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+// 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));
+}