Solving Quaternionic Hermitian Matrices using Eigen - c++

Question

Does Eigen allow for spectral decomposition of Quaternionic Matrices? I'm trying to generate matrices from the Gaussian Symplectic Ensemble (Quaternionic Hermitian/Self-Adjoint Matrices) to experiment with the eigenvalue spacings (Wigner Surmise) but after fiddling around for awhile, I'm not sure how to do this.
Do I need to extend the MatrixBase class with the quaternion plugin in order to gain quaternionic matrix support, then feed the matrix into SelfAdjointEigenSolver afterwards?
I currently have only tried using Matrix<Quaternion<double>, Dynamic, Dynamic> and feeding that directly into SelfAdjointEigenSolver. This resulted in clang spitting out a wall of errors, most of which just seem like missing operator complaints.
Error dump:
/usr/include/eigen3/Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h:434:11: error: invalid operands to binary expression
('Eigen::SelfAdjointEigenSolver<Eigen::Matrix<Eigen::Quaternion<double, 0>, -1, -1, 0, -1, -1> >::RealScalar'
(aka 'Eigen::Quaternion<double, 0>') and 'Eigen::SelfAdjointEigenSolver<Eigen::Matrix<Eigen::Quaternion<double, 0>, -1, -1, 0, -1,
-1> >::RealScalar')
if(scale==RealScalar(0)) scale = RealScalar(1);
...
/usr/bin/../lib64/gcc/x86_64-pc-linux-gnu/8.2.1/../../../../include/c++/8.2.1/bits/stl_algobase.h:224:15: error: invalid operands to
binary expression ('const Eigen::Quaternion<double, 0>' and 'const Eigen::Quaternion<double, 0>')
if (__a < __b)
...
/usr/include/eigen3/Eigen/src/Core/functors/BinaryFunctors.h:361:128: error: invalid operands to binary expression
('const Eigen::Quaternion<double, 0>' and 'const Eigen::Quaternion<double, 0>')
EIGEN_DEVICE_FUNC EIGEN_STRONG_INLINE const result_type operator() (const LhsScalar& a, const RhsScalar& b) const { return a / b; }
...
/usr/include/eigen3/Eigen/src/Core/TriangularMatrix.h:769:89: error: no matching conversion for functional-style cast from 'int' to
'Eigen::internal::triangular_dense_assignment_kernel<1, 0, 0,
Eigen::internal::evaluator<Eigen::TriangularView<Eigen::Matrix<Eigen::Quaternion<double, 0>, -1, -1, 0, -1, -1>, 1> >,
Eigen::internal::evaluator<Eigen::CwiseBinaryOp<Eigen::internal::scalar_quotient_op<Eigen::Quaternion<double, 0>,
Eigen::Quaternion<double, 0> >, const Eigen::Matrix<Eigen::Quaternion<double, 0>, -1, -1, 0, -1, -1>, const
Eigen::CwiseNullaryOp<Eigen::internal::scalar_constant_op<Eigen::Quaternion<double, 0> >, const
Eigen::Matrix<Eigen::Quaternion<double, 0>, -1, -1, 0, -1, -1> > > >, Eigen::internal::assign_op<Eigen::Quaternion<double, 0>,
Eigen::Quaternion<double, 0> >, 0>::Scalar' (aka 'Eigen::Quaternion<double, 0>')
if(Mode==UnitDiag && SetOpposite) m_functor.assignCoeff(m_dst.coeffRef(id,id), Scalar(1));
...
/usr/include/eigen3/Eigen/src/Eigenvalues/./Tridiagonalization.h:365:31: error: no viable overloaded '='
matA.col(i).coeffRef(i+1) = 1;
(and then a ton more)
I couldn't seem to find anything from searching. My previous linear algebra library of choice (Armadillo) does not have quaternion support from the looks of it.