1 // This file is part of Eigen, a lightweight C++ template library 2 // for linear algebra. 3 // 4 // Copyright (C) 2010 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 verifyIsQuasiTriangular(const MatrixType& T) 15 { 16 typedef typename MatrixType::Index Index; 17 18 const Index size = T.cols(); 19 typedef typename MatrixType::Scalar Scalar; 20 21 // Check T is lower Hessenberg 22 for(int row = 2; row < size; ++row) { 23 for(int col = 0; col < row - 1; ++col) { 24 VERIFY(T(row,col) == Scalar(0)); 25 } 26 } 27 28 // Check that any non-zero on the subdiagonal is followed by a zero and is 29 // part of a 2x2 diagonal block with imaginary eigenvalues. 30 for(int row = 1; row < size; ++row) { 31 if (T(row,row-1) != Scalar(0)) { 32 VERIFY(row == size-1 || T(row+1,row) == 0); 33 Scalar tr = T(row-1,row-1) + T(row,row); 34 Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1); 35 VERIFY(4 * det > tr * tr); 36 } 37 } 38 } 39 40 template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime) 41 { 42 // Test basic functionality: T is quasi-triangular and A = U T U* 43 for(int counter = 0; counter < g_repeat; ++counter) { 44 MatrixType A = MatrixType::Random(size, size); 45 RealSchur<MatrixType> schurOfA(A); 46 VERIFY_IS_EQUAL(schurOfA.info(), Success); 47 MatrixType U = schurOfA.matrixU(); 48 MatrixType T = schurOfA.matrixT(); 49 verifyIsQuasiTriangular(T); 50 VERIFY_IS_APPROX(A, U * T * U.transpose()); 51 } 52 53 // Test asserts when not initialized 54 RealSchur<MatrixType> rsUninitialized; 55 VERIFY_RAISES_ASSERT(rsUninitialized.matrixT()); 56 VERIFY_RAISES_ASSERT(rsUninitialized.matrixU()); 57 VERIFY_RAISES_ASSERT(rsUninitialized.info()); 58 59 // Test whether compute() and constructor returns same result 60 MatrixType A = MatrixType::Random(size, size); 61 RealSchur<MatrixType> rs1; 62 rs1.compute(A); 63 RealSchur<MatrixType> rs2(A); 64 VERIFY_IS_EQUAL(rs1.info(), Success); 65 VERIFY_IS_EQUAL(rs2.info(), Success); 66 VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT()); 67 VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU()); 68 69 // Test computation of only T, not U 70 RealSchur<MatrixType> rsOnlyT(A, false); 71 VERIFY_IS_EQUAL(rsOnlyT.info(), Success); 72 VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT()); 73 VERIFY_RAISES_ASSERT(rsOnlyT.matrixU()); 74 75 if (size > 2) 76 { 77 // Test matrix with NaN 78 A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN(); 79 RealSchur<MatrixType> rsNaN(A); 80 VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence); 81 } 82 } 83 84 void test_schur_real() 85 { 86 CALL_SUBTEST_1(( schur<Matrix4f>() )); 87 CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) )); 88 CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() )); 89 CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() )); 90 91 // Test problem size constructors 92 CALL_SUBTEST_5(RealSchur<MatrixXf>(10)); 93 } 94
