[136] | 1 | // This file is part of Eigen, a lightweight C++ template library
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| 2 | // for linear algebra.
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| 3 | //
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| 4 | // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
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| 5 | //
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| 6 | // This Source Code Form is subject to the terms of the Mozilla
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| 7 | // Public License v. 2.0. If a copy of the MPL was not distributed
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| 8 | // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
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| 9 |
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| 10 | #include "main.h"
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| 11 | #include <limits>
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| 12 | #include <Eigen/Eigenvalues>
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| 13 |
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| 14 | template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
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| 15 | {
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| 16 | typedef typename MatrixType::Index Index;
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| 17 |
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| 18 | const Index size = T.cols();
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| 19 | typedef typename MatrixType::Scalar Scalar;
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| 20 |
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| 21 | // Check T is lower Hessenberg
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| 22 | for(int row = 2; row < size; ++row) {
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| 23 | for(int col = 0; col < row - 1; ++col) {
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| 24 | VERIFY(T(row,col) == Scalar(0));
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| 25 | }
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| 26 | }
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| 27 |
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| 28 | // Check that any non-zero on the subdiagonal is followed by a zero and is
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| 29 | // part of a 2x2 diagonal block with imaginary eigenvalues.
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| 30 | for(int row = 1; row < size; ++row) {
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| 31 | if (T(row,row-1) != Scalar(0)) {
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| 32 | VERIFY(row == size-1 || T(row+1,row) == 0);
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| 33 | Scalar tr = T(row-1,row-1) + T(row,row);
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| 34 | Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
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| 35 | VERIFY(4 * det > tr * tr);
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| 36 | }
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| 37 | }
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| 38 | }
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| 39 |
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| 40 | template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
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| 41 | {
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| 42 | // Test basic functionality: T is quasi-triangular and A = U T U*
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| 43 | for(int counter = 0; counter < g_repeat; ++counter) {
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| 44 | MatrixType A = MatrixType::Random(size, size);
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| 45 | RealSchur<MatrixType> schurOfA(A);
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| 46 | VERIFY_IS_EQUAL(schurOfA.info(), Success);
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| 47 | MatrixType U = schurOfA.matrixU();
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| 48 | MatrixType T = schurOfA.matrixT();
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| 49 | verifyIsQuasiTriangular(T);
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| 50 | VERIFY_IS_APPROX(A, U * T * U.transpose());
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| 51 | }
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| 52 |
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| 53 | // Test asserts when not initialized
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| 54 | RealSchur<MatrixType> rsUninitialized;
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| 55 | VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
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| 56 | VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
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| 57 | VERIFY_RAISES_ASSERT(rsUninitialized.info());
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| 58 |
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| 59 | // Test whether compute() and constructor returns same result
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| 60 | MatrixType A = MatrixType::Random(size, size);
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| 61 | RealSchur<MatrixType> rs1;
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| 62 | rs1.compute(A);
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| 63 | RealSchur<MatrixType> rs2(A);
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| 64 | VERIFY_IS_EQUAL(rs1.info(), Success);
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| 65 | VERIFY_IS_EQUAL(rs2.info(), Success);
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| 66 | VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
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| 67 | VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
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| 68 |
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| 69 | // Test maximum number of iterations
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| 70 | RealSchur<MatrixType> rs3;
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| 71 | rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
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| 72 | VERIFY_IS_EQUAL(rs3.info(), Success);
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| 73 | VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
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| 74 | VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
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| 75 | if (size > 2) {
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| 76 | rs3.setMaxIterations(1).compute(A);
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| 77 | VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
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| 78 | VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
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| 79 | }
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| 80 |
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| 81 | MatrixType Atriangular = A;
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| 82 | Atriangular.template triangularView<StrictlyLower>().setZero();
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| 83 | rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
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| 84 | VERIFY_IS_EQUAL(rs3.info(), Success);
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| 85 | VERIFY_IS_EQUAL(rs3.matrixT(), Atriangular);
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| 86 | VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
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| 87 |
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| 88 | // Test computation of only T, not U
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| 89 | RealSchur<MatrixType> rsOnlyT(A, false);
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| 90 | VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
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| 91 | VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
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| 92 | VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
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| 93 |
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| 94 | if (size > 2)
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| 95 | {
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| 96 | // Test matrix with NaN
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| 97 | A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
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| 98 | RealSchur<MatrixType> rsNaN(A);
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| 99 | VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
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| 100 | }
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| 101 | }
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| 102 |
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| 103 | void test_schur_real()
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| 104 | {
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| 105 | CALL_SUBTEST_1(( schur<Matrix4f>() ));
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| 106 | CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
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| 107 | CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
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| 108 | CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
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| 109 |
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| 110 | // Test problem size constructors
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| 111 | CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
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| 112 | }
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