template<typename _Scalar, int _Rows, int _Cols, int _Options, int _MaxRows, int _MaxCols>
class Eigen::Matrix< _Scalar, _Rows, _Cols, _Options, _MaxRows, _MaxCols >

......

typedef matrix<double, Dynamic, Dynamic> MarixXd;

typedef Matrix< double , 3 , 1> Vector3d

Vector2d a(5.0, 6.0);
Vector3d b(5.0, 6.0, 7.0);
Vector4d c(5.0, 6.0, 7.0, 8.0);

Vector2f v1(x, y);

Array3i   v2(x, y, z);
Vector4d  v3(x, y, z, w);
VectorXf  v5; // empty object
ArrayXf   v6(size);

//2D objects
atrix4f  m1;
MatrixXf  m5; // empty object
MatrixXf  m6(nb_rows, nb_columns);

// 单点赋值
Eigen::Matrix<double, 3, 3> srcPoints;
    srcPoints(0, 0) = 4;
    srcPoints(1, 0) = 0;
    srcPoints(2, 0) = 0;
    srcPoints(0, 1) = 2;
//...

//<<运算符赋值
Vector3f  v1;     
v1 << x, y, z;

ArrayXf   v2(4);  
v2 << 1, 2, 3, 4;

//
Matrix3f  m1;   
m1 << 1, 2, 3,
      4, 5, 6,
      7, 8, 9;

int rows=5, cols=5;
MatrixXf m(rows,cols);
m << (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 << m;

//vector x
x.setZero();
x.setOnes();
x.setConstant(value);
x.setRandom();
x.setLinSpaced(size, low, high);

VectorXf::Unit(4,1) == Vector4f(0,1,0,0)
                    == Vector4f::UnitY()

//matrix x
x.setZero(rows, cols);
x.setOnes(rows, cols);
x.setConstant(rows, cols, value);
x.setRandom(rows, cols);

x.setIdentity();//单位矩阵
x.setIdentity(rows, cols);     

//连续映射
float data[] = {1,2,3,4};
Map<Vector3f> v1(data);       // uses v1 as a Vector3f object
Map<ArrayXf>  v2(data,3);     // uses v2 as a ArrayXf object
Map<Array22f> m1(data);       // uses m1 as a Array22f object
Map<MatrixXf> m2(data,2,2);   // uses m2 as a MatrixXf object

//间隔映射
float data[] = {1,2,3,4,5,6,7,8,9};
Map<VectorXf,0,InnerStride<2> >  v1(data,3);                      // = [1,3,5]
Map<VectorXf,0,InnerStride<> >   v2(data,3,InnerStride<>(3));     // = [1,4,7]
Map<MatrixXf,0,OuterStride<3> >  m2(data,2,3);                    // both lines     |1,4,7|
Map<MatrixXf,0,OuterStride<> >   m1(data,2,3,OuterStride<>(3));   // are equal to:  |2,5,8|

#include <iostream>
#include <Eigen/Dense>
using namespace Eigen;
using namespace std;
int main()
{
MatrixXd m = MatrixXd::Random(3,3);
m = (m + MatrixXd::Constant(3,3,1.2)) * 50;
cout << "m =" << endl << m << endl;
VectorXd v(3);
v << 1, 2, 3;
cout << "m * v =" << endl << m * v << endl;
}

#include <iostream>
#include <Eigen/Dense>
using namespace Eigen;
using namespace std;
int main()
{
Matrix3d m = Matrix3d::Random();
m = (m + Matrix3d::Constant(1.2)) * 50;
cout << "m =" << endl << m << endl;
Vector3d v(1,2,3);
cout << "m * v =" << endl << m * v << endl;
}

#include <iostream>
#include <Eigen/Dense>
using namespace Eigen;
int main()
{
MatrixXd m(2,2);
m(0,0) = 3;
m(1,0) = 2.5;
m(0,1) = -1;
m(1,1) = m(1,0) + m(0,1);
std::cout << "Here is the matrix m:n" << m << std::endl;
VectorXd v(2);
v(0) = 4;
v(1) = v(0) - 1;
std::cout << "Here is the vector v:n" << v << std::endl;
}

Here is the matrix m:
  3  -1
2.5 1.5
Here is the vector v:
4
3

Matrix3f m;
m << 1, 2, 3,
4, 5, 6,
7, 8, 9;
std::cout << m;

