270 lines
11 KiB
C++
270 lines
11 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include "svd_fill.h"
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#include <limits>
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#include <Eigen/Eigenvalues>
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#include <Eigen/SparseCore>
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template <typename MatrixType>
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void selfadjointeigensolver_essential_check(const MatrixType& m) {
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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RealScalar eival_eps =
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numext::mini<RealScalar>(test_precision<RealScalar>(), NumTraits<Scalar>::dummy_precision() * 20000);
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SelfAdjointEigenSolver<MatrixType> eiSymm(m);
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VERIFY_IS_EQUAL(eiSymm.info(), Success);
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RealScalar scaling = m.cwiseAbs().maxCoeff();
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if (scaling < (std::numeric_limits<RealScalar>::min)()) {
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VERIFY(eiSymm.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
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} else {
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VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiSymm.eigenvectors()) / scaling,
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(eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal()) / scaling);
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}
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VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
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VERIFY_IS_UNITARY(eiSymm.eigenvectors());
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if (m.cols() <= 4) {
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SelfAdjointEigenSolver<MatrixType> eiDirect;
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eiDirect.computeDirect(m);
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VERIFY_IS_EQUAL(eiDirect.info(), Success);
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if (!eiSymm.eigenvalues().isApprox(eiDirect.eigenvalues(), eival_eps)) {
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std::cerr << "reference eigenvalues: " << eiSymm.eigenvalues().transpose() << "\n"
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<< "obtained eigenvalues: " << eiDirect.eigenvalues().transpose() << "\n"
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<< "diff: " << (eiSymm.eigenvalues() - eiDirect.eigenvalues()).transpose() << "\n"
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<< "error (eps): "
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<< (eiSymm.eigenvalues() - eiDirect.eigenvalues()).norm() / eiSymm.eigenvalues().norm() << " ("
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<< eival_eps << ")\n";
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}
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if (scaling < (std::numeric_limits<RealScalar>::min)()) {
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VERIFY(eiDirect.eigenvalues().cwiseAbs().maxCoeff() <= (std::numeric_limits<RealScalar>::min)());
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} else {
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VERIFY_IS_APPROX(eiSymm.eigenvalues() / scaling, eiDirect.eigenvalues() / scaling);
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VERIFY_IS_APPROX((m.template selfadjointView<Lower>() * eiDirect.eigenvectors()) / scaling,
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(eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal()) / scaling);
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VERIFY_IS_APPROX(m.template selfadjointView<Lower>().eigenvalues() / scaling, eiDirect.eigenvalues() / scaling);
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}
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VERIFY_IS_UNITARY(eiDirect.eigenvectors());
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}
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}
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template <typename MatrixType>
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void selfadjointeigensolver(const MatrixType& m) {
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/* this test covers the following files:
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EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h)
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*/
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Index rows = m.rows();
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Index cols = m.cols();
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typedef typename MatrixType::Scalar Scalar;
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typedef typename NumTraits<Scalar>::Real RealScalar;
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RealScalar largerEps = 10 * test_precision<RealScalar>();
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MatrixType a = MatrixType::Random(rows, cols);
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MatrixType a1 = MatrixType::Random(rows, cols);
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MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
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MatrixType symmC = symmA;
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svd_fill_random(symmA, Symmetric);
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symmA.template triangularView<StrictlyUpper>().setZero();
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symmC.template triangularView<StrictlyUpper>().setZero();
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MatrixType b = MatrixType::Random(rows, cols);
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MatrixType b1 = MatrixType::Random(rows, cols);
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MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
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symmB.template triangularView<StrictlyUpper>().setZero();
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CALL_SUBTEST(selfadjointeigensolver_essential_check(symmA));
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SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
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// generalized eigen pb
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GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
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SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
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VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
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VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
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// generalized eigen problem Ax = lBx
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eiSymmGen.compute(symmC, symmB, Ax_lBx);
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VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())
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.isApprox(symmB.template selfadjointView<Lower>() *
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(eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()),
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largerEps));
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// generalized eigen problem BAx = lx
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eiSymmGen.compute(symmC, symmB, BAx_lx);
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VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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VERIFY(
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(symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()))
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.isApprox((eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
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// generalized eigen problem ABx = lx
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eiSymmGen.compute(symmC, symmB, ABx_lx);
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VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
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VERIFY(
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(symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()))
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.isApprox((eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
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eiSymm.compute(symmC);
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MatrixType sqrtSymmA = eiSymm.operatorSqrt();
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VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA * sqrtSymmA);
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VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>() * eiSymm.operatorInverseSqrt());
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MatrixType id = MatrixType::Identity(rows, cols);
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VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
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SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
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eiSymmUninitialized.compute(symmA, false);
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
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VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
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// test Tridiagonalization's methods
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Tridiagonalization<MatrixType> tridiag(symmC);
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VERIFY_IS_APPROX(tridiag.diagonal(), tridiag.matrixT().diagonal());
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VERIFY_IS_APPROX(tridiag.subDiagonal(), tridiag.matrixT().template diagonal<-1>());
