.);
VERIFY_IS_APPROX((a * eig.pseudoEigenvectors()).norm()+1., 1.);
VERIFY_IS_APPROX((eig.pseudoEigenvectors() * eig.pseudoEigenvalueMatrix()).norm()+1., 1.);
VERIFY_IS_APPROX((a * eig.eigenvectors()).norm()+1., 1.);
VERIFY_IS_APPROX((eig.eigenvectors() * eig.eigenvalues().asDiagonal()).norm()+1., 1.);
}
// regression test for bug 933
{
{
VectorXd coeffs(5); coeffs << 1, -3, -175, -225, 2250;
MatrixXd C = make_companion(coeffs);
EigenSolver<MatrixXd> eig(C);
CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
}
{
// this test is tricky because it requires high accuracy in smallest eigenvalues
VectorXd coeffs(5); coeffs << 6.154671e-15, -1.003870e-10, -9.819570e-01, 3.995715e+03, 2.211511e+08;
MatrixXd C = make_companion(coeffs);
EigenSolver<MatrixXd> eig(C);
CALL_SUBTEST( check_eigensolver_for_given_mat(eig,C) );
Index n = C.rows();
for(Index i=0;i<n;++i)
{
typedef std::complex<double> Complex;
MatrixXcd ac = C.cast<Complex>();
ac.diagonal().array() -= eig.eigenvalues()(i);
VectorXd sv = ac.jacobiSvd().singularValues();
// comparing to sv(0) is not enough here to catch the "bug",
// the hard-coded 1.0 is important!
VERIFY_IS_MUCH_SMALLER_THAN(sv(n-1), 1.0);
}
}
}
// regression test for bug 1557
{
// this test is interesting because it contains zeros on the diagonal.
MatrixXd A_bug1557(3,3);
A_bug1557 << 0, 0, 0, 1, 0, 0.5887907064808635127, 0, 1, 0;
EigenSolver<MatrixXd> eig(A_bug1557);
CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1557) );
}
// regression test for bug 1174
{
Index n = 12;
MatrixXf A_bug1174(n,n);
A_bug1174 << 262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
262144, 0, 0, 262144, 786432, 0, 0, 0, 0, 0, 0, 786432,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0,
0, 262144, 262144, 0, 0, 262144, 262144, 262144, 262144, 262144, 262144, 0;
EigenSolver<MatrixXf> eig(A_bug1174);
CALL_SUBTEST( check_eigensolver_for_given_mat(eig,A_bug1174) );
}
}
EIGEN_DECLARE_TEST(eigensolver_generic)
{
int s = 0;
for(int i = 0; i < g_repeat; i++) {
CALL_SUBTEST_1( eigensolver(Matrix4f()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
TEST_SET_BUT_UNUSED_VARIABLE(s)
// some trivial but implementation-wise tricky cases
CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
CALL_SUBTEST_4( eigensolver(Matrix2d()) );
}
CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
// Test problem size constructors
CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
// regression test for bug 410
CALL_SUBTEST_2(
{
MatrixXd A(1,1);
A(0,0) = std::sqrt(-1.); // is Not-a-Number
Eigen::EigenSolver<MatrixXd> solver(A);
VERIFY_IS_EQUAL(solver.info(), NumericalIssue);
}
);
CALL_SUBTEST_2( eigensolver_generic_extra<0>() );
TEST_SET_BUT_UNUSED_VARIABLE(s)
}
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