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 (at) 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 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 && size < 20) 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 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
