Eigen

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Description

Eigen is an open-source C++ library dedicated to matrix computations, linear algebra, and numerical operations.

It provides efficient data structures and algorithms for manipulating vectors, matrices, matrix decompositions, linear systems, and geometric transformations.

Eigen is a “header-only” library, which means that it does not require any additional compilation or linking step.

The goal is to provide a library that is easy to use, portable, and optimized for scientific applications, engineering, robotics, and high-performance computing.

Set up the environment

ml libs/eigen
  • Available version(s) : 3.4.1

Tutorials

Use case: Solving a linear system

  • The objective of this example is to solve a linear system of the form:Ax=bAx = b
    • where AA is the coefficient matrix, bb is the right-hand-side vector, and xx is the vector of unknowns.
  • Create the file resolution.cpp
#include <iostream>
#include <Eigen/Dense>

using namespace Eigen;

int main()
{
    // Definition of the matrix A
    Matrix3d A;
    A <<  3,  2, -1,
          2, -2,  4,
         -1, 0.5, -1;

    // Definition of the vector b
    Vector3d b;
    b << 1, -2, 0;

    // Solving the linear system A*x = b
    Vector3d x = A.colPivHouseholderQr().solve(b);

    // Display results
    std::cout << "Solving the linear system A * x = b\n\n";

    std::cout << "Matrix A =\n";
    std::cout << A << "\n\n";

    std::cout << "Vector b =\n";
    std::cout << b << "\n\n";

    std::cout << "Solution x =\n";
    std::cout << x << std::endl;

    return 0;
}
  • Compile
ml libs/eigen
g++ -O3 -std=c++17 resolution.cpp -o resolution
  • Run the program in a job
srun ./resolution

Note: The libs/eigen module must be loaded in the shell or job environment before compiling and before running the program.

Documentation