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 typedef Matrix<Scalar, MatrixType::RowsAtCompileTime, 1> VectorType; 27 typedef Matrix<RealScalar, MatrixType::RowsAtCompileTime, 1> RealVectorType; 28 typedef typename std::complex<typename NumTraits<typename MatrixType::Scalar>::Real> Complex; 29 30 RealScalar largerEps = 10*test_precision<RealScalar>(); 31 32 MatrixType a = MatrixType::Random(rows,cols); 33 MatrixType a1 = MatrixType::Random(rows,cols); 34 MatrixType symmA = a.adjoint() * a + a1.adjoint() * a1; 35 symmA.template triangularView<StrictlyUpper>().setZero(); 36 37 MatrixType b = MatrixType::Random(rows,cols); 38 MatrixType b1 = MatrixType::Random(rows,cols); 39 MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1; 40 symmB.template triangularView<StrictlyUpper>().setZero(); 41 42 SelfAdjointEigenSolver<MatrixType> eiSymm(symmA); 43 SelfAdjointEigenSolver<MatrixType> eiDirect; 44 eiDirect.computeDirect(symmA); 45 // generalized eigen pb 46 GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmA, symmB); 47 48 VERIFY_IS_EQUAL(eiSymm.info(), Success); 49 VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox( 50 eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps)); 51 VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues()); 52 53 VERIFY_IS_EQUAL(eiDirect.info(), Success); 54 VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox( 55 eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps)); 56 VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues()); 57 58 SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false); 59 VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success); 60 VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues()); 61 62 // generalized eigen problem Ax = lBx 63 eiSymmGen.compute(symmA, symmB,Ax_lBx); 64 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 65 VERIFY((symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox( 66 symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 67 68 // generalized eigen problem BAx = lx 69 eiSymmGen.compute(symmA, symmB,BAx_lx); 70 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 71 VERIFY((symmB.template selfadjointView<Lower>() * (symmA.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 72 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 73 74 // generalized eigen problem ABx = lx 75 eiSymmGen.compute(symmA, symmB,ABx_lx); 76 VERIFY_IS_EQUAL(eiSymmGen.info(), Success); 77 VERIFY((symmA.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox( 78 (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps)); 79 80 81 MatrixType sqrtSymmA = eiSymm.operatorSqrt(); 82 VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA); 83 VERIFY_IS_APPROX(sqrtSymmA, symmA.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt()); 84 85 MatrixType id = MatrixType::Identity(rows, cols); 86 VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1)); 87 88 SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized; 89 VERIFY_RAISES_ASSERT(eiSymmUninitialized.info()); 90 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues()); 91 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 92 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 93 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 94 95 eiSymmUninitialized.compute(symmA, false); 96 VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors()); 97 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt()); 98 VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt()); 99 100 // test Tridiagonalization's methods 101 Tridiagonalization<MatrixType> tridiag(symmA); 102 // FIXME tridiag.matrixQ().adjoint() does not work 103 VERIFY_IS_APPROX(MatrixType(symmA.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint()); 104 105 if (rows > 1) 106 { 107 // Test matrix with NaN 108 symmA(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN(); 109 SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmA); 110 VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence); 111 } 112 } 113 114 void test_eigensolver_selfadjoint() 115 { 116 int s; 117 for(int i = 0; i < g_repeat; i++) { 118 // very important to test 3x3 and 2x2 matrices since we provide special paths for them 119 CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) ); 120 CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) ); 121 CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) ); 122 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 123 CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) ); 124 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 125 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) ); 126 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 127 CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) ); 128 129 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 130 CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) ); 131 132 // some trivial but implementation-wise tricky cases 133 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) ); 134 CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) ); 135 CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) ); 136 CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) ); 137 } 138 139 // Test problem size constructors 140 s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4); 141 CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf>(s)); 142 CALL_SUBTEST_8(Tridiagonalization<MatrixXf>(s)); 143 144 EIGEN_UNUSED_VARIABLE(s) 145 } 146 147
