[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud@inria.fr>
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| 5 | // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
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| 6 | //
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| 7 | // This Source Code Form is subject to the terms of the Mozilla
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| 8 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 9 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 10 |
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| 11 | #include "main.h"
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| 12 | #include <limits>
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| 13 | #include <Eigen/Eigenvalues>
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| 14 |
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| 15 | template<typename MatrixType> void eigensolver(const MatrixType& m)
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| 16 | {
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| 17 | typedef typename MatrixType::Index Index;
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| 18 | /* this test covers the following files:
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| 19 | EigenSolver.h
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| 20 | */
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| 21 | Index rows = m.rows();
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| 22 | Index cols = m.cols();
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| 23 |
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| 24 | typedef typename MatrixType::Scalar Scalar;
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| 25 | typedef typename NumTraits<Scalar>::Real RealScalar;
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| 26 | typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType;
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| 27 | typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex;
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| 28 |
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| 29 | MatrixType a = MatrixType::Random(rows,cols);
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| 30 | MatrixType a1 = MatrixType::Random(rows,cols);
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| 31 | MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1;
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| 32 |
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| 33 | EigenSolver<MatrixType> ei0(symmA);
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| 34 | VERIFY_IS_EQUAL(ei0.info(), Success);
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| 35 | VERIFY_IS_APPROX(symmA * ei0.pseudoEigenvectors(), ei0.pseudoEigenvectors() * ei0.pseudoEigenvalueMatrix());
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| 36 | VERIFY_IS_APPROX((symmA.template cast<Complex>()) * (ei0.pseudoEigenvectors().template cast<Complex>()),
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| 37 | (ei0.pseudoEigenvectors().template cast<Complex>()) * (ei0.eigenvalues().asDiagonal()));
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| 38 |
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| 39 | EigenSolver<MatrixType> ei1(a);
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| 40 | VERIFY_IS_EQUAL(ei1.info(), Success);
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| 41 | VERIFY_IS_APPROX(a * ei1.pseudoEigenvectors(), ei1.pseudoEigenvectors() * ei1.pseudoEigenvalueMatrix());
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| 42 | VERIFY_IS_APPROX(a.template cast<Complex>() * ei1.eigenvectors(),
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| 43 | ei1.eigenvectors() * ei1.eigenvalues().asDiagonal());
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| 44 | VERIFY_IS_APPROX(ei1.eigenvectors().colwise().norm(), RealVectorType::Ones(rows).transpose());
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| 45 | VERIFY_IS_APPROX(a.eigenvalues(), ei1.eigenvalues());
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| 46 |
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| 47 | EigenSolver<MatrixType> ei2;
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| 48 | ei2.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * rows).compute(a);
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| 49 | VERIFY_IS_EQUAL(ei2.info(), Success);
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| 50 | VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors());
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| 51 | VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues());
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| 52 | if (rows > 2) {
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| 53 | ei2.setMaxIterations(1).compute(a);
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| 54 | VERIFY_IS_EQUAL(ei2.info(), NoConvergence);
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| 55 | VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1);
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| 56 | }
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| 57 |
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| 58 | EigenSolver<MatrixType> eiNoEivecs(a, false);
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| 59 | VERIFY_IS_EQUAL(eiNoEivecs.info(), Success);
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| 60 | VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues());
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| 61 | VERIFY_IS_APPROX(ei1.pseudoEigenvalueMatrix(), eiNoEivecs.pseudoEigenvalueMatrix());
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| 62 |
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| 63 | MatrixType id = MatrixType::Identity(rows, cols);
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| 64 | VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1));
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| 65 |
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| 66 | if (rows > 2)
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| 67 | {
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| 68 | // Test matrix with NaN
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| 69 | a(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
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| 70 | EigenSolver<MatrixType> eiNaN(a);
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| 71 | VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence);
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| 72 | }
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| 73 | }
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| 74 |
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| 75 | template<typename MatrixType> void eigensolver_verify_assert(const MatrixType& m)
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| 76 | {
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| 77 | EigenSolver<MatrixType> eig;
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| 78 | VERIFY_RAISES_ASSERT(eig.eigenvectors());
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| 79 | VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
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| 80 | VERIFY_RAISES_ASSERT(eig.pseudoEigenvalueMatrix());
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| 81 | VERIFY_RAISES_ASSERT(eig.eigenvalues());
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| 82 |
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| 83 | MatrixType a = MatrixType::Random(m.rows(),m.cols());
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| 84 | eig.compute(a, false);
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| 85 | VERIFY_RAISES_ASSERT(eig.eigenvectors());
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| 86 | VERIFY_RAISES_ASSERT(eig.pseudoEigenvectors());
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| 87 | }
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| 88 |
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| 89 | void test_eigensolver_generic()
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| 90 | {
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| 91 | int s = 0;
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| 92 | for(int i = 0; i < g_repeat; i++) {
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| 93 | CALL_SUBTEST_1( eigensolver(Matrix4f()) );
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| 94 | s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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| 95 | CALL_SUBTEST_2( eigensolver(MatrixXd(s,s)) );
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| 96 |
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| 97 | // some trivial but implementation-wise tricky cases
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| 98 | CALL_SUBTEST_2( eigensolver(MatrixXd(1,1)) );
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| 99 | CALL_SUBTEST_2( eigensolver(MatrixXd(2,2)) );
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| 100 | CALL_SUBTEST_3( eigensolver(Matrix<double,1,1>()) );
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| 101 | CALL_SUBTEST_4( eigensolver(Matrix2d()) );
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| 102 | }
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| 103 |
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| 104 | CALL_SUBTEST_1( eigensolver_verify_assert(Matrix4f()) );
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| 105 | s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
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| 106 | CALL_SUBTEST_2( eigensolver_verify_assert(MatrixXd(s,s)) );
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| 107 | CALL_SUBTEST_3( eigensolver_verify_assert(Matrix<double,1,1>()) );
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| 108 | CALL_SUBTEST_4( eigensolver_verify_assert(Matrix2d()) );
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| 109 |
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| 110 | // Test problem size constructors
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| 111 | CALL_SUBTEST_5(EigenSolver<MatrixXf> tmp(s));
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| 112 |
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| 113 | // regression test for bug 410
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| 114 | CALL_SUBTEST_2(
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| 115 | {
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| 116 | MatrixXd A(1,1);
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| 117 | A(0,0) = std::sqrt(-1.);
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| 118 | Eigen::EigenSolver<MatrixXd> solver(A);
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| 119 | MatrixXd V(1, 1);
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| 120 | V(0,0) = solver.eigenvectors()(0,0).real();
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| 121 | }
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| 122 | );
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| 123 |
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| 124 | TEST_SET_BUT_UNUSED_VARIABLE(s)
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| 125 | }
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