eigen 初探

转自：http://blog.csdn.net/abcjennifer/article/details/7781936

最近和一些朋友讨论到了C++中数学工具的问题，以前总是很2地自己写矩阵运算，或者有时候在matlab里计算了一些数据再往C程序里倒，唉~想想那些年，我们白写的代码啊……人家早已封装好了！首先推荐几个可以在C++中调用的数学平台：eigen、bias、lapack、svd、CMatrix，本文着重eigen做以讲解，希望对各位有所帮助。

下面是本文主线，主要围绕下面几点进行讲解：

**********************************************************************************************

Eigen是什么？

Eigen3哪里下载？

Eigen3的配置

Eigen3 样例代码有没有？

去哪里更深入学习？

**********************************************************************************************

Eigen是什么？

Eigen是C++中可以用来调用并进行矩阵计算的一个库，里面封装了一些类，需要的头文件和功能如下：

Eigen的主页上有一些更详细的Eigen介绍。

Eigen3哪里下载？

这里是我下好的，这里是官网主页，请自行下载，是个code包，不用安装。

Eigen的配置

直接上图了，附加包含目录那里填上你放Eigen文件夹的位置即可。

Eigen的样例代码有没有？

当然有，这篇文章重点就是这里！

以下是我整理的一些常用操作，基本的矩阵运算就在下面了，算是个入门吧~主要分以下几部分：

建议大家放到编译环境里去看，因为我这里有一些region的东西，编译器下更方便看~

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

//using Eigen::MatrixXd;
using namespace Eigen;
using namespace Eigen::internal;
using namespace Eigen::Architecture;

using namespace std;


int main()
{

#pragma region one_d_object

    cout<<"*******************1D-object****************"<<endl;

    Vector4d v1;
    v1<< 1,2,3,4;
    cout<<"v1=\n"<<v1<<endl;

    VectorXd v2(3);
    v2<<1,2,3;
    cout<<"v2=\n"<<v2<<endl;

    Array4i v3;
    v3<<1,2,3,4;
    cout<<"v3=\n"<<v3<<endl;

    ArrayXf v4(3);
    v4<<1,2,3;
    cout<<"v4=\n"<<v4<<endl;

#pragma endregion

#pragma region two_d_object

    cout<<"*******************2D-object****************"<<endl;
    //2D objects:
    MatrixXd m(2,2);

    //method 1
    m(0,0) = 3;
    m(1,0) = 2.5;
    m(0,1) = -1;
    m(1,1) = m(1,0) + m(0,1);

    //method 2
    m<<3,-1,
        2.5,-1.5;
    cout <<"m=\n"<< m << endl;

#pragma endregion

#pragma region Comma_initializer

    cout<<"*******************Initialization****************"<<endl;

    int rows=5;
    int cols=5;
    MatrixXf m1(rows,cols);
    m1<<( Matrix3f()<<1,2,3,4,5,6,7,8,9 ).finished(),
        MatrixXf::Zero(3,cols-3),
        MatrixXf::Zero(rows-3,3),
        MatrixXf::Identity(rows-3,cols-3);
    cout<<"m1=\n"<<m1<<endl;

#pragma endregion

#pragma region Runtime_info

    cout<<"*******************Runtime Info****************"<<endl;

    MatrixXf m2(5,4);
    m2<<MatrixXf::Identity(5,4);
    cout<<"m2=\n"<<m2<<endl;

    MatrixXf m3;
    m3=m1*m2;
    cout<<"m3.rows()="<<m3.rows()<<"  ;  "
             <<"m3.cols()="<< m3.cols()<<endl;

    cout<<"m3=\n"<<m3<<endl;

#pragma endregion

#pragma region Resizing

    cout<<"*******************Resizing****************"<<endl;

    //1D-resize
    v1.resize(4);
    cout<<"Recover v1 to 4*1 array : v1=\n"<<v1<<endl;