1 2 3
4 5 6
7 8 9

VectorXf m_Vector_A;
MatrixXf m_matrix_B;
int m_iN =-1;
 
bool InitData(int pSrc[100][100], int iWidth, int iHeight)
{
    if (NULL == pSrc || iWidth <=0 || iHeight <= 0)
        return false;
    m_iN = iWidth*iHeight;
    VectorXf tmp_A(m_iN);
    MatrixXf tmp_B(m_iN, 5);
    int i =0, j=0, iPos =0;
    while(i<iWidth)
    {
         j=0;
        while(j<iHeight)
        {
            tmp_A(iPos) = pSrc[i][j] * log((float)pSrc[i][j]);
 
            tmp_B(iPos,0) = pSrc[i][j] ;
            tmp_B(iPos,1) = pSrc[i][j] * i;
            tmp_B(iPos,2) = pSrc[i][j] * j;
            tmp_B(iPos,3) = pSrc[i][j] * i * i;
            tmp_B(iPos,4) = pSrc[i][j] * j * j;
            ++iPos;
            ++j;
        }
        ++i;
    }
    m_Vector_A = tmp_A;
    m_matrix_B = tmp_B;
}

#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;
}
*/

matrix.block(i,j,p,q);      （1）
 
matrix.block<p,q>(i,j);    （2）

#include <Eigen/Dense>
#include <iostream>
using namespace std;
int main()
{
Eigen::MatrixXf m(4,4);
m << 1, 2, 3, 4,
5, 6, 7, 8,
9,10,11,12,
13,14,15,16;
cout << "Block in the middle" << endl;
cout << m.block<2,2>(1,1) << endl << endl;
for (int i = 1; i <= 3; ++i)
{
cout << "Block of size " << i << "x" << i << endl;
cout << m.block(0,0,i,i) << endl << endl;
}
}

Block in the middle
6  7
10 11
Block of size 1x1
1
Block of size 2x2
1 2
5 6
Block of size 3x3
1  2  3
5  6  7
9 10 11

#include <Eigen/Dense>
#include <iostream>
using namespace std;
int main()
{
Eigen::MatrixXf m(3,3);
m << 1,2,3,
4,5,6,
7,8,9;
cout << "Here is the matrix m:" << endl << m << endl;
cout << "2nd Row: " << m.row(1) << endl;
m.col(2) += 3 * m.col(0);
cout << "After adding 3 times the first column into the third column, the matrix m is:n";
cout << m << endl;
}

Here is the matrix m:
1 2 3
4 5 6
7 8 9
2nd Row: 4 5 6
After adding 3 times the first column into the third column, the matrix m is:
 1  2  6
 4  5 18
 7  8 30

#include <Eigen/Dense>
#include <iostream>
using namespace std;
int main()
{
Eigen::ArrayXf v(6);
v << 1, 2, 3, 4, 5, 6;
cout << "v.head(3) =" << endl << v.head(3) << endl << endl;
cout << "v.tail<3>() = " << endl << v.tail<3>() << endl << endl;
v.segment(1,4) *= 2;
cout << "after 'v.segment(1,4) *= 2', v =" << endl << v << endl;
}

v.head(3) =
1
2
3
v.tail<3>() = 
4
5
6
after 'v.segment(1,4) *= 2', v =
1
4
6
8
10
6

#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;
}

void QR2()
{
    Matrix3d A;
    A<<1,1,1,
       2,-1,-1,
       2,-4,5;

    HouseholderQR<Matrix3d> qr;
    qr.compute(A);
    MatrixXd R = qr.matrixQR().triangularView<Upper>();
    MatrixXd Q =  qr.householderQ();
    std::cout << "QR2(): HouseholderQR---------------------------------------------"<< std::endl;
    std::cout << "A "<< std::endl <<A << std::endl << std::endl;
    std::cout <<"qr.matrixQR()"<< std::endl << qr.matrixQR() << std::endl << std::endl;
    std::cout << "R"<< std::endl <<R << std::endl << std::endl;
    std::cout << "Q "<< std::endl <<Q << std::endl << std::endl;
    std::cout <<"Q*R" << std::endl <<Q*R << std::endl << std::endl;
}

QR2(): HouseholderQR---------------------------------------------
A 
 1  1  1
 2 -1 -1
 2 -4  5

qr.matrixQR()
 -3   3  -3
0.5  -3   3
0.5  -1  -3

R
-3  3 -3
 0 -3  3
 0  0 -3

Q 
-0.333333 -0.666667 -0.666667
-0.666667 -0.333333  0.666667
-0.666667  0.666667 -0.333333

Q*R
 1  1  1
 2 -1 -1
 2 -4  5

#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 x1 = A.colPivHouseholderQr().solve(b);
   

