diff options
Diffstat (limited to 'eigen/test/eigensolver_selfadjoint.cpp')
| -rw-r--r-- | eigen/test/eigensolver_selfadjoint.cpp | 180 |
1 files changed, 147 insertions, 33 deletions
diff --git a/eigen/test/eigensolver_selfadjoint.cpp b/eigen/test/eigensolver_selfadjoint.cpp index 38689cf..39ad413 100644 --- a/eigen/test/eigensolver_selfadjoint.cpp +++ b/eigen/test/eigensolver_selfadjoint.cpp @@ -9,8 +9,62 @@ // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #include "main.h" +#include "svd_fill.h" #include <limits> #include <Eigen/Eigenvalues> +#include <Eigen/SparseCore> + + +template<typename MatrixType> void selfadjointeigensolver_essential_check(const MatrixType& m) +{ + typedef typename MatrixType::Scalar Scalar; + typedef typename NumTraits<Scalar>::Real RealScalar; + RealScalar eival_eps = numext::mini<RealScalar>(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision()*20000); + + SelfAdjointEigenSolver<MatrixType> eiSymm(m); + VERIFY_IS_EQUAL(eiSymm.info(), Success); + + RealScalar scaling = m.cwiseAbs().maxCoeff(); + + if(scaling<(std::numeric_limits<RealScalar>::min)()) + { + VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); + } + else + { + VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors())/scaling, + (eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal())/scaling); + } + 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); + 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"; + } + if(scaling<(std::numeric_limits<RealScalar>::min)()) + { + VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)()); + } + else + { + VERIFY_IS_APPROX(eiSymm.eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors())/scaling, + (eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal())/scaling); + VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues()/scaling, eiDirect.eigenvalues()/scaling); + } + + VERIFY_IS_UNITARY(eiDirect.eigenvectors()); + } +} template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) { @@ -31,17 +85,8 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) 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(); - } - } - + svd_fill_random(symmA,Symmetric); + symmA.template triangularView<StrictlyUpper>().setZero(); symmC.template triangularView<StrictlyUpper>().setZero(); @@ -49,23 +94,13 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) 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); - 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()); @@ -111,37 +146,111 @@ template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) // test Tridiagonalization's methods Tridiagonalization<MatrixType> tridiag(symmC); - // FIXME tridiag.matrixQ().adjoint() does not work + 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()); - if (rows > 1) + // 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 && rows < 20) { // 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); } + + // regression test for bug 1098 + { + SelfAdjointEigenSolver<MatrixType> eig(a.adjoint() * a); + eig.compute(a.adjoint() * a); + } + + // regression test for bug 478 + { + a.setZero(); + SelfAdjointEigenSolver<MatrixType> ei3(a); + VERIFY_IS_EQUAL(ei3.info(), Success); + VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(),RealScalar(1)); + VERIFY((ei3.eigenvectors().transpose()*ei3.eigenvectors().transpose()).eval().isIdentity()); + } +} + +template<int> +void bug_854() +{ + Matrix3d m; + m << 850.961, 51.966, 0, + 51.966, 254.841, 0, + 0, 0, 0; + selfadjointeigensolver_essential_check(m); +} + +template<int> +void bug_1014() +{ + Matrix3d m; + m << 0.11111111111111114658, 0, 0, + 0, 0.11111111111111109107, 0, + 0, 0, 0.11111111111111107719; + selfadjointeigensolver_essential_check(m); +} + +template<int> +void bug_1225() +{ + Matrix3d m1, m2; + m1.setRandom(); + m1 = m1*m1.transpose(); + m2 = m1.triangularView<Upper>(); + SelfAdjointEigenSolver<Matrix3d> eig1(m1); + SelfAdjointEigenSolver<Matrix3d> eig2(m2.selfadjointView<Upper>()); + VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues()); +} + +template<int> +void bug_1204() +{ + SparseMatrix<double> A(2,2); + A.setIdentity(); + SelfAdjointEigenSolver<Eigen::SparseMatrix<double> > eig(A); } void test_eigensolver_selfadjoint() { int s = 0; for(int i = 0; i < g_repeat; i++) { + // trivial test for 1x1 matrices: + CALL_SUBTEST_1( selfadjointeigensolver(Matrix<float, 1, 1>())); + CALL_SUBTEST_1( selfadjointeigensolver(Matrix<double, 1, 1>())); // 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_12( selfadjointeigensolver(Matrix2f()) ); + CALL_SUBTEST_12( selfadjointeigensolver(Matrix2d()) ); + CALL_SUBTEST_13( selfadjointeigensolver(Matrix3f()) ); + CALL_SUBTEST_13( selfadjointeigensolver(Matrix3d()) ); CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); + s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); - s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); - s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); - - s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) ); + TEST_SET_BUT_UNUSED_VARIABLE(s) // some trivial but implementation-wise tricky cases CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); @@ -149,6 +258,11 @@ void test_eigensolver_selfadjoint() CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) ); CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) ); } + + CALL_SUBTEST_13( bug_854<0>() ); + CALL_SUBTEST_13( bug_1014<0>() ); + CALL_SUBTEST_13( bug_1204<0>() ); + CALL_SUBTEST_13( bug_1225<0>() ); // Test problem size constructors s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); |