    //2D-resize
    m.resize(2,3);
    m.resize(Eigen::NoChange, 3);
    m.resizeLike(m2);
    m.resize(2,2);

#pragma endregion

#pragma region Coeff_access

    cout<<"*******************Coefficient access****************"<<endl;

    float tx=v1(1);
    tx=m1(1,1);
    cout<<endl;

#pragma endregion

#pragma  region Predefined_matrix

    cout<<"*******************Predefined Matrix****************"<<endl;

    //1D-object
    typedef  Matrix3f   FixedXD;
    FixedXD x;

    x=FixedXD::Zero();
    x=FixedXD::Ones();
    x=FixedXD::Constant(tx);//tx is the value
    x=FixedXD::Random();
    cout<<"x=\n"<<x<<endl;

    typedef ArrayXf Dynamic1D;
    //或者 typedef VectorXf Dynamic1D
    int size=3;
    Dynamic1D xx;
    xx=Dynamic1D::Zero(size);
    xx=Dynamic1D::Ones(size);
    xx=Dynamic1D::Constant(size,tx);
    xx=Dynamic1D::Random(size);
    cout<<"xx=\n"<<x<<endl;

    //2D-object
    typedef MatrixXf Dynamic2D;
    Dynamic2D y;
    y=Dynamic2D::Zero(rows,cols);
    y=Dynamic2D::Ones(rows,cols);
    y=Dynamic2D::Constant(rows,cols,tx);//tx is the value
    y=Dynamic2D::Random(rows,cols);

#pragma endregion

#pragma region Arithmetic_Operators

    cout<<"******************* Arithmetic_Operators****************"<<endl;

    //add & sub
    MatrixXf m4(5,4);
    MatrixXf m5;
    m4=m2+m3;
    m3-=m2;

    //product
    m3=m1*m2;

    //transposition
    m5=m4.transpose();
    //m5=m.adjoint();//伴随矩阵

    //dot product
    double xtt;
    cout<<"v1=\n"<<v1<<endl;
    v2.resize(4);
    v2<<VectorXd::Ones(4);
    cout<<"v2=\n"<<v2<<endl;

    cout<<"*************dot product*************"<<endl;
    xtt=v1.dot(v2);
    cout<<"v1.*v2="<<xtt<<endl;

    //vector norm

    cout<<"*************matrix norm*************"<<endl;
    xtt=v1.norm();
    cout<<"norm of v1="<<xtt<<endl;
    xtt=v1.squaredNorm();
    cout<<"SquareNorm of v1="<<xtt<<endl;

#pragma endregion

cout<<endl;
}

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

//using Eigen::MatrixXd;
using namespace Eigen;
using namespace Eigen::internal;
using namespace Eigen::Architecture;

using namespace std;


int main()
{

#pragma region one_d_object

	cout<<"*******************1D-object****************"<<endl;

	Vector4d v1;
	v1<< 1,2,3,4;
	cout<<"v1=\n"<<v1<<endl;

	VectorXd v2(3);
	v2<<1,2,3;
	cout<<"v2=\n"<<v2<<endl;

	Array4i v3;
	v3<<1,2,3,4;
	cout<<"v3=\n"<<v3<<endl;

	ArrayXf v4(3);
	v4<<1,2,3;
	cout<<"v4=\n"<<v4<<endl;

#pragma endregion

#pragma region two_d_object
	
	cout<<"*******************2D-object****************"<<endl;
	//2D objects:
	MatrixXd m(2,2);

	//method 1
	m(0,0) = 3;
	m(1,0) = 2.5;
	m(0,1) = -1;
	m(1,1) = m(1,0) + m(0,1);

	//method 2
	m<<3,-1,
		2.5,-1.5;
	cout <<"m=\n"<< m << endl;

