What is the usage of the Eigen library in C++?

Eigen is a C++ template library designed for linear algebra operations, offering various functionalities including matrix and vector operations such as matrix multiplication, inverse calculation, and eigenvalue decomposition. The Eigen library assists developers in performing efficient linear algebra computations with excellent performance and portability.

When using the Eigen library, the first step is to include the Eigen header file, then define matrix and vector objects in Eigen, and perform corresponding operations. For example:

#include <Eigen/Dense>

int main()
{
    Eigen::MatrixXd A(2,2);
    A << 1, 2,
         3, 4;

    Eigen::VectorXd b(2);
    b << 5, 6;

    Eigen::VectorXd x = A.colPivHouseholderQr().solve(b);

    std::cout << "Solution: " << x << std::endl;

    return 0;
}

In the code example above, a 2×2 matrix A and a vector b of length 2 are first defined. The solve function from the Eigen library is then used to solve the linear equation Ax=b, and finally, the solution x of the equation is outputted.

In addition to matrix and vector operations, the Eigen library also provides other functions such as matrix decomposition and matrix differentiation. Developers can choose the appropriate functions to use Eigen library according to their own needs. The official documentation of Eigen library contains detailed instructions and examples to help developers better understand and use the library.