有关eigen库的一些基本使用方法

#include <iostream>#include "Eigen/Dense"using namespace Eigen;int main(){    MatrixXf m1(3,4);   //动态矩阵，建立3行4列。    MatrixXf m2(4,3);   //4行3列，依此类推。    MatrixXf m3(3,3);    Vector3f v1;        //若是静态数组，则不用指定行或者列    /* 初始化 */    Matrix3d m = Matrix3d::Random();    m1 = MatrixXf::Zero(3,4);       //用0矩阵初始化,要指定行列数    m2 = MatrixXf::Zero(4,3);    m3 = MatrixXf::Identity(3,3);   //用单位矩阵初始化    v1 = Vector3f::Zero();          //同理，若是静态的，不用指定行列数    m1 << 1,0,0,1,      //也可以以这种方式初始化        1,5,0,1,        0,0,9,1;    m2 << 1,0,0,        0,4,0,        0,0,7,        1,1,1;    //向量初始化，与矩阵类似    Vector3d v3(1,2,3);    VectorXf vx(30);}
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C++数组和矩阵转换

使用Map函数，可以实现Eigen的矩阵和c++中的数组直接转换,语法如下：

//@param MatrixType 矩阵类型//@param MapOptions 可选参数，指的是指针是否对齐，Aligned, or Unaligned. The default is Unaligned.//@param StrideType 可选参数，步长/*    Map<typename MatrixType,        int MapOptions,        typename StrideType>*/    int i;    //数组转矩阵    double *aMat = new double[20];    for(i =0;i<20;i++)    {        aMat[i] = rand()%11;    }    //静态矩阵，编译时确定维数 Matrix<double,4,5>     Eigen:Map<Matrix<double,4,5> > staMat(aMat);    //输出    for (int i = 0; i < staMat.size(); i++)        std::cout << *(staMat.data() + i) << " ";    std::cout << std::endl << std::endl;    //动态矩阵，运行时确定 MatrixXd    Map<MatrixXd> dymMat(aMat,4,5);    //输出，应该和上面一致    for (int i = 0; i < dymMat.size(); i++)        std::cout << *(dymMat.data() + i) << " ";    std::cout << std::endl << std::endl;    //Matrix中的数据存在一维数组中，默认是行优先的格式，即一行行的存    //data()返回Matrix中的指针    dymMat.data();
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矩阵基础操作

eigen重载了基础的+ - * / += -= = /= 可以表示标量和矩阵或者矩阵和矩阵

#include <iostream>#include <Eigen/Dense>using namespace Eigen;int main(){    //单个取值，单个赋值    double value00 = staMat(0,0);    double value10 = staMat(1,0);    staMat(0,0) = 100;    std::cout << value00 <<value10<<std::endl;    std::cout <<staMat<<std::endl<<std::endl;    //加减乘除示例 Matrix2d 等同于 Matrix<double,2,2>    Matrix2d a;     a << 1, 2,     3, 4;    MatrixXd b(2,2);     b << 2, 3,     1, 4;    Matrix2d c = a + b;    std::cout<< c<<std::endl<<std::endl;    c = a - b;    std::cout<<c<<std::endl<<std::endl;    c = a * 2;    std::cout<<c<<std::endl<<std::endl;    c = 2.5 * a;    std::cout<<c<<std::endl<<std::endl;    c = a / 2;    std::cout<<c<<std::endl<<std::endl;    c = a * b;    std::cout<<c<<std::endl<<std::endl;
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点积和叉积

#include <iostream>#include <Eigen/Dense>using namespace Eigen;using namespace std;int main(){    //点积、叉积(针对向量的)    Vector3d v(1,2,3);    Vector3d w(0,1,2);    std::cout<<v.dot(w)<<std::endl<<std::endl;    std::cout<<w.cross(v)<<std::endl<<std::endl;}*/
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转置、伴随、行列式、逆矩阵

