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91 lines
3.6 KiB
C++
91 lines
3.6 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 schur(int size = MatrixType::ColsAtCompileTime) {
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typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
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typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
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// Test basic functionality: T is 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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ComplexSchur<MatrixType> schurOfA(A);
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VERIFY_IS_EQUAL(schurOfA.info(), Success);
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ComplexMatrixType U = schurOfA.matrixU();
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ComplexMatrixType T = schurOfA.matrixT();
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for (int row = 1; row < size; ++row) {
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for (int col = 0; col < row; ++col) {
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VERIFY(T(row, col) == (typename MatrixType::Scalar)0);
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}
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}
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VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
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}
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// Test asserts when not initialized
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ComplexSchur<MatrixType> csUninitialized;
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VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
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VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
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VERIFY_RAISES_ASSERT(csUninitialized.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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ComplexSchur<MatrixType> cs1;
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cs1.compute(A);
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ComplexSchur<MatrixType> cs2(A);
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VERIFY_IS_EQUAL(cs1.info(), Success);
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VERIFY_IS_EQUAL(cs2.info(), Success);
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VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
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VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
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// Test maximum number of iterations
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ComplexSchur<MatrixType> cs3;
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cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
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VERIFY_IS_EQUAL(cs3.info(), Success);
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VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
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VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
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cs3.setMaxIterations(1).compute(A);
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// The schur decomposition does often converge with a single iteration.
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// VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
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VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);
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MatrixType Atriangular = A;
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Atriangular.template triangularView<StrictlyLower>().setZero();
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cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
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VERIFY_IS_EQUAL(cs3.info(), Success);
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VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
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VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));
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// Test computation of only T, not U
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ComplexSchur<MatrixType> csOnlyT(A, false);
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VERIFY_IS_EQUAL(csOnlyT.info(), Success);
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VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
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VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
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if (size > 1 && size < 20) {
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// Test matrix with NaN
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A(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
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ComplexSchur<MatrixType> csNaN(A);
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VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
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}
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}
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EIGEN_DECLARE_TEST(schur_complex) {
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CALL_SUBTEST_1((schur<Matrix4cd>()));
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CALL_SUBTEST_2((schur<MatrixXcf>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
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CALL_SUBTEST_3((schur<Matrix<std::complex<float>, 1, 1> >()));
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CALL_SUBTEST_4((schur<Matrix<float, 3, 3, Eigen::RowMajor> >()));
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// Test problem size constructors
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CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
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}
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