hessenberg.cpp File Reference

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

Functions
template<typename Scalar , int Size>
void	hessenberg (int size=Size)
	EIGEN_DECLARE_TEST (hessenberg)

Function Documentation

EIGEN_DECLARE_TEST()

EIGEN_DECLARE_TEST

(

hessenberg

)

                               {
  CALL_SUBTEST_1((hessenberg<std::complex<double>, 1>()));
  CALL_SUBTEST_2((hessenberg<std::complex<double>, 2>()));
  CALL_SUBTEST_3((hessenberg<std::complex<float>, 4>()));
  CALL_SUBTEST_4((hessenberg<float, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
  CALL_SUBTEST_5((hessenberg<std::complex<double>, Dynamic>(internal::random<int>(1, EIGEN_TEST_MAX_SIZE))));
 
  // Test problem size constructors
  CALL_SUBTEST_6(HessenbergDecomposition<MatrixXf>(10));
}

References CALL_SUBTEST_1, CALL_SUBTEST_2, CALL_SUBTEST_3, CALL_SUBTEST_4, CALL_SUBTEST_5, CALL_SUBTEST_6, Eigen::Dynamic, EIGEN_TEST_MAX_SIZE, and hessenberg().

hessenberg()

template<typename Scalar , int Size>

void hessenberg

(

int

size = Size

)

                                 {
  typedef Matrix<Scalar, Size, Size> MatrixType;
 
  // Test basic functionality: A = U H U* and H is Hessenberg
  for (int counter = 0; counter < g_repeat; ++counter) {
    MatrixType m = MatrixType::Random(size, size);
    HessenbergDecomposition<MatrixType> hess(m);
    MatrixType Q = hess.matrixQ();
    MatrixType H = hess.matrixH();
    VERIFY_IS_APPROX(m, Q * H * Q.adjoint());
    for (int row = 2; row < size; ++row) {
      for (int col = 0; col < row - 1; ++col) {
        VERIFY(H(row, col) == (typename MatrixType::Scalar)0);
      }
    }
  }
 
  // Test whether compute() and constructor returns same result
  MatrixType A = MatrixType::Random(size, size);
  HessenbergDecomposition<MatrixType> cs1;
  cs1.compute(A);
  HessenbergDecomposition<MatrixType> cs2(A);
  VERIFY_IS_EQUAL(cs1.matrixH().eval(), cs2.matrixH().eval());
  MatrixType cs1Q = cs1.matrixQ();
  MatrixType cs2Q = cs2.matrixQ();
  VERIFY_IS_EQUAL(cs1Q, cs2Q);
 
  // Test assertions for when used uninitialized
  HessenbergDecomposition<MatrixType> hessUninitialized;
  VERIFY_RAISES_ASSERT(hessUninitialized.matrixH());
  VERIFY_RAISES_ASSERT(hessUninitialized.matrixQ());
  VERIFY_RAISES_ASSERT(hessUninitialized.householderCoefficients());
  VERIFY_RAISES_ASSERT(hessUninitialized.packedMatrix());
 
  // TODO: Add tests for packedMatrix() and householderCoefficients()
}

References col(), Eigen::HessenbergDecomposition< MatrixType_ >::compute(), Eigen::g_repeat, H, Eigen::HessenbergDecomposition< MatrixType_ >::householderCoefficients(), m, Eigen::HessenbergDecomposition< MatrixType_ >::matrixH(), Eigen::HessenbergDecomposition< MatrixType_ >::matrixQ(), Eigen::HessenbergDecomposition< MatrixType_ >::packedMatrix(), Q, row(), size, VERIFY, VERIFY_IS_APPROX, VERIFY_IS_EQUAL, and VERIFY_RAISES_ASSERT.

Referenced by oomph::ComplexGMRES< MATRIX >::complex_solve_helper(), EIGEN_DECLARE_TEST(), oomph::HelmholtzGMRESMG< MATRIX >::solve_helper(), oomph::HelmholtzFGMRESMG< MATRIX >::solve_helper(), oomph::ComplexGMRES< MATRIX >::update(), oomph::HelmholtzGMRESMG< MATRIX >::update(), and oomph::HelmholtzFGMRESMG< MATRIX >::update().