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);
}
}
