Dense Eigensolver Dependency for Model Initialization

Summary

Either an in-house or a dependency for solving the generalized eigenvalue problem for small dense matrices, for the purpose of model initialization. A Shur/QR factorization would also complement this well.

Rationale

Some models in EMT require us to compute the left and right eigenvectors and the eigenvalues of a phase-domain matrix (whose dimension is $\leq$ the number of conductors) at initialization. This is absolutely necessary for passivity enforcement.

Description

An equivalent of Eigen C++ library, allowing us to solve small dense eigenvalue problems.

Additional information

While related, this does not necessarily need to use the same tool requested in a related issue #448, which is for sparse matrices.

Example: Frequency-dependent transmission line parameter modeling can be expressed in the form $0=F(\omega, y, \dot{y})$. To obtain the modal representation $\forall \omega$, we can use a dynamic eigenvalue tracking approach so we only need to solve the eigenvalue problem at initialization.

Start by reviewing the requirements in this issue and the related sparse-matrix request in issue #448. Determine how small dense generalized eigenvalue problems, left and right eigenvectors, eigenvalues, and optional Schur/QR factorization should support EMT model initialization. Done means an in-house implementation or dependency is selected and integrated for the required passivity-enforcement workflow.