// This file is part of Eigen, a lightweight C++ template library // for linear algebra. // // Copyright (C) 2008-2009 Gael Guennebaud // Copyright (C) 2010 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 #include template bool find_pivot(typename MatrixType::Scalar tol, MatrixType& diffs, Index col = 0) { bool match = diffs.diagonal().sum() <= tol; if (match || col == diffs.cols()) { return match; } else { Index n = diffs.cols(); std::vector > transpositions; for (Index i = col; i < n; ++i) { Index best_index(0); if (diffs.col(col).segment(col, n - i).minCoeff(&best_index) > tol) break; best_index += col; diffs.row(col).swap(diffs.row(best_index)); if (find_pivot(tol, diffs, col + 1)) return true; diffs.row(col).swap(diffs.row(best_index)); // move current pivot to the end diffs.row(n - (i - col) - 1).swap(diffs.row(best_index)); transpositions.push_back(std::pair(n - (i - col) - 1, best_index)); } // restore for (Index k = transpositions.size() - 1; k >= 0; --k) diffs.row(transpositions[k].first).swap(diffs.row(transpositions[k].second)); } return false; } /* Check that two column vectors are approximately equal up to permutations. * Initially, this method checked that the k-th power sums are equal for all k = 1, ..., vec1.rows(), * however this strategy is numerically inaccurate because of numerical cancellation issues. */ template void verify_is_approx_upto_permutation(const VectorType& vec1, const VectorType& vec2) { typedef typename VectorType::Scalar Scalar; typedef typename NumTraits::Real RealScalar; VERIFY(vec1.cols() == 1); VERIFY(vec2.cols() == 1); VERIFY(vec1.rows() == vec2.rows()); Index n = vec1.rows(); RealScalar tol = test_precision() * test_precision() * numext::maxi(vec1.squaredNorm(), vec2.squaredNorm()); Matrix diffs = (vec1.rowwise().replicate(n) - vec2.rowwise().replicate(n).transpose()).cwiseAbs2(); VERIFY(find_pivot(tol, diffs)); } template void eigensolver(const MatrixType& m) { /* this test covers the following files: ComplexEigenSolver.h, and indirectly ComplexSchur.h */ Index rows = m.rows(); Index cols = m.cols(); typedef typename MatrixType::Scalar Scalar; typedef typename NumTraits::Real RealScalar; MatrixType a = MatrixType::Random(rows, cols); MatrixType symmA = a.adjoint() * a; ComplexEigenSolver ei0(symmA); VERIFY_IS_EQUAL(ei0.info(), Success); VERIFY_IS_APPROX(symmA * ei0.eigenvectors(), ei0.eigenvectors() * ei0.eigenvalues().asDiagonal()); ComplexEigenSolver ei1(a); VERIFY_IS_EQUAL(ei1.info(), Success); VERIFY_IS_APPROX(a * ei1.eigenvectors(), ei1.eigenvectors() * ei1.eigenvalues().asDiagonal()); // Note: If MatrixType is real then a.eigenvalues() uses EigenSolver and thus // another algorithm so results may differ slightly verify_is_approx_upto_permutation(a.eigenvalues(), ei1.eigenvalues()); ComplexEigenSolver ei2; ei2.setMaxIterations(ComplexSchur::m_maxIterationsPerRow * rows).compute(a); VERIFY_IS_EQUAL(ei2.info(), Success); VERIFY_IS_EQUAL(ei2.eigenvectors(), ei1.eigenvectors()); VERIFY_IS_EQUAL(ei2.eigenvalues(), ei1.eigenvalues()); if (rows > 2) { ei2.setMaxIterations(1).compute(a); VERIFY_IS_EQUAL(ei2.info(), NoConvergence); VERIFY_IS_EQUAL(ei2.getMaxIterations(), 1); } ComplexEigenSolver eiNoEivecs(a, false); VERIFY_IS_EQUAL(eiNoEivecs.info(), Success); VERIFY_IS_APPROX(ei1.eigenvalues(), eiNoEivecs.eigenvalues()); // Regression test for issue #66 MatrixType z = MatrixType::Zero(rows, cols); ComplexEigenSolver eiz(z); VERIFY((eiz.eigenvalues().cwiseEqual(0)).all()); MatrixType id = MatrixType::Identity(rows, cols); VERIFY_IS_APPROX(id.operatorNorm(), RealScalar(1)); if (rows > 1 && rows < 20) { // Test matrix with NaN a(0, 0) = std::numeric_limits::quiet_NaN(); ComplexEigenSolver eiNaN(a); VERIFY_IS_EQUAL(eiNaN.info(), NoConvergence); } // regression test for bug 1098 { ComplexEigenSolver eig(a.adjoint() * a); eig.compute(a.adjoint() * a); } // regression test for bug 478 { a.setZero(); ComplexEigenSolver ei3(a); VERIFY_IS_EQUAL(ei3.info(), Success); VERIFY_IS_MUCH_SMALLER_THAN(ei3.eigenvalues().norm(), RealScalar(1)); VERIFY((ei3.eigenvectors().transpose() * ei3.eigenvectors().transpose()).eval().isIdentity()); } } template void eigensolver_verify_assert(const MatrixType& m) { ComplexEigenSolver eig; VERIFY_RAISES_ASSERT(eig.eigenvectors()); VERIFY_RAISES_ASSERT(eig.eigenvalues()); MatrixType a = MatrixType::Random(m.rows(), m.cols()); eig.compute(a, false); VERIFY_RAISES_ASSERT(eig.eigenvectors()); } EIGEN_DECLARE_TEST(eigensolver_complex) { int s = 0; for (int i = 0; i < g_repeat; i++) { CALL_SUBTEST_1(eigensolver(Matrix4cf())); s = internal::random(1, EIGEN_TEST_MAX_SIZE / 4); CALL_SUBTEST_2(eigensolver(MatrixXcd(s, s))); CALL_SUBTEST_3(eigensolver(Matrix, 1, 1>())); CALL_SUBTEST_4(eigensolver(Matrix3f())); TEST_SET_BUT_UNUSED_VARIABLE(s) } CALL_SUBTEST_1(eigensolver_verify_assert(Matrix4cf())); s = internal::random(1, EIGEN_TEST_MAX_SIZE / 4); CALL_SUBTEST_2(eigensolver_verify_assert(MatrixXcd(s, s))); CALL_SUBTEST_3(eigensolver_verify_assert(Matrix, 1, 1>())); CALL_SUBTEST_4(eigensolver_verify_assert(Matrix3f())); // Test problem size constructors CALL_SUBTEST_5(ComplexEigenSolver tmp(s)); TEST_SET_BUT_UNUSED_VARIABLE(s) }