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
schur(int size=MatrixType::ColsAtCompileTime)14 template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
15 {
16 typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
17 typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
18
19 // Test basic functionality: T is triangular and A = U T U*
20 for(int counter = 0; counter < g_repeat; ++counter) {
21 MatrixType A = MatrixType::Random(size, size);
22 ComplexSchur<MatrixType> schurOfA(A);
23 VERIFY_IS_EQUAL(schurOfA.info(), Success);
24 ComplexMatrixType U = schurOfA.matrixU();
25 ComplexMatrixType T = schurOfA.matrixT();
26 for(int row = 1; row < size; ++row) {
27 for(int col = 0; col < row; ++col) {
28 VERIFY(T(row,col) == (typename MatrixType::Scalar)0);
29 }
30 }
31 VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
32 }
33
34 // Test asserts when not initialized
35 ComplexSchur<MatrixType> csUninitialized;
36 VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
37 VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
38 VERIFY_RAISES_ASSERT(csUninitialized.info());
39
40 // Test whether compute() and constructor returns same result
41 MatrixType A = MatrixType::Random(size, size);
42 ComplexSchur<MatrixType> cs1;
43 cs1.compute(A);
44 ComplexSchur<MatrixType> cs2(A);
45 VERIFY_IS_EQUAL(cs1.info(), Success);
46 VERIFY_IS_EQUAL(cs2.info(), Success);
47 VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
48 VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
49
50 // Test maximum number of iterations
51 ComplexSchur<MatrixType> cs3;
52 cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
53 VERIFY_IS_EQUAL(cs3.info(), Success);
54 VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
55 VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
56 cs3.setMaxIterations(1).compute(A);
57 VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
58 VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);
59
60 MatrixType Atriangular = A;
61 Atriangular.template triangularView<StrictlyLower>().setZero();
62 cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
63 VERIFY_IS_EQUAL(cs3.info(), Success);
64 VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
65 VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));
66
67 // Test computation of only T, not U
68 ComplexSchur<MatrixType> csOnlyT(A, false);
69 VERIFY_IS_EQUAL(csOnlyT.info(), Success);
70 VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
71 VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
72
73 if (size > 1)
74 {
75 // Test matrix with NaN
76 A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
77 ComplexSchur<MatrixType> csNaN(A);
78 VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
79 }
80 }
81
test_schur_complex()82 void test_schur_complex()
83 {
84 CALL_SUBTEST_1(( schur<Matrix4cd>() ));
85 CALL_SUBTEST_2(( schur<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
86 CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));
87 CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
88
89 // Test problem size constructors
90 CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
91 }
92