cart-elc

Source code for CART-ELC
git clone git://git.laack.co/cart-elc.git
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schur_real.cpp (3964B)

      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   const Index size = T.cols();
     17   typedef typename MatrixType::Scalar Scalar;
     18 
     19   // Check T is lower Hessenberg
     20   for(int row = 2; row < size; ++row) {
     21     for(int col = 0; col < row - 1; ++col) {
     22       VERIFY(T(row,col) == Scalar(0));
     23     }
     24   }
     25 
     26   // Check that any non-zero on the subdiagonal is followed by a zero and is
     27   // part of a 2x2 diagonal block with imaginary eigenvalues.
     28   for(int row = 1; row < size; ++row) {
     29     if (T(row,row-1) != Scalar(0)) {
     30       VERIFY(row == size-1 || T(row+1,row) == 0);
     31       Scalar tr = T(row-1,row-1) + T(row,row);
     32       Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
     33       VERIFY(4 * det > tr * tr);
     34     }
     35   }
     36 }
     37 
     38 template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
     39 {
     40   // Test basic functionality: T is quasi-triangular and A = U T U*
     41   for(int counter = 0; counter < g_repeat; ++counter) {
     42     MatrixType A = MatrixType::Random(size, size);
     43     RealSchur<MatrixType> schurOfA(A);
     44     VERIFY_IS_EQUAL(schurOfA.info(), Success);
     45     MatrixType U = schurOfA.matrixU();
     46     MatrixType T = schurOfA.matrixT();
     47     verifyIsQuasiTriangular(T);
     48     VERIFY_IS_APPROX(A, U * T * U.transpose());
     49   }
     50 
     51   // Test asserts when not initialized
     52   RealSchur<MatrixType> rsUninitialized;
     53   VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
     54   VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
     55   VERIFY_RAISES_ASSERT(rsUninitialized.info());
     56   
     57   // Test whether compute() and constructor returns same result
     58   MatrixType A = MatrixType::Random(size, size);
     59   RealSchur<MatrixType> rs1;
     60   rs1.compute(A);
     61   RealSchur<MatrixType> rs2(A);
     62   VERIFY_IS_EQUAL(rs1.info(), Success);
     63   VERIFY_IS_EQUAL(rs2.info(), Success);
     64   VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
     65   VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
     66 
     67   // Test maximum number of iterations
     68   RealSchur<MatrixType> rs3;
     69   rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
     70   VERIFY_IS_EQUAL(rs3.info(), Success);
     71   VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
     72   VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
     73   if (size > 2) {
     74     rs3.setMaxIterations(1).compute(A);
     75     VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
     76     VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
     77   }
     78 
     79   MatrixType Atriangular = A;
     80   Atriangular.template triangularView<StrictlyLower>().setZero(); 
     81   rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
     82   VERIFY_IS_EQUAL(rs3.info(), Success);
     83   VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
     84   VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
     85 
     86   // Test computation of only T, not U
     87   RealSchur<MatrixType> rsOnlyT(A, false);
     88   VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
     89   VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
     90   VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
     91 
     92   if (size > 2 && size < 20)
     93   {
     94     // Test matrix with NaN
     95     A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
     96     RealSchur<MatrixType> rsNaN(A);
     97     VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
     98   }
     99 }
    100 
    101 EIGEN_DECLARE_TEST(schur_real)
    102 {
    103   CALL_SUBTEST_1(( schur<Matrix4f>() ));
    104   CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
    105   CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
    106   CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
    107 
    108   // Test problem size constructors
    109   CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
    110 }