test/hessenberg.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2009 Gael Guennebaud <gael.guennebaud@inria.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// 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/.

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

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()
}

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));
}