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bug #854: fix numerical issue in SelfAdjointEigenSolver::computeDirect for 3x3 matrices. The tolerance to detect stable cross products was too optimistic.

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Add respective unit tests.
This commit is contained in:
Gael Guennebaud 2014-08-21 10:49:09 +02:00
parent eeadc06e83
commit 9c0aa81fbf
2 changed files with 44 additions and 17 deletions
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18
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
View File

@ -605,7 +605,6 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
if(computeEigenvectors)
{
Scalar safeNorm2 = Eigen::NumTraits<Scalar>::epsilon();
safeNorm2 *= safeNorm2;
if((eivals(2)-eivals(0))<=Eigen::NumTraits<Scalar>::epsilon())
{
eivecs.setIdentity();
@ -619,7 +618,7 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
Scalar d0 = eivals(2) - eivals(1);
Scalar d1 = eivals(1) - eivals(0);
int k = d0 > d1 ? 2 : 0;
d0 = d0 > d1 ? d1 : d0;
d0 = d0 > d1 ? d0 : d1;
tmp.diagonal().array () -= eivals(k);
VectorType cross;
@ -627,19 +626,25 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
n = (cross = tmp.row(0).cross(tmp.row(1))).squaredNorm();
if(n>safeNorm2)
{
eivecs.col(k) = cross / sqrt(n);
}
else
{
n = (cross = tmp.row(0).cross(tmp.row(2))).squaredNorm();
if(n>safeNorm2)
{
eivecs.col(k) = cross / sqrt(n);
}
else
{
n = (cross = tmp.row(1).cross(tmp.row(2))).squaredNorm();
if(n>safeNorm2)
{
eivecs.col(k) = cross / sqrt(n);
}
else
{
// the input matrix and/or the eigenvaues probably contains some inf/NaN,
@ -659,12 +664,16 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
tmp.diagonal().array() -= eivals(1);
if(d0<=Eigen::NumTraits<Scalar>::epsilon())
{
eivecs.col(1) = eivecs.col(k).unitOrthogonal();
}
else
{
n = (cross = eivecs.col(k).cross(tmp.row(0).normalized())).squaredNorm();
n = (cross = eivecs.col(k).cross(tmp.row(0))).squaredNorm();
if(n>safeNorm2)
{
eivecs.col(1) = cross / sqrt(n);
}
else
{
n = (cross = eivecs.col(k).cross(tmp.row(1))).squaredNorm();
@ -678,13 +687,14 @@ template<typename SolverType> struct direct_selfadjoint_eigenvalues<SolverType,3
else
{
// we should never reach this point,
// if so the last two eigenvalues are likely to ve very closed to each other
// if so the last two eigenvalues are likely to be very close to each other
eivecs.col(1) = eivecs.col(k).unitOrthogonal();
}
}
}
// make sure that eivecs[1] is orthogonal to eivecs[2]
// FIXME: this step should not be needed
Scalar d = eivecs.col(1).dot(eivecs.col(k));
eivecs.col(1) = (eivecs.col(1) - d * eivecs.col(k)).normalized();
}

43
test/eigensolver_selfadjoint.cpp
View File

@ -29,7 +29,21 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType symmC = symmA;
// randomly nullify some rows/columns
{
Index count = 1;//internal::random<Index>(-cols,cols);
for(Index k=0; k<count; ++k)
{
Index i = internal::random<Index>(0,cols-1);
symmA.row(i).setZero();
symmA.col(i).setZero();
}
}
symmA.template triangularView<StrictlyUpper>().setZero();
symmC.template triangularView<StrictlyUpper>().setZero();
MatrixType b = MatrixType::Random(rows,cols);
MatrixType b1 = MatrixType::Random(rows,cols);
@ -40,7 +54,7 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
SelfAdjointEigenSolver<MatrixType> eiDirect;
eiDirect.computeDirect(symmA);
// generalized eigen pb
GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
VERIFY_IS_EQUAL(eiSymm.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
@ -57,27 +71,28 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
// generalized eigen problem Ax = lBx
eiSymmGen.compute(symmA, symmB,Ax_lBx);
eiSymmGen.compute(symmC, symmB,Ax_lBx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
// generalized eigen problem BAx = lx
eiSymmGen.compute(symmA, symmB,BAx_lx);
eiSymmGen.compute(symmC, symmB,BAx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
(eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
// generalized eigen problem ABx = lx
eiSymmGen.compute(symmA, symmB,ABx_lx);
eiSymmGen.compute(symmC, symmB,ABx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
(eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
eiSymm.compute(symmC);
MatrixType sqrtSymmA = eiSymm.operatorSqrt();
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
@ -95,9 +110,9 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
// test Tridiagonalization's methods
Tridiagonalization<MatrixType> tridiag(symmA);
Tridiagonalization<MatrixType> tridiag(symmC);
// FIXME tridiag.matrixQ().adjoint() does not work
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
// Test computation of eigenvalues from tridiagonal matrix
if(rows > 1)
@ -111,8 +126,8 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
if (rows > 1)
{
// Test matrix with NaN
symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA);
symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
}
}
@ -122,8 +137,10 @@ void test_eigensolver_selfadjoint()
int s = 0;
for(int i = 0; i < g_repeat; i++) {
// very important to test 3x3 and 2x2 matrices since we provide special paths for them
CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );