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@inria.fr>
5 // Copyright (C) 2010 Jitse Niesen <jitse@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
selfadjointeigensolver(const MatrixType & m)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
test_eigensolver_selfadjoint()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