eigen的簡單用法匯總

Eigen幫助文檔的地址：http://eigen.tuxfamily.org/dox/pages.html
Eigen的論壇:http://forum.kde.org/viewforum.php?f=74

1.一些基本運算

#include <iostream>
using namespace std;
#include <ctime>
//核心部分
#include <Eigen/Core>
//稠密矩陣的運算
#include <Eigen/Dense>
using namespace Eigen;

#define MATRIX_SIZE 50
int main() {
    //eigen中的所有向量和矩陣都是Eigen::Matrix,三個參數為數據類型，行，列
    //聲明一個2*3的float矩陣
    Matrix<float,2,3> matrix_23;
    
    Matrix3d m1; //旋轉矩陣3*3 雙精度，也可改為f
    AngleAxisd m2; //旋轉向量 3*1
    Vector3d m3; //歐拉角 3*1
    Quaterniond m4; //四元數 4*1
    Isometry3d m5; //歐氏變換矩陣 4*4
    Affine3d m6; //仿射變換4*4
    Projective3d m7; //射影變換4*4

    //Vector3d 本質上還是Eigen::Matrix<double,3,1>即三維向量
    Vector3d v_3d;
    Matrix<float,3,1> vd_3d; //類似

    //本質上是Eigen::Matrix<double,3,3>
    Matrix3d matrix_33 = Matrix3d::Zero();  //初始化為0

    //不確定矩陣大小，使用動態矩陣
    Matrix<double, Dynamic,Dynamic> matrix_dynamic;

    //更簡單的:
    MatrixXd matrix_x;
    
    matrix_23 << 1,2,3,4,5,6;
    
    cout << matrix_23 << endl;

    v_3d << 3,2,1;
    vd_3d << 4,5,6;

    //乘法，不同類型需要顯性的轉換
    Matrix<double,2,1> result = matrix_23.cast<double>() * v_3d;
    cout << "[1,2,3;4,5,6]*[3,2,1]=\n" << result << endl;
    
    /*******矩陣運算*********/
    matrix_33 = Matrix3d::Random();
    cout << "random matrix33:\n" << matrix_33 << endl;
    cout << "transpose:\n" << matrix_33.transpose() << endl; //轉置
    cout << "sum:" << matrix_33.sum() << endl; //各元素求和
    cout << "trace:" << matrix_33.trace() << endl; //跡
    cout << "times 10:\n" << matrix_33 * 10 << endl; //數乘
    cout << "inverse:\n" << matrix_33.inverse() << endl; //逆
    cout << "det:" << matrix_33.determinant() << endl; //行列式

    /***********************/

    //特征值
    //實對稱矩陣可以保證對角化成功
    SelfAdjointEigenSolver<Matrix3d> eigen_solver(matrix_33.transpose() * matrix_33);
    cout << "eigen values = \n" << eigen_solver.eigenvalues() << endl;
    cout << "Eigen vectors = \n" << eigen_solver.eigenvectors() << endl;


    //解方程
    //求解matrix_nn * x = v_Nd這個方程
    //直接求逆最直接，但是運算較大
    Matrix<double,MATRIX_SIZE,MATRIX_SIZE> matrix_NN 
        = MatrixXd::Random(MATRIX_SIZE,MATRIX_SIZE);
    matrix_NN = matrix_NN * matrix_NN.transpose(); //保證半正定

    Matrix<double,MATRIX_SIZE,1> v_Nd = MatrixXd::Random(MATRIX_SIZE,1);

    clock_t time_str = clock();

    //直接求逆
    Matrix<double,MATRIX_SIZE,1> x = matrix_NN.inverse() * v_Nd;
    cout << "time is:" << 1000*(clock() - time_str) / (double) CLOCKS_PER_SEC << "ms" << endl;
    cout << "x=" << x.transpose() << endl;

    //QR分解，速度快很多
    time_str = clock();
    x = matrix_NN.colPivHouseholderQr().solve(v_Nd);
    cout << "time is:" << 1000*(clock() - time_str) / (double) CLOCKS_PER_SEC << "ms" << endl;
    cout << "x=" << x.transpose() << endl;

    //對於正定矩陣，還可以用cholesky分解來解方程
     time_str = clock();
    x = matrix_NN.ldlt().solve(v_Nd);
    cout << "time is:" << 1000*(clock() - time_str) / (double) CLOCKS_PER_SEC << "ms" << endl;
    cout << "x=" << x.transpose() << endl;

    return 0;
}

CMakeLists.txt

cmake_minimum_required(VERSION 2.8.3)

project (main)

set(CMAKE_BUILD_TYPE "Release")
set(CMAKE_CXX_FLAGS "-O3")

add_definitions(-std=c++11)

include_directories(inc)

aux_source_directory(src DIR_SRCS)

SET(SOUR_FILE ${DIR_SRCS})
include_directories("/usr/include/eigen3")

add_executable(main ${SOUR_FILE})