鉴于中文资料中Eigen资料鱼目混珠，纷乱庞杂。现参考Eigen官网，整理常用Eigen矩阵操作。 基于版本：/usr/include/eigen3/Eigen/src/Core/util/Macros.h显示的3.2.92 Eigen有2中矩阵结构：Dense和Sparse。Dense矩阵存储读写为正常处理，Sparse由于其特殊的存储格式和操作，处理不一样。以下介绍Dense矩阵的块操作处理。

1. 矩阵块操作

1.1 定义

Eigen中的矩阵块操作使用 .block() 指令，有2中版本：

意义动态size (dynamic-size)固定size (fixed-size block)从 (i,j) 开始，大小为 (p,q) 矩阵块matrix.block(i,j,p,q);matrix.block<p,q>(i,j);

适用于固定尺寸、动态尺寸、array取值，其中固定尺寸读取稍快些。

1.2 栗子

Eg1:

#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; } }

Output:

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

Eg2: block赋值

#include <Eigen/Dense> #include <iostream> using namespace std; using namespace Eigen; int main() { Array22f m; m << 1,2, 3,4; Array44f a = Array44f::Constant(0.6); cout << "Here is the array a:" << endl << a << endl << endl; a.block<2,2>(1,1) = m; cout << "Here is now a with m copied into its central 2x2 block:" << endl << a << endl << endl; a.block(0,0,2,3) = a.block(2,1,2,3); cout << "Here is now a with bottom-right 2x3 block copied into top-left 2x2 block:" << endl << a << endl << endl; }

Output:

Here is the array a: 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 0.6 Here is now a with m copied into its central 2x2 block: 0.6 0.6 0.6 0.6 0.6 1 2 0.6 0.6 3 4 0.6 0.6 0.6 0.6 0.6 Here is now a with bottom-right 2x3 block copied into top-left 2x2 block: 3 4 0.6 0.6 0.6 0.6 0.6 0.6 0.6 3 4 0.6 0.6 0.6 0.6 0.6

2. 矩阵行列操作

2.1 定义

按行、列读取变化，使用指令 .col() and .row()

2.2 栗子

#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; }

OutPut：

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

3. 矩阵Corner操作

3.1 定义

Eigen特别地提供了矩阵的一角，或者是数列的某一端的块操作

意义动态size (dynamic-size)固定size (fixed-size block)左上matrix.topLeftCorner(p,q);matrix.topLeftCorner<p,q>();左下matrix.bottomLeftCorner(p,q);matrix.bottomLeftCorner<p,q>();右上matrix.topRightCorner(p,q);matrix.topRightCorner<p,q>();右下matrix.bottomRightCorner(p,q);matrix.bottomRightCorner<p,q>();前q行块matrix.topRows(q);matrix.topRows<q>();后q行块matrix.bottomRows(q);matrix.bottomRows<q>();前p列块matrix.leftCols(p);matrix.leftCols<p>();后q列块matrix.rightCols(q);matrix.rightCols<q>();

3.2 栗子

#include <Eigen/Dense> #include <iostream> using namespace std; int main() { Eigen::Matrix4f m; m << 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,11,12, 13,14,15,16; cout << "m.leftCols(2) =" << endl << m.leftCols(2) << endl << endl; cout << "m.bottomRows<2>() =" << endl << m.bottomRows<2>() << endl << endl; m.topLeftCorner(1,3) = m.bottomRightCorner(3,1).transpose(); cout << "After assignment, m = " << endl << m << endl; }

Output:

m.leftCols(2) = 1 2 5 6 9 10 13 14 m.bottomRows<2>() = 9 10 11 12 13 14 15 16 After assignment, m = 8 12 16 4 5 6 7 8 9 10 11 12 13 14 15 16

4. 矩阵Vector操作

4.1 定义

意义动态size (dynamic-size)固定size (fixed-size block)前n元素块vector.head(n);vector.head<n>();后n元素块vector.tail(n);vector.tail<n>();从i位置开始的n元素块vector.segment(i,n);vector.segment<n>(i);

4.2 栗子

#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; }

Output

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

Ref: http://eigen.tuxfamily.org/dox-3.2/group__TutorialBlockOperations.html http://eigen.tuxfamily.org/dox-3.2/ 本文基于版本 Eigen 3.2.10