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* bug fixes in: Dot, generalized eigen problem, singular matrix detetection in Cholesky

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* fix all numerical instabilies in the unit tests, now all tests can be run 2000 times
  with almost zero failures.
This commit is contained in:
Gael Guennebaud
2008-08-23 15:14:20 +00:00
parent 312013a089
commit 2120fed849
20 changed files with 632 additions and 103 deletions
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81
test/eigensolver.cpp
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@@ -25,6 +25,10 @@
#include "main.h"
#include <Eigen/QR>
#ifdef HAS_GSL
#include "gsl_helper.h"
#endif
template<typename MatrixType> void eigensolver(const MatrixType& m)
{
/* this test covers the following files:
@@ -33,19 +37,76 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
int rows = m.rows();
int cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType;
typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
MatrixType a = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a;
RealScalar largerEps = 10*test_precision<RealScalar>();
MatrixType a = test_random_matrix<MatrixType>(rows,cols);
MatrixType a1 = test_random_matrix<MatrixType>(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType b = test_random_matrix<MatrixType>(rows,cols);
MatrixType b1 = test_random_matrix<MatrixType>(rows,cols);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
VERIFY_IS_APPROX(symmA * eiSymm.eigenvectors(), (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval()));
// generalized eigen pb
SelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
#ifdef HAS_GSL
if (ei_is_same_type<RealScalar,double>::ret)
{
typedef GslTraits<Scalar> Gsl;
typename Gsl::Matrix gEvec=0, gSymmA=0, gSymmB=0;
typename GslTraits<RealScalar>::Vector gEval=0;
RealVectorType _eval;
MatrixType _evec;
convert<MatrixType>(symmA, gSymmA);
convert<MatrixType>(symmB, gSymmB);
convert<MatrixType>(symmA, gEvec);
gEval = GslTraits<RealScalar>::createVector(rows);
Gsl::eigen_symm(gSymmA, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test gsl itself !
VERIFY((symmA * _evec).isApprox(_evec * _eval.asDiagonal().eval(), largerEps));
// compare with eigen
VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues());
VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymm.eigenvectors().cwise().abs());
// generalized pb
Gsl::eigen_symm_gen(gSymmA, gSymmB, gEval, gEvec);
convert(gEval, _eval);
convert(gEvec, _evec);
// test GSL itself:
VERIFY((symmA * _evec).isApprox(symmB * (_evec * _eval.asDiagonal().eval()), largerEps));
// compare with eigen
// std::cerr << _eval.transpose() << "\n" << eiSymmGen.eigenvalues().transpose() << "\n\n";
// std::cerr << _evec.format(6) << "\n\n" << eiSymmGen.eigenvectors().format(6) << "\n\n\n";
VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
VERIFY_IS_APPROX(_evec.cwise().abs(), eiSymmGen.eigenvectors().cwise().abs());
Gsl::free(gSymmA);
Gsl::free(gSymmB);
GslTraits<RealScalar>::free(gEval);
Gsl::free(gEvec);
}
#endif
VERIFY((symmA * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval(), largerEps));
// generalized eigen problem Ax = lBx
MatrixType b = MatrixType::Random(rows,cols);
MatrixType symmB = b.adjoint() * b;
eiSymm.compute(symmA,symmB);
VERIFY_IS_APPROX(symmA * eiSymm.eigenvectors(), symmB * (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal().eval()));
VERIFY((symmA * eiSymmGen.eigenvectors()).isApprox(
symmB * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal().eval()), largerEps));
// EigenSolver<MatrixType> eiNotSymmButSymm(covMat);
// VERIFY_IS_APPROX((covMat.template cast<Complex>()) * (eiNotSymmButSymm.eigenvectors().template cast<Complex>()),
@@ -59,12 +120,12 @@ template<typename MatrixType> void eigensolver(const MatrixType& m)
void test_eigensolver()
{
for(int i = 0; i < 1; i++) {
for(int i = 0; i < g_repeat; i++) {
// very important to test a 3x3 matrix since we provide a special path for it
CALL_SUBTEST( eigensolver(Matrix3f()) );
CALL_SUBTEST( eigensolver(Matrix4d()) );
CALL_SUBTEST( eigensolver(MatrixXf(7,7)) );
CALL_SUBTEST( eigensolver(MatrixXcd(6,6)) );
CALL_SUBTEST( eigensolver(MatrixXcf(3,3)) );
CALL_SUBTEST( eigensolver(MatrixXcd(5,5)) );
CALL_SUBTEST( eigensolver(MatrixXd(19,19)) );
}
}