因為最近在研究卡爾曼濾波，要用到矩陣運算，就想著用C++一次性把矩陣運算寫好吧，寫一半覺得這麼基礎的工具應該有人寫過吧，發現有很多庫！！！

有人做了總結：

大家用得比較多的是Eigen，Eigen的特點：

(1) 使用方便、無需預編譯，呼叫開銷小

(2) 函式豐富，風格有點近似MATLAB，易上手；

(3) 速度中規中矩，比opencv快，比MKL、openBLAS慢；

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
 

// 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.
 

// 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)'
 

// 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;