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1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
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 
real_qz(const MatrixType & m)14 template<typename MatrixType> void real_qz(const MatrixType& m)
15 {
16   /* this test covers the following files:
17      RealQZ.h
18   */
19   using std::abs;
20   typedef typename MatrixType::Index Index;
21   typedef typename MatrixType::Scalar Scalar;
22 
23   Index dim = m.cols();
24 
25   MatrixType A = MatrixType::Random(dim,dim),
26              B = MatrixType::Random(dim,dim);
27 
28   RealQZ<MatrixType> qz(A,B);
29 
30   VERIFY_IS_EQUAL(qz.info(), Success);
31   // check for zeros
32   bool all_zeros = true;
33   for (Index i=0; i<A.cols(); i++)
34     for (Index j=0; j<i; j++) {
35       if (abs(qz.matrixT()(i,j))!=Scalar(0.0))
36         all_zeros = false;
37       if (j<i-1 && abs(qz.matrixS()(i,j))!=Scalar(0.0))
38         all_zeros = false;
39       if (j==i-1 && j>0 && abs(qz.matrixS()(i,j))!=Scalar(0.0) && abs(qz.matrixS()(i-1,j-1))!=Scalar(0.0))
40         all_zeros = false;
41     }
42   VERIFY_IS_EQUAL(all_zeros, true);
43   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
44   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
45   VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
46   VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
47 }
48 
test_real_qz()49 void test_real_qz()
50 {
51   int s = 0;
52   for(int i = 0; i < g_repeat; i++) {
53     CALL_SUBTEST_1( real_qz(Matrix4f()) );
54     s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
55     CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );
56 
57     // some trivial but implementation-wise tricky cases
58     CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
59     CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
60     CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
61     CALL_SUBTEST_4( real_qz(Matrix2d()) );
62   }
63 
64   TEST_SET_BUT_UNUSED_VARIABLE(s)
65 }
66