#pragma endregion

#pragma region Comma_initializer

	cout<<"*******************Initialization****************"<<endl;

	int rows=5;
	int cols=5;
	MatrixXf m1(rows,cols);
	m1<<( Matrix3f()<<1,2,3,4,5,6,7,8,9 ).finished(),
		MatrixXf::Zero(3,cols-3),
		MatrixXf::Zero(rows-3,3),
		MatrixXf::Identity(rows-3,cols-3);
	cout<<"m1=\n"<<m1<<endl;

#pragma endregion

#pragma region Runtime_info
	
	cout<<"*******************Runtime Info****************"<<endl;

	MatrixXf m2(5,4);
	m2<<MatrixXf::Identity(5,4);
	cout<<"m2=\n"<<m2<<endl;

	MatrixXf m3;
	m3=m1*m2;
	cout<<"m3.rows()="<<m3.rows()<<"  ;  "
		     <<"m3.cols()="<< m3.cols()<<endl;
	
	cout<<"m3=\n"<<m3<<endl;

#pragma endregion
	
#pragma region Resizing
	
	cout<<"*******************Resizing****************"<<endl;

	//1D-resize	
	v1.resize(4);
	cout<<"Recover v1 to 4*1 array : v1=\n"<<v1<<endl;

	//2D-resize
	m.resize(2,3);
	m.resize(Eigen::NoChange, 3);
	m.resizeLike(m2);
	m.resize(2,2);
	
#pragma endregion

#pragma region Coeff_access
	
	cout<<"*******************Coefficient access****************"<<endl;

	float tx=v1(1);
	tx=m1(1,1);
	cout<<endl;

#pragma endregion

#pragma  region Predefined_matrix

	cout<<"*******************Predefined Matrix****************"<<endl;

	//1D-object
	typedef  Matrix3f   FixedXD;
	FixedXD x;
	
	x=FixedXD::Zero();
	x=FixedXD::Ones();
	x=FixedXD::Constant(tx);//tx is the value
	x=FixedXD::Random();
	cout<<"x=\n"<<x<<endl;

	typedef ArrayXf Dynamic1D;
	//或者 typedef VectorXf Dynamic1D
	int size=3;
	Dynamic1D xx;
	xx=Dynamic1D::Zero(size);
	xx=Dynamic1D::Ones(size);
	xx=Dynamic1D::Constant(size,tx);
	xx=Dynamic1D::Random(size);
	cout<<"xx=\n"<<x<<endl;

	//2D-object
	typedef MatrixXf Dynamic2D;
	Dynamic2D y;
	y=Dynamic2D::Zero(rows,cols);
	y=Dynamic2D::Ones(rows,cols);
	y=Dynamic2D::Constant(rows,cols,tx);//tx is the value
	y=Dynamic2D::Random(rows,cols);

#pragma endregion

#pragma region Arithmetic_Operators

	cout<<"******************* Arithmetic_Operators****************"<<endl;

	//add & sub
	MatrixXf m4(5,4);
	MatrixXf m5;
	m4=m2+m3;
	m3-=m2;

	//product
	m3=m1*m2;
 
	//transposition
	m5=m4.transpose();
	//m5=m.adjoint();//伴随矩阵	
	
	//dot product
	double xtt;
	cout<<"v1=\n"<<v1<<endl;
	v2.resize(4);
	v2<<VectorXd::Ones(4);
	cout<<"v2=\n"<<v2<<endl;

	cout<<"*************dot product*************"<<endl;
	xtt=v1.dot(v2);
	cout<<"v1.*v2="<<xtt<<endl;

	//vector norm

	cout<<"*************matrix norm*************"<<endl;
	xtt=v1.norm();
	cout<<"norm of v1="<<xtt<<endl;
	xtt=v1.squaredNorm();
	cout<<"SquareNorm of v1="<<xtt<<endl;

#pragma endregion

cout<<endl;
}

 

 

去哪里更深入学习？

Please refer to Eigen中的类及函数、Eigen的官方教程，和一些教程上的相关内容。