schur_complex.cpp File Reference

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

Functions
template<typename MatrixType >
void	schur (int size=MatrixType::ColsAtCompileTime)
	EIGEN_DECLARE_TEST (schur_complex)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

schur_complex

)

                                  {
  CALL_SUBTEST_1((schur<Matrix4cd>()));
  CALL_SUBTEST_2((schur<MatrixXcf>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE / 4))));
  CALL_SUBTEST_3((schur<Matrix<std::complex<float>, 1, 1> >()));
  CALL_SUBTEST_4((schur<Matrix<float, 3, 3, Eigen::RowMajor> >()));
 
  // Test problem size constructors
  CALL_SUBTEST_5(ComplexSchur<MatrixXf>(10));
}

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

schur()

template<typename MatrixType >

void schur

(

int

size = MatrixType::ColsAtCompileTime

)

                                                   {
  typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
  typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
 
  // Test basic functionality: T is triangular and A = U T U*
  for (int counter = 0; counter < g_repeat; ++counter) {
    MatrixType A = MatrixType::Random(size, size);
    ComplexSchur<MatrixType> schurOfA(A);
    VERIFY_IS_EQUAL(schurOfA.info(), Success);
    ComplexMatrixType U = schurOfA.matrixU();
    ComplexMatrixType T = schurOfA.matrixT();
    for (int row = 1; row < size; ++row) {
      for (int col = 0; col < row; ++col) {
        VERIFY(T(row, col) == (typename MatrixType::Scalar)0);
      }
    }
    VERIFY_IS_APPROX(A.template cast<ComplexScalar>(), U * T * U.adjoint());
  }
 
  // Test asserts when not initialized
  ComplexSchur<MatrixType> csUninitialized;
  VERIFY_RAISES_ASSERT(csUninitialized.matrixT());
  VERIFY_RAISES_ASSERT(csUninitialized.matrixU());
  VERIFY_RAISES_ASSERT(csUninitialized.info());
 
  // Test whether compute() and constructor returns same result
  MatrixType A = MatrixType::Random(size, size);
  ComplexSchur<MatrixType> cs1;
  cs1.compute(A);
  ComplexSchur<MatrixType> cs2(A);
  VERIFY_IS_EQUAL(cs1.info(), Success);
  VERIFY_IS_EQUAL(cs2.info(), Success);
  VERIFY_IS_EQUAL(cs1.matrixT(), cs2.matrixT());
  VERIFY_IS_EQUAL(cs1.matrixU(), cs2.matrixU());
 
  // Test maximum number of iterations
  ComplexSchur<MatrixType> cs3;
  cs3.setMaxIterations(ComplexSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
  VERIFY_IS_EQUAL(cs3.info(), Success);
  VERIFY_IS_EQUAL(cs3.matrixT(), cs1.matrixT());
  VERIFY_IS_EQUAL(cs3.matrixU(), cs1.matrixU());
  cs3.setMaxIterations(1).compute(A);
  // The schur decomposition does often converge with a single iteration.
  // VERIFY_IS_EQUAL(cs3.info(), size > 1 ? NoConvergence : Success);
  VERIFY_IS_EQUAL(cs3.getMaxIterations(), 1);
 
  MatrixType Atriangular = A;
  Atriangular.template triangularView<StrictlyLower>().setZero();
  cs3.setMaxIterations(1).compute(Atriangular);  // triangular matrices do not need any iterations
  VERIFY_IS_EQUAL(cs3.info(), Success);
  VERIFY_IS_EQUAL(cs3.matrixT(), Atriangular.template cast<ComplexScalar>());
  VERIFY_IS_EQUAL(cs3.matrixU(), ComplexMatrixType::Identity(size, size));
 
  // Test computation of only T, not U
  ComplexSchur<MatrixType> csOnlyT(A, false);
  VERIFY_IS_EQUAL(csOnlyT.info(), Success);
  VERIFY_IS_EQUAL(cs1.matrixT(), csOnlyT.matrixT());
  VERIFY_RAISES_ASSERT(csOnlyT.matrixU());
 
  if (size > 1 && size < 20) {
    // Test matrix with NaN
    A(0, 0) = std::numeric_limits<typename MatrixType::RealScalar>::quiet_NaN();
    ComplexSchur<MatrixType> csNaN(A);
    VERIFY_IS_EQUAL(csNaN.info(), NoConvergence);
  }
}

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

Referenced by EIGEN_DECLARE_TEST().