template<typename MatrixType> void selfadjointeigensolver_essential_check(const MatrixType& m)
{
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real 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_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());
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)
{
typedef typename MatrixType::Index Index;
/* this test covers the following files:
EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
RealScalar largerEps = 10*test_precision<RealScalar>();
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
MatrixType symmC = symmA;
svd_fill_random(symmA,Symmetric);
symmA.template triangularView<StrictlyUpper>().setZero();
symmC.template triangularView<StrictlyUpper>().setZero();
MatrixType b = MatrixType::Random(rows,cols);
MatrixType b1 = MatrixType::Random(rows,cols);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
symmB.template triangularView<StrictlyUpper>().setZero();
CALL_SUBTEST( selfadjointeigensolver_essential_check(symmA) );
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
// generalized eigen pb
GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
// generalized eigen problem Ax = lBx
eiSymmGen.compute(symmC, symmB,Ax_lBx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(symmC, symmB,BAx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(symmC, symmB,ABx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(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));
SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
eiSymmUninitialized.compute(symmA, false);
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
// test Tridiagonalization's methods
Tridiagonalization<MatrixType> tridiag(symmC);
VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal());
VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>());
Matrix<RealScalar,Dynamic,Dynamic> T = tridiag.matrixT();
if(rows>1 && cols>1) {
// FIXME check that upper and lower part are 0:
//VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero());
}
VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal());
VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>());
VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());
// Test computation of eigenvalues from tridiagonal matrix
if(rows > 1)
{
SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;
eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1), ComputeEigenvectors);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());
VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() * eiSymmTridiag.eigenvectors().real().transpose());
}
if (rows > 1)
{
// Test matrix with NaN
symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
}
}
bool HSpatialDivision2::divide(int target_count)
{
/* - variables - */
HSDVertexCluster2 vc;
int i, lastClusterCount = 1, continuousUnchangeCount = 0;
float diff;
// maximum/minimum curvature and the direction
float maxCurvature; // maximum curvature
float minCurvature; // minimum curvature
HNormal maxDir; // maximum curvature direction
HNormal minDir; // maximum curvature direction
SelfAdjointEigenSolver<Matrix3f> eigensolver;
solver = &eigensolver;
Matrix3f M;
htime.setCheckPoint();
/* - routines - */
// init the first cluster
for (i = 0; i < vertexCount; i ++)
if (vertices[i].clusterIndex != INVALID_CLUSTER_INDEX)
vc.addVertex(i, vertices[i]);
cout << "\t-----------------------------------------------" << endl
<< "\tnon-referenced vertices count:\t" << vertexCount - vc.vIndices->size() << endl
<< "\tminimum normal-vari factor:\t" << HSDVertexCluster2::MINIMUM_NORMAL_VARI << endl
<< "\tvalid vertices count:\t" << vc.vIndices->size() << endl;
flog << "\t-----------------------------------------------" << endl
<< "\tnon-referenced vertices count:\t" << vertexCount - vc.vIndices->size() << endl
<< "\tminimum normal-vari factor:\t" << HSDVertexCluster2::MINIMUM_NORMAL_VARI << endl
<< "\tvalid vertices count:\t" << vc.vIndices->size() << endl;
for (i = 0; i < faceCount; i ++) {
vc.addFace(i);
}
vc.importance = vc.getImportance();
clusters.addElement(vc);
vector<int> index; // index of eigenvalues in eigensolver.eigenvalues()
index.push_back(0);
index.push_back(1);
index.push_back(2);
// subdivide until the divided clusters reach the target count
while(clusters.count() < target_count)
{
//diff = ((float)target_count - (float)clusters.count()) / target_count;
//if (diff < 0.01) {
// break;
//}
if (clusters.count() == lastClusterCount) {
continuousUnchangeCount ++;
}
else {
continuousUnchangeCount = 0;
}
if (continuousUnchangeCount >= 50) {
cout << "\tstop without reaching the target count because of unchanged cluster count" << endl;
flog << "\tstop without reaching the target count because of unchanged cluster count" << endl;
break;
}
if (clusters.empty()) {
cerr << "#error: don't know why but the clusters heap have came to empty" << endl;
flog << "#error: don't know why but the clusters heap have came to empty" << endl;
return false;
}
// get the value of the top in the heap of clusters and delete it
lastClusterCount = clusters.count();
vc = clusters.getTop();
clusters.deleteTop();
//PrintHeap(fout, clusters);
// get the eigenvalue
M << vc.awQ.a11, vc.awQ.a12, vc.awQ.a13,
vc.awQ.a12, vc.awQ.a22, vc.awQ.a23,
vc.awQ.a13, vc.awQ.a23, vc.awQ.a33;
eigensolver.compute(M);
if (eigensolver.info() != Success) {
cerr << "#error: eigenvalues computing error" << endl;
flog << "#error: eigenvalues computing error" << endl;
return false;
}
// sort the eigenvalues in descending order by the index
std::sort(index.begin(), index.end(), cmp);
// get the maximum/minimum curvature and the direction
maxCurvature = eigensolver.eigenvalues()(index[1]); // maximum curvature
minCurvature = eigensolver.eigenvalues()(index[2]); // minimum curvature
maxDir.Set(eigensolver.eigenvectors()(0, index[1]),
