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   MatrixType symmC = symmA;
33 
34   // randomly nullify some rows/columns
35   {
36     Index count = 1;//internal::random<Index>(-cols,cols);
37     for(Index k=0; k<count; ++k)
38     {
39       Index i = internal::random<Index>(0,cols-1);
40       symmA.row(i).setZero();
41       symmA.col(i).setZero();
42     }
43   }
44 
45   symmA.template triangularView<StrictlyUpper>().setZero();
46   symmC.template triangularView<StrictlyUpper>().setZero();
47 
48   MatrixType b = MatrixType::Random(rows,cols);
49   MatrixType b1 = MatrixType::Random(rows,cols);
50   MatrixType symmB = b.adjoint() * b + b1.adjoint() * b1;
51   symmB.template triangularView<StrictlyUpper>().setZero();
52 
53   SelfAdjointEigenSolver<MatrixType> eiSymm(symmA);
54   SelfAdjointEigenSolver<MatrixType> eiDirect;
55   eiDirect.computeDirect(symmA);
56   // generalized eigen pb
57   GeneralizedSelfAdjointEigenSolver<MatrixType> eiSymmGen(symmC, symmB);
58 
59   VERIFY_IS_EQUAL(eiSymm.info(), Success);
60   VERIFY((symmA.template selfadjointView<Lower>() * eiSymm.eigenvectors()).isApprox(
61           eiSymm.eigenvectors() * eiSymm.eigenvalues().asDiagonal(), largerEps));
62   VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiSymm.eigenvalues());
63 
64   VERIFY_IS_EQUAL(eiDirect.info(), Success);
65   VERIFY((symmA.template selfadjointView<Lower>() * eiDirect.eigenvectors()).isApprox(
66           eiDirect.eigenvectors() * eiDirect.eigenvalues().asDiagonal(), largerEps));
67   VERIFY_IS_APPROX(symmA.template selfadjointView<Lower>().eigenvalues(), eiDirect.eigenvalues());
68 
69   SelfAdjointEigenSolver<MatrixType> eiSymmNoEivecs(symmA, false);
70   VERIFY_IS_EQUAL(eiSymmNoEivecs.info(), Success);
71   VERIFY_IS_APPROX(eiSymm.eigenvalues(), eiSymmNoEivecs.eigenvalues());
72 
73   // generalized eigen problem Ax = lBx
74   eiSymmGen.compute(symmC, symmB,Ax_lBx);
75   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
76   VERIFY((symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors()).isApprox(
77           symmB.template selfadjointView<Lower>() * (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
78 
79   // generalized eigen problem BAx = lx
80   eiSymmGen.compute(symmC, symmB,BAx_lx);
81   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
82   VERIFY((symmB.template selfadjointView<Lower>() * (symmC.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
83          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
84 
85   // generalized eigen problem ABx = lx
86   eiSymmGen.compute(symmC, symmB,ABx_lx);
87   VERIFY_IS_EQUAL(eiSymmGen.info(), Success);
88   VERIFY((symmC.template selfadjointView<Lower>() * (symmB.template selfadjointView<Lower>() * eiSymmGen.eigenvectors())).isApprox(
89          (eiSymmGen.eigenvectors() * eiSymmGen.eigenvalues().asDiagonal()), largerEps));
90 
91 
92   eiSymm.compute(symmC);
93   MatrixType sqrtSymmA = eiSymm.operatorSqrt();
94   VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), sqrtSymmA*sqrtSymmA);
95   VERIFY_IS_APPROX(sqrtSymmA, symmC.template selfadjointView<Lower>()*eiSymm.operatorInverseSqrt());
96 
97   MatrixType id = MatrixType::Identity(rows, cols);
98   VERIFY_IS_APPROX(id.template selfadjointView<Lower>().operatorNorm(), RealScalar(1));
99 
100   SelfAdjointEigenSolver<MatrixType> eiSymmUninitialized;
101   VERIFY_RAISES_ASSERT(eiSymmUninitialized.info());
102   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvalues());
103   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
104   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
105   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
106 
107   eiSymmUninitialized.compute(symmA, false);
108   VERIFY_RAISES_ASSERT(eiSymmUninitialized.eigenvectors());
109   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorSqrt());
110   VERIFY_RAISES_ASSERT(eiSymmUninitialized.operatorInverseSqrt());
111 
112   // test Tridiagonalization's methods
113   Tridiagonalization<MatrixType> tridiag(symmC);
114   // FIXME tridiag.matrixQ().adjoint() does not work
115   VERIFY_IS_APPROX(MatrixType(symmC.template selfadjointView<Lower>()), tridiag.matrixQ() * tridiag.matrixT().eval() * MatrixType(tridiag.matrixQ()).adjoint());
116 
117   if (rows > 1)
118   {
119     // Test matrix with NaN
120     symmC(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
121     SelfAdjointEigenSolver<MatrixType> eiSymmNaN(symmC);
122     VERIFY_IS_EQUAL(eiSymmNaN.info(), NoConvergence);
123   }
124 }
125 
test_eigensolver_selfadjoint()126 void test_eigensolver_selfadjoint()
127 {
128   int s = 0;
129   for(int i = 0; i < g_repeat; i++) {
130     // very important to test 3x3 and 2x2 matrices since we provide special paths for them
131     CALL_SUBTEST_1( selfadjointeigensolver(Matrix2f()) );
132     CALL_SUBTEST_1( selfadjointeigensolver(Matrix2d()) );
133     CALL_SUBTEST_1( selfadjointeigensolver(Matrix3f()) );
134     CALL_SUBTEST_1( selfadjointeigensolver(Matrix3d()) );
135     CALL_SUBTEST_2( selfadjointeigensolver(Matrix4d()) );
136     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
137     CALL_SUBTEST_3( selfadjointeigensolver(MatrixXf(s,s)) );
138     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
139     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(s,s)) );
140     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
141     CALL_SUBTEST_5( selfadjointeigensolver(MatrixXcd(s,s)) );
142 
143     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
144     CALL_SUBTEST_9( selfadjointeigensolver(Matrix<std::complex<double>,Dynamic,Dynamic,RowMajor>(s,s)) );
145 
146     // some trivial but implementation-wise tricky cases
147     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(1,1)) );
148     CALL_SUBTEST_4( selfadjointeigensolver(MatrixXd(2,2)) );
149     CALL_SUBTEST_6( selfadjointeigensolver(Matrix<double,1,1>()) );
150     CALL_SUBTEST_7( selfadjointeigensolver(Matrix<double,2,2>()) );
151   }
152 
153   // Test problem size constructors
154   s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
155   CALL_SUBTEST_8(SelfAdjointEigenSolver<MatrixXf> tmp1(s));
156   CALL_SUBTEST_8(Tridiagonalization<MatrixXf> tmp2(s));
157 
158   TEST_SET_BUT_UNUSED_VARIABLE(s)
159 }
160 
161