Vector4d x2

 = A.ldlt().solve(b));  // A sym. p.s.d.    #include <Eigen/Cholesky>

Vector4d x3

 = A.llt().solve(b));  // A sym. p.d.      #include <Eigen/Cholesky>

Vector4d x4

 = A.lu().solve(b));  // Stable and fast. #include <Eigen/LU>

Vector4d x5

 = A.qr().solve(b));  // No pivoting.     #include <Eigen/QR>

Vector4d x6

 = A.svd().solve(b));  // Stable, slowest. #include <Eigen/SVD>

// .ldlt() -> .matrixL() and .matrixD()
// .llt()  -> .matrixL()
// .lu()   -> .matrixL() and .matrixU()
// .qr()   -> .matrixQ() and .matrixR()
// .svd()  -> .matrixU(), .singularValues(), and .matrixV()

    std::cout << "The solution is:n" << x <<"nn"<<x2<<"nn"<<x3 <<std::endl;
}

 0
-1
-4
-3

-289.143
 448.714
 29.9082
 3.97959

  1.52903
   0.1758
-0.340206
0.0423223

#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;
}

Here is the matrix A:
 0.680375   0.59688
-0.211234  0.823295
 0.566198 -0.604897
Here is the right hand side b:
-0.329554
 0.536459
-0.444451
The least-squares solution is:
-0.669626
 0.314253
The least-squares solution is:
-0.669626
 0.314253

#include <Eigen/SparseCore>
#include <Eigen/SparseCholesky>
#include <Eigen/IterativeLinearSolvers>
#include <Eigen/Sparse>

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!

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

sm1.real() sm1.imag() -sm1 0.5*sm1
sm1+sm2 sm1-sm2 sm1.cwiseProduct(sm2)

//dm表示普通矩阵
dm2 = sm1 + dm1;

//@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为列优先，如下返回指针
    dymMat.data();

#include<Eigen/Dense>

Matrix A; // Fixed rows and cols. Same as Matrix3d. Matrix B; // Fixed rows, dynamic cols.

Matrix C; // Full dynamic. Same as MatrixXd.

Matrix 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

// Basic usage

// 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)'

// Matrix slicing and blocks. All expressions listed here are read/write.

// Templated size versions are faster. Note that Matlab is 1-based (a size N // vector is x(1)...x(N)).

// Eigen // Matlab

x.head(n) // x(1:n)

x.head() // x(1:n)

x.tail(n) // x(end - n + 1: end)

x.tail() // x(end - n + 1: end)

x.segment(i, n) // x(i+1 : i+n)

x.segment(i) // x(i+1 : i+n)

P.block(i, j, rows, cols) // P(i+1 : i+rows, j+1 : j+cols)

P.block(i, j) // P(i+1 : i+rows, j+1 : j+cols)

P.row(i) // P(i+1, :)

P.col(j) // P(:, j+1)

P.leftCols() // P(:, 1:cols)

P.leftCols(cols) // P(:, 1:cols)

P.middleCols(j) // P(:, j+1:j+cols)

P.middleCols(j, cols) // P(:, j+1:j+cols)

P.rightCols() // P(:, end-cols+1:end)

P.rightCols(cols) // P(:, end-cols+1:end)

P.topRows() // P(1:rows, :)

P.topRows(rows) // P(1:rows, :)

P.middleRows(i) // P(i+1:i+rows, :)

P.middleRows(i, rows) // P(i+1:i+rows, :)

P.bottomRows() // P(end-rows+1:end, :)

P.bottomRows(rows) // P(end-rows+1:end, :)

P.topLeftCorner(rows, cols) // P(1:rows, 1:cols)

P.topRightCorner(rows, cols) // P(1:rows, end-cols+1:end)

P.bottomLeftCorner(rows, cols) // P(end-rows+1:end, 1:cols)

P.bottomRightCorner(rows, cols) // P(end-rows+1:end, end-cols+1:end) P.topLeftCorner<rows,cols>() // P(1:rows, 1:cols)

P.topRightCorner<rows,cols>() // P(1:rows, end-cols+1:end)

P.bottomLeftCorner<rows,cols>() // P(end-rows+1:end, 1:cols)

P.bottomRightCorner<rows,cols>() // P(end-rows+1:end, end-cols+1:end)

// Of particular note is Eigen's swap function which is highly optimized. 

// Eigen 　　　　　　　　　　// Matlab

R.row(i) = P.col(j); 　　// R(i, :) = P(:, i)

R.col(j1).swap(mat1.col(j2)); // R(:, [j1 j2]) = R(:, [j2, j1])

// Views, transpose, etc; all read-write except for .adjoint().