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Matrix<RealScalar, Dynamic, Dynamic> T = tridiag.matrixT();
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if (rows > 1 && cols > 1) {
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// FIXME check that upper and lower part are 0:
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// VERIFY(T.topRightCorner(rows-2, cols-2).template triangularView<Upper>().isZero());
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}
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VERIFY_IS_APPROX(tridiag.diagonal(), T.diagonal());
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VERIFY_IS_APPROX(tridiag.subDiagonal(), T.template diagonal<1>());
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VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()),
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tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
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VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()),
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tridiag.matrixQ() * tridiag.matrixT() * tridiag.matrixQ().adjoint());
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// Test computation of eigenvalues from tridiagonal matrix
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if (rows > 1) {
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SelfAdjointEigenSolver<MatrixType> eiSymmTridiag;
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eiSymmTridiag.computeFromTridiagonal(tridiag.matrixT().diagonal(), tridiag.matrixT().diagonal(-1),
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ComputeEigenvectors);
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VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmTridiag.eigenvalues());
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VERIFY_IS_APPROX(tridiag.matrixT(), eiSymmTridiag.eigenvectors().real() * eiSymmTridiag.eigenvalues().asDiagonal() *
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eiSymmTridiag.eigenvectors().real().transpose());
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}
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if (rows > 1 && rows < 20) {
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// Test matrix with NaN
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symmC(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
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SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
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VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
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}
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// regression test for bug 1098
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{
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SelfAdjointEigenSolver<MatrixType> eig(a.adjoint() * a);
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eig.compute(a.adjoint() * a);
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}
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// regression test for bug 478
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{
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a.setZero();
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SelfAdjointEigenSolver<MatrixType> ei3(a);
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VERIFY_IS_EQUAL(ei3.info(), Success);
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VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1));
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VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity());
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}
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}
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template <int>
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void bug_854() {
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Matrix3d m;
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m << 850.961, 51.966, 0, 51.966, 254.841, 0, 0, 0, 0;
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selfadjointeigensolver_essential_check(m);
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}
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template <int>
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void bug_1014() {
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Matrix3d m;
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m << 0.11111111111111114658, 0, 0, 0, 0.11111111111111109107, 0, 0, 0, 0.11111111111111107719;
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selfadjointeigensolver_essential_check(m);
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}
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template <int>
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void bug_1225() {
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Matrix3d m1, m2;
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m1.setRandom();
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m1 = m1 * m1.transpose();
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m2 = m1.triangularView<Upper>();
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SelfAdjointEigenSolver<Matrix3d> eig1(m1);
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SelfAdjointEigenSolver<Matrix3d> eig2(m2.selfadjointView<Upper>());
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VERIFY_IS_APPROX(eig1.eigenvalues(), eig2.eigenvalues());
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}
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template <int>
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void bug_1204() {
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SparseMatrix<double> A(2, 2);
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A.setIdentity();
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SelfAdjointEigenSolver<Eigen::SparseMatrix<double> > eig(A);
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}
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EIGEN_DECLARE_TEST(eigensolver_selfadjoint) {
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int s = 0;
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for (int i = 0; i < g_repeat; i++) {
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// trivial test for 1x1 matrices:
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CALL_SUBTEST_1(selfadjointeigensolver(Matrix<float, 1, 1>()));
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CALL_SUBTEST_1(selfadjointeigensolver(Matrix<double, 1, 1>()));
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CALL_SUBTEST_1(selfadjointeigensolver(Matrix<std::complex<double>, 1, 1>()));
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// very important to test 3x3 and 2x2 matrices since we provide special paths for them
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CALL_SUBTEST_12(selfadjointeigensolver(Matrix2f()));
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CALL_SUBTEST_12(selfadjointeigensolver(Matrix2d()));
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CALL_SUBTEST_12(selfadjointeigensolver(Matrix2cd()));
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CALL_SUBTEST_13(selfadjointeigensolver(Matrix3f()));
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CALL_SUBTEST_13(selfadjointeigensolver(Matrix3d()));
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CALL_SUBTEST_13(selfadjointeigensolver(Matrix3cd()));
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CALL_SUBTEST_2(selfadjointeigensolver(Matrix4d()));
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CALL_SUBTEST_2(selfadjointeigensolver(Matrix4cd()));
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s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
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CALL_SUBTEST_3(selfadjointeigensolver(MatrixXf(s, s)));
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CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(s, s)));
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CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(s, s)));
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CALL_SUBTEST_9(selfadjointeigensolver(Matrix<std::complex<double>, Dynamic, Dynamic, RowMajor>(s, s)));
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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// some trivial but implementation-wise tricky cases
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CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(1, 1)));
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CALL_SUBTEST_4(selfadjointeigensolver(MatrixXd(2, 2)));
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CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(1, 1)));
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CALL_SUBTEST_5(selfadjointeigensolver(MatrixXcd(2, 2)));
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CALL_SUBTEST_6(selfadjointeigensolver(Matrix<double, 1, 1>()));
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CALL_SUBTEST_7(selfadjointeigensolver(Matrix<double, 2, 2>()));
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}
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CALL_SUBTEST_13(bug_854<0>());
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CALL_SUBTEST_13(bug_1014<0>());
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CALL_SUBTEST_13(bug_1204<0>());
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CALL_SUBTEST_13(bug_1225<0>());
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// Test problem size constructors
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s = internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4);
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CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
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CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
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TEST_SET_BUT_UNUSED_VARIABLE(s)
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}
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