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      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 (at) 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 }
     92