eigensolver.eigenvectors()(1, index[1]),
eigensolver.eigenvectors()(2, index[1])); // maximum curvature direction
minDir.Set(eigensolver.eigenvectors()(0, index[2]),
eigensolver.eigenvectors()(1, index[2]),
eigensolver.eigenvectors()(2, index[2])); // maximum curvature direction
// partition to 8
if (vc.awN.Length() / vc.area < SPHERE_MEAN_NORMAL_THRESH)
{
HNormal p_nm = maxDir ^ minDir;
partition8(vc,
p_nm, HFaceFormula::calcD(p_nm, vc.meanVertex),
maxDir, HFaceFormula::calcD(maxDir, vc.meanVertex),
minDir, HFaceFormula::calcD(minDir, vc.meanVertex));
}
// partition to 4
else if (maxCurvature / minCurvature < MAX_MIN_CURVATURE_RATIO_TREATED_AS_HEMISPHERE)
{
partition4(vc,
maxDir, HFaceFormula::calcD(maxDir, vc.meanVertex),
minDir, HFaceFormula::calcD(minDir, vc.meanVertex));
}
// partition to 2
else {
partition2(vc, maxDir, HFaceFormula::calcD(maxDir, vc.meanVertex));
}
#ifdef PRINT_DEBUG_INFO
PrintHeap(fdebug, clusters);
#endif
}
//PrintHeap(cout, clusters);
cout << "\tsimplification time:\t" << htime.printElapseSec() << endl << endl;
flog << "\tsimplification time:\t" << htime.printElapseSec() << endl << endl;
return true;
}
template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
/* this test covers the following files:
EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
*/
Index rows = m.rows();
Index 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;
RealScalar largerEps = 10*test_precision<RealScalar>();
MatrixType a = MatrixType::Random(rows,cols);
MatrixType a1 = MatrixType::Random(rows,cols);
MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
symmA.template triangularView<StrictlyUpper>().setZero();
MatrixType b = MatrixType::Random(rows,cols);
MatrixType b1 = MatrixType::Random(rows,cols);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
symmB.template triangularView<StrictlyUpper>().setZero();
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
// generalized eigen pb
GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB);
#ifdef HAS_GSL
if (internal::is_same<RealScalar,double>::value)
{
// restore symmA and symmB.
symmA = MatrixType(symmA.template selfadjointView<Lower>());
symmB = MatrixType(symmB.template selfadjointView<Lower>());
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(), largerEps));
// compare with eigen
VERIFY_IS_APPROX(_eval, eiSymm.eigenvalues());
VERIFY_IS_APPROX(_evec.cwiseAbs(), eiSymm.eigenvectors().cwiseAbs());
// 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()), largerEps));
// compare with eigen
MatrixType normalized_eivec = eiSymmGen.eigenvectors()*eiSymmGen.eigenvectors().colwise().norm().asDiagonal().inverse();
VERIFY_IS_APPROX(_eval, eiSymmGen.eigenvalues());
VERIFY_IS_APPROX(_evec.cwiseAbs(), normalized_eivec.cwiseAbs());
Gsl::free(gSymmA);
Gsl::free(gSymmB);
GslTraits<RealScalar>::free(gEval);
Gsl::free(gEvec);
}
#endif
VERIFY_IS_EQUAL(eiSymm.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
// generalized eigen problem Ax = lBx
eiSymmGen.compute(symmA, symmB,Ax_lBx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmA.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);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
(eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
// generalized eigen problem ABx = lx
eiSymmGen.compute(symmA, symmB,ABx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
(eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
MatrixType sqrtSymmA = eiSymm.operatorSqrt();
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
MatrixType id = MatrixType::Identity(rows, cols);
VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
eiSymmUninitialized.compute(symmA, false);
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
// test Tridiagonalization's methods
Tridiagonalization<MatrixType> tridiag(symmA);
// FIXME tridiag.matrixQ().adjoint() does not work
VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
if (rows > 1)
{
// Test matrix with NaN
symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA);
VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
}
}
template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m)
{
typedef typename MatrixType::Index Index;
/* this test covers the following files:
EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
*/
Index rows = m.rows();
Index cols = m.cols();
typedef typename MatrixType::Scalar Scalar;
typedef typename NumTraits<Scalar>::Real RealScalar;
RealScalar largerEps = 10*test_precision<RealScalar>();
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);
MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
symmB.template triangularView<StrictlyUpper>().setZero();
SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
SelfAdjointEigenSolver<MatrixType> eiDirect;
eiDirect.computeDirect(symmA);
// generalized eigen pb
GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
VERIFY_IS_EQUAL(eiSymm.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
VERIFY_IS_EQUAL(eiDirect.info(), Success);
VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
// generalized eigen problem Ax = lBx
eiSymmGen.compute(symmC, symmB,Ax_lBx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(symmC, symmB,BAx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(symmC, symmB,ABx_lx);
VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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(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));
SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
eiSymmUninitialized.compute(symmA, false);
VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
// test Tridiagonalization's methods
Tridiagonalization<MatrixType> tridiag(symmC);
// FIXME tridiag.matrixQ().adjoint() does not work
VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
if (rows > 1)
{
// Test matrix with NaN
symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
}
}