Add Eigen as an optional backend for Vector and Array classes

Use Case

For the Vector.h and Array.h files we currently implement custom Vector and Array objects. Eigen is a high-level C++ library of template headers for linear algebra, matrix and vector operations, geometrical transformations, numerical solvers and related algorithms. Often Eigen or another such robust linear algebra library is used within large scientific computation or industry projects for clean, clear, and optimized data abstractions. Ultimately, leveraging Eigen can allow for many routines in svMultiPhysics to be expressed algebraically while accelerating computation with library vectorization.

Problem

Custom Vector.h and Array.h classes offer straightforward but non-optimized mathematical operations and lack of advanced linear algebra functionalities. These implementations typically require manual management of memory and computations, leading to increased code complexity and a higher risk of bugs and numerical inaccuracies. Additionally these custom classes may struggle with scalability and efficiency, making it difficult to handle large datasets or perform complex operations efficiently. This may result in code redundancies, performance inefficiencies, and limited extensibility of the current code base.

Solution

• Add flexible configuration flag USE_EIGEN to CMAKE to allow for Vector.h and Array.h to be built using Eigen::Map objects.
• Add Eigen linear algebra algorithms to mat_fun.h/mat_fun.cpp files

Alternatives considered

Eigen seems the most convenient to add as a backend; however other libraries such as Boost might be considered with this same interfacing scheme.

Additional context

No response

Code of Conduct

• I agree to follow this project's Code of Conduct and Contributing Guidelines

Start by reviewing Vector.h, Array.h, mat_fun.h, mat_fun.cpp, and the CMake configuration to understand the existing interfaces and build options. Done means a USE_EIGEN option can select Eigen::Map-based Vector and Array implementations, with Eigen linear algebra algorithms added to the matrix-function files.