test/real_qz.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2012 Alexey Korepanov <kaikaikai@yandex.ru>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#define EIGEN_RUNTIME_NO_MALLOC
#include "main.h"
#include <limits>
#include <Eigen/Eigenvalues>

template<typename MatrixType> void real_qz(const MatrixType& m)
{
  /* this test covers the following files:
     RealQZ.h
  */
  using std::abs;
  
  Index dim = m.cols();
  
  MatrixType A = MatrixType::Random(dim,dim),
             B = MatrixType::Random(dim,dim);


  // Regression test for bug 985: Randomly set rows or columns to zero
  Index k=internal::random<Index>(0, dim-1);
  switch(internal::random<int>(0,10)) {
  case 0:
    A.row(k).setZero(); break;
  case 1:
    A.col(k).setZero(); break;
  case 2:
    B.row(k).setZero(); break;
  case 3:
    B.col(k).setZero(); break;
  default:
    break;
  }

  RealQZ<MatrixType> qz(dim);
  // TODO enable full-prealocation of required memory, this probably requires an in-place mode for HessenbergDecomposition
  //Eigen::internal::set_is_malloc_allowed(false);
  qz.compute(A,B);
  //Eigen::internal::set_is_malloc_allowed(true);
  
  VERIFY_IS_EQUAL(qz.info(), Success);
  // check for zeros
  bool all_zeros = true;
  for (Index i=0; i<A.cols(); i++)
    for (Index j=0; j<i; j++) {
      if (!numext::is_exactly_zero(abs(qz.matrixT()(i, j))))
      {
        std::cerr << "Error: T(" << i << "," << j << ") = " << qz.matrixT()(i,j) << std::endl;
        all_zeros = false;
      }
      if (j<i-1 && !numext::is_exactly_zero(abs(qz.matrixS()(i, j))))
      {
        std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j) << std::endl;
        all_zeros = false;
      }
      if (j==i-1 && j>0 && !numext::is_exactly_zero(abs(qz.matrixS()(i, j))) &&
              !numext::is_exactly_zero(abs(qz.matrixS()(i - 1, j - 1))))
      {
        std::cerr << "Error: S(" << i << "," << j << ") = " << qz.matrixS()(i,j)  << " && S(" << i-1 << "," << j-1 << ") = " << qz.matrixS()(i-1,j-1) << std::endl;
        all_zeros = false;
      }
    }
  VERIFY_IS_EQUAL(all_zeros, true);
  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixS()*qz.matrixZ(), A);
  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixT()*qz.matrixZ(), B);
  VERIFY_IS_APPROX(qz.matrixQ()*qz.matrixQ().adjoint(), MatrixType::Identity(dim,dim));
  VERIFY_IS_APPROX(qz.matrixZ()*qz.matrixZ().adjoint(), MatrixType::Identity(dim,dim));
}

EIGEN_DECLARE_TEST(real_qz)
{
  int s = 0;
  for(int i = 0; i < g_repeat; i++) {
    CALL_SUBTEST_1( real_qz(Matrix4f()) );
    s = internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4);
    CALL_SUBTEST_2( real_qz(MatrixXd(s,s)) );

    // some trivial but implementation-wise tricky cases
    CALL_SUBTEST_2( real_qz(MatrixXd(1,1)) );
    CALL_SUBTEST_2( real_qz(MatrixXd(2,2)) );
    CALL_SUBTEST_3( real_qz(Matrix<double,1,1>()) );
    CALL_SUBTEST_4( real_qz(Matrix2d()) );
  }
  
  TEST_SET_BUT_UNUSED_VARIABLE(s)
}