1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #include "main.h"
11 #include <limits>
12 #include <Eigen/Eigenvalues>
13
verifyIsQuasiTriangular(const MatrixType & T)14 template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
15 {
16 const Index size = T.cols();
17 typedef typename MatrixType::Scalar Scalar;
18
19 // Check T is lower Hessenberg
20 for(int row = 2; row < size; ++row) {
21 for(int col = 0; col < row - 1; ++col) {
22 VERIFY(T(row,col) == Scalar(0));
23 }
24 }
25
26 // Check that any non-zero on the subdiagonal is followed by a zero and is
27 // part of a 2x2 diagonal block with imaginary eigenvalues.
28 for(int row = 1; row < size; ++row) {
29 if (T(row,row-1) != Scalar(0)) {
30 VERIFY(row == size-1 || T(row+1,row) == 0);
31 Scalar tr = T(row-1,row-1) + T(row,row);
32 Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
33 VERIFY(4 * det > tr * tr);
34 }
35 }
36 }
37
schur(int size=MatrixType::ColsAtCompileTime)38 template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
39 {
40 // Test basic functionality: T is quasi-triangular and A = U T U*
41 for(int counter = 0; counter < g_repeat; ++counter) {
42 MatrixType A = MatrixType::Random(size, size);
43 RealSchur<MatrixType> schurOfA(A);
44 VERIFY_IS_EQUAL(schurOfA.info(), Success);
45 MatrixType U = schurOfA.matrixU();
46 MatrixType T = schurOfA.matrixT();
47 verifyIsQuasiTriangular(T);
48 VERIFY_IS_APPROX(A, U * T * U.transpose());
49 }
50
51 // Test asserts when not initialized
52 RealSchur<MatrixType> rsUninitialized;
53 VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
54 VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
55 VERIFY_RAISES_ASSERT(rsUninitialized.info());
56
57 // Test whether compute() and constructor returns same result
58 MatrixType A = MatrixType::Random(size, size);
59 RealSchur<MatrixType> rs1;
60 rs1.compute(A);
61 RealSchur<MatrixType> rs2(A);
62 VERIFY_IS_EQUAL(rs1.info(), Success);
63 VERIFY_IS_EQUAL(rs2.info(), Success);
64 VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
65 VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
66
67 // Test maximum number of iterations
68 RealSchur<MatrixType> rs3;
69 rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
70 VERIFY_IS_EQUAL(rs3.info(), Success);
71 VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
72 VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
73 if (size > 2) {
74 rs3.setMaxIterations(1).compute(A);
75 VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
76 VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
77 }
78
79 MatrixType Atriangular = A;
80 Atriangular.template triangularView<StrictlyLower>().setZero();
81 rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
82 VERIFY_IS_EQUAL(rs3.info(), Success);
83 VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
84 VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
85
86 // Test computation of only T, not U
87 RealSchur<MatrixType> rsOnlyT(A, false);
88 VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
89 VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
90 VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
91
92 if (size > 2 && size < 20)
93 {
94 // Test matrix with NaN
95 A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
96 RealSchur<MatrixType> rsNaN(A);
97 VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
98 }
99 }
100
EIGEN_DECLARE_TEST(schur_real)101 EIGEN_DECLARE_TEST(schur_real)
102 {
103 CALL_SUBTEST_1(( schur<Matrix4f>() ));
104 CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
105 CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
106 CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
107
108 // Test problem size constructors
109 CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
110 }
111