void bdcsvd(const MatrixType& a = MatrixType(), bool pickrandom = true) { MatrixType m = a; if(pickrandom) svd_fill_random(m); CALL_SUBTEST(( svd_test_all_computation_options<BDCSVD<MatrixType> >(m, false) )); }
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); } }