ground/gcs/src/libs/eigen/test/schur_real.cpp

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