schur_real.cpp File Reference

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

Functions
template<typename MatrixType >
void	verifyIsQuasiTriangular (const MatrixType &T)
template<typename MatrixType >
void	schur (int size=MatrixType::ColsAtCompileTime)
void	test_bug2633 ()
	EIGEN_DECLARE_TEST (schur_real)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

schur_real

)

                               {
  CALL_SUBTEST_1((schur<Matrix4f>()));
  CALL_SUBTEST_2((schur<MatrixXd>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
  CALL_SUBTEST_3((schur<Matrix<float, 1, 1> >()));
  CALL_SUBTEST_4((schur<Matrix<double, 3, 3, Eigen::RowMajor> >()));
 
  // Test problem size constructors
  CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
 
  CALL_SUBTEST_6((test_bug2633()));
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, EIGEN_TEST_MAX_SIZE, schur(), and test_bug2633().

schur()

template<typename MatrixType >

void schur

(

int

size = MatrixType::ColsAtCompileTime

)

                                                   {
  // Test basic functionality: T is quasi-triangular and A = U T U*
  for (int counter = 0; counter < g_repeat; ++counter) {
    MatrixType A = MatrixType::Random(size, size);
    RealSchur<MatrixType> schurOfA(A);
    VERIFY_IS_EQUAL(schurOfA.info(), Success);
    MatrixType U = schurOfA.matrixU();
    MatrixType T = schurOfA.matrixT();
    verifyIsQuasiTriangular(T);
    VERIFY_IS_APPROX(A, U * T * U.transpose());
  }
 
  // Test asserts when not initialized
  RealSchur<MatrixType> rsUninitialized;
  VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
  VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
  VERIFY_RAISES_ASSERT(rsUninitialized.info());
 
  // Test whether compute() and constructor returns same result
  MatrixType A = MatrixType::Random(size, size);
  RealSchur<MatrixType> rs1;
  rs1.compute(A);
  RealSchur<MatrixType> rs2(A);
  VERIFY_IS_EQUAL(rs1.info(), Success);
  VERIFY_IS_EQUAL(rs2.info(), Success);
  VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
  VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
 
  // Test maximum number of iterations
  RealSchur<MatrixType> rs3;
  rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
  VERIFY_IS_EQUAL(rs3.info(), Success);
  VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
  VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
  if (size > 2) {
    rs3.setMaxIterations(1).compute(A);
    VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
    VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
  }
 
  MatrixType Atriangular = A;
  Atriangular.template triangularView<StrictlyLower>().setZero();
  rs3.setMaxIterations(1).compute(Atriangular);  // triangular matrices do not need any iterations
  VERIFY_IS_EQUAL(rs3.info(), Success);
  VERIFY_IS_APPROX(rs3.matrixT(), Atriangular);  // approx because of scaling...
  VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
 
  // Test computation of only T, not U
  RealSchur<MatrixType> rsOnlyT(A, false);
  VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
  VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
  VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
 
  if (size > 2 && size < 20) {
    // Test matrix with NaN
    A(0, 0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
    RealSchur<MatrixType> rsNaN(A);
    VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
  }
}

References Eigen::RealSchur< MatrixType_ >::compute(), Eigen::g_repeat, Eigen::RealSchur< MatrixType_ >::getMaxIterations(), Eigen::RealSchur< MatrixType_ >::info(), Eigen::RealSchur< MatrixType_ >::matrixT(), Eigen::RealSchur< MatrixType_ >::matrixU(), Eigen::NoConvergence, schurOfA(), Eigen::RealSchur< MatrixType_ >::setMaxIterations(), size, Eigen::Success, RachelsAdvectionDiffusion::U, VERIFY_IS_APPROX, VERIFY_IS_EQUAL, VERIFY_RAISES_ASSERT, and verifyIsQuasiTriangular().

Referenced by EIGEN_DECLARE_TEST(), and test_bug2633().

test_bug2633()

void test_bug2633

(

)

                    {
  Eigen::MatrixXd A(4, 4);
  A << 0, 0, 0, -2, 1, 0, 0, -0, 0, 1, 0, 2, 0, 0, 2, -0;
  RealSchur<Eigen::MatrixXd> schur(A);
  VERIFY(schur.info() == Eigen::Success);
}

References schur(), Eigen::Success, and VERIFY.

Referenced by EIGEN_DECLARE_TEST().

verifyIsQuasiTriangular()

template<typename MatrixType >

void verifyIsQuasiTriangular

(

const MatrixType &

T

)

                                                  {
  const Index size = T.cols();
  typedef typename MatrixType::Scalar Scalar;
 
  // Check T is lower Hessenberg
  for (int row = 2; row < size; ++row) {
    for (int col = 0; col < row - 1; ++col) {
      VERIFY_IS_EQUAL(T(row, col), Scalar(0));
    }
  }
 
  // Check that any non-zero on the subdiagonal is followed by a zero and is
  // part of a 2x2 diagonal block with imaginary eigenvalues.
  for (int row = 1; row < size; ++row) {
    if (!numext::is_exactly_zero(T(row, row - 1))) {
      VERIFY(row == size - 1 || numext::is_exactly_zero(T(row + 1, row)));
      Scalar tr = T(row - 1, row - 1) + T(row, row);
      Scalar det = T(row - 1, row - 1) * T(row, row) - T(row - 1, row) * T(row, row - 1);
      VERIFY(4 * det > tr * tr);
    }
  }
}

References col(), Eigen::numext::is_exactly_zero(), row(), size, VERIFY, and VERIFY_IS_EQUAL.

Referenced by schur().