1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2008 Gael Guennebaud <gael.guennebaud (at) inria.fr> 5 // Copyright (C) 2010 Jitse Niesen <jitse (at) maths.leeds.ac.uk> 6 // 7 // This Source Code Form is subject to the terms of the Mozilla 8 // Public License v. 2.0. If a copy of the MPL was not distributed 9 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. 10 11 #include "main.h" 12 #include <limits> 13 #include <Eigen/Eigenvalues> 14 15 template<typename MatrixType> void selfadjointeigensolver(const MatrixType& m) 16 { 17 typedef typename MatrixType::Index Index; 18 /* this test covers the following files: 19 EigenSolver.h, SelfAdjointEigenSolver.h (and indirectly: Tridiagonalization.h) 20 */ 21 Index rows = m.rows(); 22 Index cols = m.cols(); 23 24 typedef typename MatrixType::Scalar Scalar; 25 typedef typename NumTraits<Scalar>::Real RealScalar; 26 27 RealScalar largerEps = 10*test_precision<RealScalar>(); 28 29 MatrixType a = MatrixType::Random(rows,cols); 30 MatrixType a1 = MatrixType::Random(rows,cols); 31 MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 32 symmA.template triangularView<StrictlyUpper>().setZero(); 33 34 MatrixType b = MatrixType::Random(rows,cols); 35 MatrixType b1 = MatrixType::Random(rows,cols); 36 MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; 37 symmB.template triangularView<StrictlyUpper>().setZero(); 38 39 SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); 40 SelfAdjointEigenSolver<MatrixType> eiDirect; 41 eiDirect.computeDirect(symmA); 42 // generalized eigen pb 43 GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB); 44 45 VERIFY_IS_EQUAL(eiSymm.info(), Success); 46 VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox( 47 eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps)); 48 VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); 49 50 VERIFY_IS_EQUAL(eiDirect.info(), Success); 51 VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox( 52 eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps)); 53 VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues()); 54 55 SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false); 56 VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); 57 VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); 58 59 // generalized eigen problem Ax = lBx 60 eiSymmGen.compute(symmA, symmB,Ax_lBx); 61 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 62 VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( 63 symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 64 65 // generalized eigen problem BAx = lx 66 eiSymmGen.compute(symmA, symmB,BAx_lx); 67 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 68 VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 69 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 70 71 // generalized eigen problem ABx = lx 72 eiSymmGen.compute(symmA, symmB,ABx_lx); 73 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 74 VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 75 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 76 77 78 MatrixType sqrtSymmA = eiSymm.operatorSqrt(); 79 VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA); 80 VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt()); 81 82 MatrixType id = MatrixType::Identity(rows, cols); 83 VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1)); 84 85 SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized; 86 VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); 87 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); 88 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 89 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 90 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 91 92 eiSymmUninitialized.compute(symmA, false); 93 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 94 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 95 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 96 97 // test Tridiagonalization's methods 98 Tridiagonalization<MatrixType> tridiag(symmA); 99 // FIXME tridiag.matrixQ().adjoint() does not work 100 VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); 101 102 if (rows > 1) 103 { 104 // Test matrix with NaN 105 symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 106 SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA); 107 VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); 108 } 109 } 110 111 void test_eigensolver_selfadjoint() 112 { 113 int s = 0; 114 for(int i = 0; i < g_repeat; i++) { 115 // very important to test 3x3 and 2x2 matrices since we provide special paths for them 116 CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) ); 117 CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) ); 118 CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); 119 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 120 CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); 121 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 122 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); 123 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 124 CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); 125 126 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 127 CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) ); 128 129 // some trivial but implementation-wise tricky cases 130 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); 131 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) ); 132 CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) ); 133 CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) ); 134 } 135 136 // Test problem size constructors 137 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 138 CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s)); 139 CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s)); 140 141 TEST_SET_BUT_UNUSED_VARIABLE(s) 142 } 143 144
