ZjuMatrix: C plus plus vector and matrix class library for finite element method

Finite element analysis is an indispensable and valuable tool widely used in the field of science and technology. It involves a multitude of matrix operations, storage of large banded matrices, and calculation of large-scale algebraic equations and associated eigenvalue problems. To facilitate these computations, a static library ZjuMatrix is developed based on the object-oriented design techniques and leverages the power of the C++ programming language. ZjuMatrix provides a comprehensive set of vector and matrix classes, offering efficient data storage management. The library supports various matrix types, including general matrices, square matrices, symmetric matrices, and symmetric banded matrices. Essential matrix operations such as addition, subtraction and multiplication are implemented. Furthermore, ZjuMatrix also offers advanced functionalities including LU factorization of a square matrix, LDL factorization of a symmetric positive definite matrix, determinant and inverse of a square matrix. In addition, ZjuMatrix equips researchers with methods to solve the standard eigenvalue problem of symmetric matrices and generalized eigenvalue problems of symmetric banded matrices. This robust support system lays a solid foundation for the implementation of the structural finite element analysis.