109 lines
3.9 KiB
C++
109 lines
3.9 KiB
C++
// This file is part of Eigen, a lightweight C++ template library
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// for linear algebra.
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//
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// Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
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//
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// This Source Code Form is subject to the terms of the Mozilla
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// Public License v. 2.0. If a copy of the MPL was not distributed
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// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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#include "main.h"
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#include <limits>
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#include <Eigen/Eigenvalues>
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template <typename MatrixType>
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void verifyIsQuasiTriangular(const MatrixType& T) {
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const Index size = T.cols();
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typedef typename MatrixType::Scalar Scalar;
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// Check T is lower Hessenberg
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for (int row = 2; row < size; ++row) {
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for (int col = 0; col < row - 1; ++col) {
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VERIFY_IS_EQUAL(T(row, col), Scalar(0));
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}
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}
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// Check that any non-zero on the subdiagonal is followed by a zero and is
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// part of a 2x2 diagonal block with imaginary eigenvalues.
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for (int row = 1; row < size; ++row) {
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if (!numext::is_exactly_zero(T(row, row - 1))) {
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VERIFY(row == size - 1 || numext::is_exactly_zero(T(row + 1, row)));
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Scalar tr = T(row - 1, row - 1) + T(row, row);
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Scalar det = T(row - 1, row - 1) * T(row, row) - T(row - 1, row) * T(row, row - 1);
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VERIFY(4 * det > tr * tr);
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}
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}
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}
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template <typename MatrixType>
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void schur(int size = MatrixType::ColsAtCompileTime) {
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// Test basic functionality: T is quasi-triangular and A = U T U*
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for (int counter = 0; counter < g_repeat; ++counter) {
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MatrixType A = MatrixType::Random(size, size);
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RealSchur<MatrixType> schurOfA(A);
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VERIFY_IS_EQUAL(schurOfA.info(), Success);
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MatrixType U = schurOfA.matrixU();
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MatrixType T = schurOfA.matrixT();
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verifyIsQuasiTriangular(T);
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VERIFY_IS_APPROX(A, U * T * U.transpose());
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}
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// Test asserts when not initialized
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RealSchur<MatrixType> rsUninitialized;
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VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
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VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
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VERIFY_RAISES_ASSERT(rsUninitialized.info());
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// Test whether compute() and constructor returns same result
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MatrixType A = MatrixType::Random(size, size);
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RealSchur<MatrixType> rs1;
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rs1.compute(A);
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RealSchur<MatrixType> rs2(A);
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VERIFY_IS_EQUAL(rs1.info(), Success);
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VERIFY_IS_EQUAL(rs2.info(), Success);
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VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
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VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
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// Test maximum number of iterations
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RealSchur<MatrixType> rs3;
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rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
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VERIFY_IS_EQUAL(rs3.info(), Success);
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VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
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VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
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if (size > 2) {
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rs3.setMaxIterations(1).compute(A);
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VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
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VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
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}
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MatrixType Atriangular = A;
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Atriangular.template triangularView<StrictlyLower>().setZero();
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rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
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VERIFY_IS_EQUAL(rs3.info(), Success);
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VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
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VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
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// Test computation of only T, not U
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RealSchur<MatrixType> rsOnlyT(A, false);
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VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
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VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
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VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
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if (size > 2 && size < 20) {
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// Test matrix with NaN
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A(0, 0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
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RealSchur<MatrixType> rsNaN(A);
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VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
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}
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}
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EIGEN_DECLARE_TEST(schur_real) {
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CALL_SUBTEST_1((schur<Matrix4f>()));
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CALL_SUBTEST_2((schur<MatrixXd>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
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CALL_SUBTEST_3((schur<Matrix<float, 1, 1> >()));
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CALL_SUBTEST_4((schur<Matrix<double, 3, 3, Eigen::RowMajor> >()));
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// Test problem size constructors
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CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
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}
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