Eigen: C++开源矩阵计算工具——安装与使用

因为最近在研究卡尔曼滤波，要用到矩阵运算，就想着用C++一次性把矩阵运算写好吧，写一半觉得这么基础的工具应该有人写过吧，发现有很多库！！！

有人做了总结：

C++矩阵运算库推荐 

矩阵运算库Armadillo,Eigen,MATCOM在windows+vs2010环境下的安装和测评

大家用得比较多的是Eigen，Eigen的特点：

(1) 使用方便、无需预编译，调用开销小(2) 函数丰富，风格有点近似MATLAB，易上手；(3) 速度中规中矩，比opencv快，比MKL、openBLAS慢；

Eigen的下载与安装，可参考：C++矩阵处理工具——Eigen
Eigen的简单使用
参考：C++开源矩阵计算工具——Eigen的简单用法（一）C++开源矩阵计算工具——Eigen的简单用法（二）
C++开源矩阵计算工具——Eigen的简单用法（三）
Eigen矩阵运算库使用记录

使用方法很简单：下载Eigen后解压，然后包含解压路径，最后只需要在程序里引用头文件和使用命名空间#include <Eigen/Dense> using namespace Eigen;
矩阵定义

Matrix<double, 3, 3> A;               // Fixed rows and cols. Same as Matrix3d.
Matrix<double, 3, Dynamic> B;         // Fixed rows, dynamic cols.
Matrix<double, Dynamic, Dynamic> C;   // Full dynamic. Same as MatrixXd.
Matrix<double, 3, 3, RowMajor> E;     // Row major; default is column-major.
Matrix3f P, Q, R;                     // 3x3 float matrix.
Vector3f x, y, z;                     // 3x1 float matrix.
RowVector3f a, b, c;                  // 1x3 float matrix.
VectorXd v;                           // Dynamic column vector of doubles

基本使用方法

// Eigen          // Matlab           // comments
x.size()          // length(x)        // vector size
C.rows()          // size(C,1)        // number of rows
C.cols()          // size(C,2)        // number of columns
x(i)              // x(i+1)           // Matlab is 1-based
C(i,j)            // C(i+1,j+1)       //

A.resize(4, 4);   // Runtime error if assertions are on.
B.resize(4, 9);   // Runtime error if assertions are on.
A.resize(3, 3);   // Ok; size didn't change.
B.resize(3, 9);   // Ok; only dynamic cols changed.

A << 1, 2, 3,     // Initialize A. The elements can also be
4, 5, 6,     // matrices, which are stacked along cols
7, 8, 9;     // and then the rows are stacked.
B << A, A, A;     // B is three horizontally stacked A's.
A.fill(10);       // Fill A with all 10's.

特殊矩阵生成

// Eigen                            // Matlab
MatrixXd::Identity(rows,cols)       // eye(rows,cols)
C.setIdentity(rows,cols)            // C = eye(rows,cols)
MatrixXd::Zero(rows,cols)           // zeros(rows,cols)
C.setZero(rows,cols)                // C = ones(rows,cols)
MatrixXd::Ones(rows,cols)           // ones(rows,cols)
C.setOnes(rows,cols)                // C = ones(rows,cols)
MatrixXd::Random(rows,cols)         // rand(rows,cols)*2-1    // MatrixXd::Random returns uniform random numbers in (-1, 1).
C.setRandom(rows,cols)              // C = rand(rows,cols)*2-1
VectorXd::LinSpaced(size,low,high)  // linspace(low,high,size)'
v.setLinSpaced(size,low,high)       // v = linspace(low,high,size)'

矩阵四则运算

// All the same as Matlab, but matlab doesn't have *= style operators.
// Matrix-vector.
y  = M*x;
a  = b*M;
a *= M;

// Matrix-matrix.
R  = P*Q;
R  = P - Q;
R  = P + Q;
R *= Q;
R += Q;
R -= Q;

//Matrix-scalar.
R  = P*s;
R  = s*P;
R  = P/s;
R  = s*P;
R *= s;
R /= s;