eigen的简单用法汇总

Eigen帮助文档的地址：http://eigen.tuxfamily.org/dox/pages.html

Eigen的论坛:http://forum.kde.org/viewforum.php?f=74

1.一些基本运算

#include <iostream>

using namespace std;

#include <ctime>

//核心部分

#include <Eigen/Core>

//稠密矩阵的运算

#include <Eigen/Dense>

using namespace Eigen;

#define MATRIX_SIZE 50

int main() {

    //eigen中的所有向量和矩阵都是Eigen::Matrix,三个参数为数据类型，行，列

    //声明一个2*3的float矩阵

    Matrix<float,2,3> matrix_23;

    Matrix3d m1; //旋转矩阵3*3 双精度，也可改为f

    AngleAxisd m2; //旋转向量 3*1

    Vector3d m3; //欧拉角 3*1

    Quaterniond m4; //四元数 4*1

    Isometry3d m5; //欧氏变换矩阵 4*4

    Affine3d m6; //仿射变换4*4

    Projective3d m7; //射影变换4*4

    //Vector3d 本质上还是Eigen::Matrix<double,3,1>即三维向量

    Vector3d v_3d;

    Matrix<float,3,1> vd_3d; //类似

    //本质上是Eigen::Matrix<double,3,3>

    Matrix3d matrix_33 = Matrix3d::Zero();  //初始化为0

    //不确定矩阵大小，使用动态矩阵

    Matrix<double, Dynamic,Dynamic> matrix_dynamic;

    //更简单的:

    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;

    //基本操作

    cout << matrix_23.row(2);  //取第二行的元素

    cout << matrix_23.col(1);  //取第一列的元素

    matrix_23.dot(matrix_23);  //点积，对应元素相乘后相加，结果为一个数

    matrix_23.cross(matrix_23); //叉乘，结果为一个矩阵

    //乘法，不同类型需要显性的转换

    Matrix<double,2,1> result = matrix_23.cast<double>() * v_3d;

    cout << "[1,2,3;4,5,6]*[3,2,1]=\n" << result << endl;

    /*******矩阵运算*********/

    matrix_33 = Matrix3d::Random();

    cout << "random matrix33:\n" << matrix_33 << endl;

    cout << "transpose:\n" << matrix_33.transpose() << endl; //转置

    cout << "sum:" << matrix_33.sum() << endl; //各元素求和

    cout << "trace:" << matrix_33.trace() << endl; //迹

    cout << "times 10:\n" << matrix_33 * 10 << endl; //数乘

    cout << "inverse:\n" << matrix_33.inverse() << endl; //逆

    cout << "det:" << matrix_33.determinant() << endl; //行列式

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

    //特征值

    //实对称矩阵可以保证对角化成功

    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这个方程

    //直接求逆最直接，但是运算较大

    Matrix<double,MATRIX_SIZE,MATRIX_SIZE> matrix_NN

        = MatrixXd::Random(MATRIX_SIZE,MATRIX_SIZE);

    matrix_NN = matrix_NN * matrix_NN.transpose(); //保证半正定

    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;

    //对于正定矩阵，还可以用cholesky分解来解方程

     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;

    //旋转

    double theta = n * 2 * M_PI / (poseNums * 4); // 1/4 圆

    R = Eigen::AngleAxisd(theta, Eigen::Vector3d::UnitZ());

    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})

巴特西

eigen的简单用法汇总

1.一些基本运算

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