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
14template<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
49void 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