Eigen
Version
查看当前Eigen的版本
for apt package
dpkg -l | grep eigen
看头文件宏
more /usr/include/eigen3/Eigen/src/Core/util/Macros.h | grep VERSION
CMake
find_package(Eigen3 REQUIRED)
include_directories(${EIGEN3_INCLUDE_DIRS})
Header
#include <Eigen/Dense>
其内部实际包含了：
#include "Core"
#include "LU"
#include "Cholesky"
#include "QR"
#include "SVD"
#include "Geometry"
#include "Eigenvalues"
Matrix
Accessors
#include <iostream>
#include <Eigen/Dense>
int main()
{
Eigen::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);
}
Assignment
逗号操作符初始化
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.
Construct
默认构造函数（不进行动态内存分配和值的初始化）
using namespace Eigen;
// 创建静态数组（进行空间分配）
Matrix<double, 3, 3> A; // Fixed rows and cols. Same as Matrix3d.
Matrix3f P; // 创建3×3方阵
Vector3f x, y, z; // 3x1 float matrix.
RowVector3f a, b, c; // 1x3 float matrix.
// 创建动态数组，不进行内存分配
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; // 设置行优先
VectorXd v; // Dynamic column vector of doubles
// 创建随机矩阵
Eigen::MatrixXi mat = Eigen::MatrixXi::Random(2, 3);
// 单位阵
MatrixXd mat = MatrixXd::Identity(5, 3);
// Resizes to the given size, and writes the identity expression
mat.setIdentity(5, 3);
// 1矩阵
MatrixXd mat = MatrixXd::Ones(5, 3);
mat.setZero(5, 3);
// 0矩阵
MatrixXd mat = MatrixXd::Zero(5, 3);
mat.setZero(5, 3);
// 常数矩阵
MatrixXd::Constant(5, 3, 10);
Equation
// Solve Ax = b. Result stored in x. Matlab: x = A b.
x = A.ldlt().solve(b); // A sym. p.s.d. #include <Eigen/Cholesky>
x = A.llt() .solve(b); // A sym. p.d. #include <Eigen/Cholesky>
x = A.lu() .solve(b); // Stable and fast. #include <Eigen/LU>
x = A.qr() .solve(b); // No pivoting. #include <Eigen/QR>
x = 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()
Hstack
auto a = Eigen::MatrixXd::Random(3, 2);
auto b = Eigen::MatrixXd::Ones(3, 1);
Eigen::MatrixXd c(a.rows(), a.cols() + b.cols());
c << a, b;
Index
Slice
start from
Eigen 3.4
Eigen::MatrixXd mat = Eigen::MatrixXd::Random(10, 4);
// mat[:,0:2]，seq：为左闭右闭
// note: 这种方法得到的矩阵为深拷贝
Eigen::MatrixXd submat = mat(Eigen::all, Eigen::seq(0, 2));
Map
// vector(9) -> eigen(3, 3)
// Eigen::Matrix<double, 3, 3> camera_intrinsic(camera_intrinsic_yaml.data());
Eigen::Matrix<double, 3, 3> camera_intrinsic = Eigen::Map<Eigen::Matrix<double, 3, 3> >(camera_intrinsic_yaml.data());
Mathematics
// 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;
MatrixXd mat = MatrixXd::Random(3, 3);
cout << mat << endl;
// 伴随矩阵
cout << mat.adjoint() << endl;
// 转置矩阵
cout << mat.transpose() << endl;
// 获取对角线上的元素
cout << mat.diagonal() << endl;
// 求逆
cout << mat.reverse() << endl;
Reshape
返回的是view（浅拷贝）
对于resize而言，如果resize前后元素个数不一样，则会返回一个0初值的数组
MatrixXi m = Matrix4i::Random();
auto m1 = m.reshaped(2, 8);
// in-place reshape
m.resize(2,8);
Size
// Eigen // comments
x.size() // 向量的大小（元素的个数）
C.rows() // 行数
C.cols() // 列数
Type Cast
MatrixXd mat = MatrixXd::Random(2, 2);
// if the original type equals destination type, no work is done
mat.cast<double>();
mat.cast<float>();
mat.cast<int>();
mat.real();
mat.imag();
// note that for most operations Eigen requires all operands to have the same type
MatrixXf F = MatrixXf::Zero(3, 3);
// mat += F; // illegal in Eigen.
mat += F.cast<double>(); // F converted to double and then added (generally, conversion happens on-the-fly)