Eigen C++: Methods, Examples, Installation

Introduction to Eigen: What It Is and Why You Need It

Eigen is a high-performance library for linear algebra in C++. It provides a wide range of capabilities for working with vectors, matrices, sparse matrices, as well as for solving systems of linear equations, computing eigenvalues and singular value decomposition. Eigen is written in pure C++ (templates) and requires no external dependencies, making it an ideal choice for embedded systems, scientific computing, computer graphics, machine learning, and robotics.

Why do you need Eigen? Unlike many other libraries (e.g., LAPACK or BLAS), Eigen offers an intuitive API that resembles working with matrices in MATLAB or NumPy. It supports lazy evaluation and vectorization (SSE, AVX, NEON), providing performance close to hand-optimized assembly. Eigen is also fully compatible with modern C++ standards (C++11 and above) and is actively maintained by the community.

Key features:

Working with dense and sparse matrices of arbitrary sizes.
Operations: addition, multiplication, transposition, inversion.
Solving linear systems (LU, QR, Cholesky, SVD).
Computing eigenvalues and eigenvectors.
Geometric transformations (rotations, quaternions).
Support for arbitrary data types (float, double, complex, user-defined types).

Installing Eigen

Eigen is a header-only library. This means you don't need to compile a separate library — just include the necessary headers in your project. Installation depends on your operating system and package manager.

Installation via Package Managers

Linux (Ubuntu/Debian):

sudo apt-get install libeigen3-dev

macOS (Homebrew):

brew install eigen

Windows (vcpkg):

vcpkg install eigen3

Windows (Conan):

conan install eigen/3.4.0@

Manual Installation (for all OS)

Download the latest version from the official website or clone the repository:

git clone https://gitlab.com/libeigen/eigen.git

Then specify the path to the Eigen folder in your compiler. For example, for g++:

g++ -I /path/to/eigen my_program.cpp -o my_program

Note: If you use CMake, add to CMakeLists.txt:

find_package(Eigen3 REQUIRED)target_link_libraries(my_target Eigen3::Eigen)

Quick Start with Code Example

Let's write a simple program that creates a matrix and a vector, performs multiplication, and outputs the result.

#include <iostream>#include <Eigen/Dense>

int main() {    // Create a 2x2 matrix    Eigen::Matrix2d A;    A << 1, 2,         3, 4;

    // Create a 2x1 vector    Eigen::Vector2d b(5, 6);

    // Multiply matrix by vector    Eigen::Vector2d x = A * b;

    // Output the result    std::cout << "A * b =" << x << std::endl;

    return 0;}

Compilation and execution:

g++ -I /path/to/eigen example.cpp -o example./example

Output:

A * b =1739

This example demonstrates how simple it is to work with Eigen: the syntax resembles mathematical operations, and the output is automatically formatted.