schur_complex.cpp revision c981c48f5bc9aefeffc0bcb0cc3934c2fae179dd 
1// This file is part of Eigen, a lightweight C++ template library
2// for linear algebra.
3//
4// Copyright (C) 2010 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
14template<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 computation of only T, not U
51  ComplexSchur<MatrixType> csOnlyT(A, false);
52  VERIFY_IS_EQUAL(csOnlyT.info(), Success);
53  VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
54  VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
55
56  if (size > 1)
57  {
58    // Test matrix with NaN
59    A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
60    ComplexSchur<MatrixType> csNaN(A);
61    VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
62  }
63}
64
65void test_schur_complex()
66{
67  CALL_SUBTEST_1(( schur<Matrix4cd>() ));
68  CALL_SUBTEST_2(( schur<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
69  CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));
70  CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
71
72  // Test problem size constructors
73  CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
74}
75