ground/gcs/src/libs/eigen/test/schur_complex.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 schur(int size = MatrixType::ColsAtCompileTime)
  15 {
  16   typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
  17   typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
  18
  19   // Test basic functionality: T is triangular and A = U T U*
  20   for(int counter = 0; counter < g_repeat; ++counter) {
  21     MatrixType A = MatrixType::Random(size, size);
  22     ComplexSchur<MatrixType> schurOfA(A);
  23     VERIFY_IS_EQUAL(schurOfA.info(), Success);
  24     ComplexMatrixType U = schurOfA.matrixU();
  25     ComplexMatrixType T = schurOfA.matrixT();
  26     for(int row = 1; row < size; ++row) {
  27       for(int col = 0; col < row; ++col) {
  28         VERIFY(T(row,col) == (typename MatrixType::Scalar)0);
  29       }
  30     }
  31     VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
  32   }
  33
  34   // Test asserts when not initialized
  35   ComplexSchur<MatrixType> csUninitialized;
  36   VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
  37   VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
  38   VERIFY_RAISES_ASSERT(csUninitialized.info());
  39
  40   // Test whether compute() and constructor returns same result
  41   MatrixType A = MatrixType::Random(size, size);
  42   ComplexSchur<MatrixType> cs1;
  43   cs1.compute(A);
  44   ComplexSchur<MatrixType> cs2(A);
  45   VERIFY_IS_EQUAL(cs1.info(), Success);
  46   VERIFY_IS_EQUAL(cs2.info(), Success);
  47   VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
  48   VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
  49
  50   // Test maximum number of iterations
  51   ComplexSchur<MatrixType> cs3;
  52   cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
  53   VERIFY_IS_EQUAL(cs3.info(), Success);
  54   VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
  55   VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
  56   cs3.setMaxIterations(1).compute(A);
  57   VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
  58   VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);
  59
  60   MatrixType Atriangular = A;
  61   Atriangular.template triangularView<StrictlyLower>().setZero();
  62   cs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
  63   VERIFY_IS_EQUAL(cs3.info(), Success);
  64   VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
  65   VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));
  66
  67   // Test computation of only T, not U
  68   ComplexSchur<MatrixType> csOnlyT(A, false);
  69   VERIFY_IS_EQUAL(csOnlyT.info(), Success);
  70   VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
  71   VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
  72
  73   if (size > 1)
  74   {
  75     // Test matrix with NaN
  76     A(0,0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
  77     ComplexSchur<MatrixType> csNaN(A);
  78     VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
  79   }
  80 }
  81
  82 void test_schur_complex()
  83 {
  84   CALL_SUBTEST_1(( schur<Matrix4cd>() ));
  85   CALL_SUBTEST_2(( schur<MatrixXcf>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
  86   CALL_SUBTEST_3(( schur<Matrix<std::complex<float>, 1, 1> >() ));
  87   CALL_SUBTEST_4(( schur<Matrix<float, 3, 3, Eigen::RowMajor> >() ));
  88
  89   // Test problem size constructors
  90   CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
  91 }