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 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
test_eigensolver_selfadjoint()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