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Extend unit test and documentation of SelfAdjointEigenSolver::computeDirect

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This commit is contained in:
Gael Guennebaud 2015-06-08 16:16:42 +02:00
parent 913a61870d
commit cd8b996f99
2 changed files with 29 additions and 13 deletions
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10
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@ -198,17 +198,21 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
EIGEN_DEVICE_FUNC
SelfAdjointEigenSolver& compute(const MatrixType& matrix, int options = ComputeEigenvectors);
/** \brief Computes eigendecomposition of given matrix using a direct algorithm
/** \brief Computes eigendecomposition of given matrix using a closed-form algorithm
*
* This is a variant of compute(const MatrixType&, int options) which
* directly solves the underlying polynomial equation.
*
* Currently only 3x3 matrices for which the sizes are known at compile time are supported (e.g., Matrix3d).
* Currently only 2x2 and 3x3 matrices for which the sizes are known at compile time are supported (e.g., Matrix3d).
*
* This method is usually significantly faster than the QR algorithm
* This method is usually significantly faster than the QR iterative algorithm
* but it might also be less accurate. It is also worth noting that
* for 3x3 matrices it involves trigonometric operations which are
* not necessarily available for all scalar types.
*
* For the 3x3 case, we observed the following worst case relative error regarding the eigenvalues:
* - double: 1e-8
* - float: 1e-3
*
* \sa compute(const MatrixType&, int options)
*/

32
test/eigensolver_selfadjoint.cpp
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@ -18,22 +18,34 @@ template<typename MatrixType> void selfadjointeigensolver_essential_check(const
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
RealScalar largerEps = 10*test_precision<RealScalar>();
RealScalar eival_eps = (std::min)(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision()*20000);
SelfAdjointEigenSolver<MatrixType> eiSymm(m);
VERIFY_IS_EQUAL(eiSymm.info(), Success);
VERIFY((m.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(m.template selfadjointView<Lower>() * eiSymm.eigenvectors(),
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal());
VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
VERIFY_IS_UNITARY(eiSymm.eigenvectors());
SelfAdjointEigenSolver<MatrixType> eiDirect;
eiDirect.computeDirect(m);
VERIFY_IS_EQUAL(eiDirect.info(), Success);
VERIFY((m.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
VERIFY_IS_UNITARY(eiDirect.eigenvectors());
if(m.cols()<=4)
{
SelfAdjointEigenSolver<MatrixType> eiDirect;
eiDirect.computeDirect(m);
VERIFY_IS_EQUAL(eiDirect.info(), Success);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiDirect.eigenvalues());
if(! eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps) )
{
std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n"
<< "obtained eigenvalues: " << eiDirect.eigenvalues().transpose() << "\n"
<< "diff: " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).transpose() << "\n"
<< "error (eps): " << (eiSymm.eigenvalues()-eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << " (" << eival_eps << ")\n";
}
VERIFY(eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps));
VERIFY_IS_APPROX(m.template selfadjointView<Lower>() * eiDirect.eigenvectors(),
eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal());
VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
VERIFY_IS_UNITARY(eiDirect.eigenvectors());
}
}
template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)