小矩阵（4 * 4及以下）eigen会自动优化，默认采用LU分解，效率不高

#include <iostream>#include <Eigen/Dense>using namespace std;using namespace Eigen;int main(){    Matrix2d c;     c << 1, 2,     3, 4;    //转置、伴随    std::cout<<c<<std::endl<<std::endl;    std::cout<<"转置\n"<<c.transpose()<<std::endl<<std::endl;    std::cout<<"伴随\n"<<c.adjoint()<<std::endl<<std::endl;    //逆矩阵、行列式    std::cout << "行列式： " << c.determinant() << std::endl;    std::cout << "逆矩阵\n" << c.inverse() << std::endl;}
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计算特征值和特征向量

#include <iostream>#include <Eigen/Dense>using namespace std;using namespace Eigen;int main(){    //特征向量、特征值    std::cout << "Here is the matrix A:\n" << a << std::endl;    SelfAdjointEigenSolver<Matrix2d> eigensolver(a);    if (eigensolver.info() != Success) abort();     std::cout << "特征值:\n" << eigensolver.eigenvalues() << std::endl;     std::cout << "Here's a matrix whose columns are eigenvectors of A \n"     << "corresponding to these eigenvalues:\n"     << eigensolver.eigenvectors() << std::endl;}
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解线性方程

#include <iostream>#include <Eigen/Dense>using namespace std;using namespace Eigen;int main(){    //线性方程求解 Ax =B;    Matrix4d A;    A << 2,-1,-1,1,        1,1,-2,1,        4,-6,2,-2,        3,6,-9,7;    Vector4d B(2,4,4,9);    Vector4d x = A.colPivHouseholderQr().solve(B);    Vector4d x2 = A.llt().solve(B);    Vector4d x3 = A.ldlt().solve(B);        std::cout << "The solution is:\n" << x <<"\n\n"<<x2<<"\n\n"<<x3 <<std::endl;}
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除了colPivHouseholderQr、LLT、LDLT，还有以下的函数可以求解线性方程组，请注意精度和速度： 解小矩阵（4*4）基本没有速度差别

最小二乘求解

最小二乘求解有两种方式，jacobiSvd或者colPivHouseholderQr，4*4以下的小矩阵速度没有区别，jacobiSvd可能更快，大矩阵最好用colPivHouseholderQr

#include <iostream>#include <Eigen/Dense>using namespace std;using namespace Eigen;int main(){    MatrixXf A1 = MatrixXf::Random(3, 2);    std::cout << "Here is the matrix A:\n" << A1 << std::endl;    VectorXf b1 = VectorXf::Random(3);    std::cout << "Here is the right hand side b:\n" << b1 << std::endl;    //jacobiSvd 方式:Slow (but fast for small matrices)    std::cout << "The least-squares solution is:\n"    << A1.jacobiSvd(ComputeThinU | ComputeThinV).solve(b1) << std::endl;    //colPivHouseholderQr方法:fast    std::cout << "The least-squares solution is:\n"    << A1.colPivHouseholderQr().solve(b1) << std::endl;}
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稀疏矩阵

稀疏矩阵的头文件包括：

#include

typedef Eigen::Triplet<double> T;std::vector<T> tripletList;triplets.reserve(estimation_of_entries); //estimation_of_entries是预估的条目for(...){    tripletList.push_back(T(i,j,v_ij));//第 i,j个有值的位置的值}SparseMatrixType mat(rows,cols);mat.setFromTriplets(tripletList.begin(), tripletList.end());// mat is ready to go!
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2.直接将已知的非0值插入

SparseMatrix<double> mat(rows,cols);mat.reserve(VectorXi::Constant(cols,6));for(...){    // i,j 个非零值 v_ij != 0    mat.insert(i,j) = v_ij;}mat.makeCompressed(); // optional
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稀疏矩阵支持大部分一元和二元运算:

sm1.real() sm1.imag() -sm1 0.5*sm1
sm1+sm2 sm1-sm2 sm1.cwiseProduct(sm2)
二元运算中，稀疏矩阵和普通矩阵可以混合使用

//dm表示普通矩阵