// Eigen // Matlab

R.adjoint() // R'

R.transpose() // R.' or conj(R')

R.diagonal() // diag(R)

x.asDiagonal() // diag(x)

R.transpose().colwise().reverse(); // rot90(R)

R.conjugate() // conj(R)

// All the same as Matlab, but matlab doesn't have *= style operators.

// Matrix-vector. Matrix-matrix.Matrix-scalar.

y = M*x; R = P*Q; R = P*s;

a = b*M; R = P - Q; R = s*P;

a *= M; R = P + Q; R = P/s;

R *= Q; R = s*P;

R += Q; R *= s;

R -= Q; R /= s;

// Vectorized operations on each element independently // Eigen // Matlab

R = P.cwiseProduct(Q); // R = P .* Q

R = P.array() * s.array();// R = P .* s

R = P.cwiseQuotient(Q); // R = P ./ Q

R = P.array() / Q.array();// R = P ./ Q

R = P.array() + s.array();// R = P + s

R = P.array() - s.array();// R = P - s

R.array() += s; // R = R + s

R.array() -= s; // R = R - s

R.array()

R.array() <= Q.array(); // R <= Q

R.cwiseInverse(); // 1 ./ P

R.array().inverse(); // 1 ./ P

R.array().sin() // sin(P)

R.array().cos() // cos(P)

R.array().pow(s) // P .^ s

R.array().square() // P .^ 2

R.array().cube() // P .^ 3

R.cwiseSqrt() // sqrt(P)

R.array().sqrt() // sqrt(P)

R.array().exp() // exp(P)

R.array().log() // log(P)

R.cwiseMax(P) // max(R, P)

R.array().max(P.array()) // max(R, P)

R.cwiseMin(P) // min(R, P)

R.array().min(P.array()) // min(R, P)

R.cwiseAbs() // abs(P)

R.array().abs() // abs(P)

R.cwiseAbs2() // abs(P.^2)

R.array().abs2() // abs(P.^2)

(R.array() < s).select(P,Q); // (R < s ? P : Q)

// Reductions.

int r, c;

// Eigen // Matlab

R.minCoeff() // min(R(:))

R.maxCoeff() // max(R(:))

s = R.minCoeff(&r, &c) // [s, i] = min(R(:)); [r, c] = ind2sub(size(R), i);

s = R.maxCoeff(&r, &c) // [s, i] = max(R(:)); [r, c] = ind2sub(size(R), i);

R.sum() // sum(R(:))

R.colwise().sum() // sum(R)

R.rowwise().sum() // sum(R, 2) or sum(R')'

R.prod() // prod(R(:))

R.colwise().prod() // prod(R)

R.rowwise().prod() // prod(R, 2) or prod(R')'

R.trace() // trace(R)

R.all() // all(R(:))

R.colwise().all() // all(R)

R.rowwise().all() // all(R, 2)

R.any() // any(R(:))

R.colwise().any() // any(R)

R.rowwise().any() // any(R, 2)

// Dot products, norms, etc.

// Eigen // Matlab
x.norm() // norm(x). Note that norm(R) doesn't work in Eigen. 
x.squaredNorm() // dot(x, x) Note the equivalence is not true for complex
x.dot(y) // dot(x, y)
x.cross(y) // cross(x, y) Requires #include

//// Type conversion

// Eigen // Matlab

A.cast(); // double(A)

A.cast(); // single(A)

A.cast(); // int32(A)

A.real(); // real(A)

A.imag(); // imag(A)

// if the original type equals destination type, no work is done

// Solve Ax = b. Result stored in x. Matlab: x = A  b.
x = A.ldlt().solve(b)); // A sym. p.s.d. #include 

x = A.llt() .solve(b)); // A sym. p.d. #include 

x = A.lu() .solve(b)); // Stable and fast. #include

x = A.qr() .solve(b)); // No pivoting. #include

x = A.svd() .solve(b)); // Stable, slowest. #include

// .ldlt() -> .matrixL() and .matrixD()

// .llt() -> .matrixL()

// .lu() -> .matrixL() and .matrixU()

// .qr() -> .matrixQ() and .matrixR()

// .svd() -> .matrixU(), .singularValues(), and .matrixV()

// Eigenvalue problems

// Eigen // Matlab

A.eigenvalues(); // eig(A);

EigenSolvereig(A); // [vecval] = eig(A)

eig.eigenvalues(); // diag(val)

eig.eigenvectors(); // vec

// For self-adjoint matrices use SelfAdjointEigenSolver<>