blob: e5229e6e8d24891c4186e95608b20b777dd6f2a6 [file] [log] [blame]
 // This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2010,2012 Jitse Niesen // // This Source Code Form is subject to the terms of the Mozilla // Public License v. 2.0. If a copy of the MPL was not distributed // with this file, You can obtain one at http://mozilla.org/MPL/2.0/. #include "main.h" #include #include template void verifyIsQuasiTriangular(const MatrixType& T) { const Index size = T.cols(); typedef typename MatrixType::Scalar Scalar; // Check T is lower Hessenberg for(int row = 2; row < size; ++row) { for(int col = 0; col < row - 1; ++col) { VERIFY(T(row,col) == Scalar(0)); } } // Check that any non-zero on the subdiagonal is followed by a zero and is // part of a 2x2 diagonal block with imaginary eigenvalues. for(int row = 1; row < size; ++row) { if (T(row,row-1) != Scalar(0)) { VERIFY(row == size-1 || T(row+1,row) == 0); Scalar tr = T(row-1,row-1) + T(row,row); Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1); VERIFY(4 * det > tr * tr); } } } template void schur(int size = MatrixType::ColsAtCompileTime) { // Test basic functionality: T is quasi-triangular and A = U T U* for(int counter = 0; counter < g_repeat; ++counter) { MatrixType A = MatrixType::Random(size, size); RealSchur schurOfA(A); VERIFY_IS_EQUAL(schurOfA.info(), Success); MatrixType U = schurOfA.matrixU(); MatrixType T = schurOfA.matrixT(); verifyIsQuasiTriangular(T); VERIFY_IS_APPROX(A, U * T * U.transpose()); } // Test asserts when not initialized RealSchur rsUninitialized; VERIFY_RAISES_ASSERT(rsUninitialized.matrixT()); VERIFY_RAISES_ASSERT(rsUninitialized.matrixU()); VERIFY_RAISES_ASSERT(rsUninitialized.info()); // Test whether compute() and constructor returns same result MatrixType A = MatrixType::Random(size, size); RealSchur rs1; rs1.compute(A); RealSchur rs2(A); VERIFY_IS_EQUAL(rs1.info(), Success); VERIFY_IS_EQUAL(rs2.info(), Success); VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT()); VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU()); // Test maximum number of iterations RealSchur rs3; rs3.setMaxIterations(RealSchur::m_maxIterationsPerRow * size).compute(A); VERIFY_IS_EQUAL(rs3.info(), Success); VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT()); VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU()); if (size > 2) { rs3.setMaxIterations(1).compute(A); VERIFY_IS_EQUAL(rs3.info(), NoConvergence); VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1); } MatrixType Atriangular = A; Atriangular.template triangularView().setZero(); rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations VERIFY_IS_EQUAL(rs3.info(), Success); VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling... VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size)); // Test computation of only T, not U RealSchur rsOnlyT(A, false); VERIFY_IS_EQUAL(rsOnlyT.info(), Success); VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT()); VERIFY_RAISES_ASSERT(rsOnlyT.matrixU()); if (size > 2 && size < 20) { // Test matrix with NaN A(0,0) = std::numeric_limits::quiet_NaN(); RealSchur rsNaN(A); VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence); } } void test_schur_real() { CALL_SUBTEST_1(( schur() )); CALL_SUBTEST_2(( schur(internal::random(1,EIGEN_TEST_MAX_SIZE/4)) )); CALL_SUBTEST_3(( schur >() )); CALL_SUBTEST_4(( schur >() )); // Test problem size constructors CALL_SUBTEST_5(RealSchur(10)); }