# Eigen学习笔记(5)-块操作

Eigen 为 Matrix 、Array 和 Vector提供了块操作方法。块是matrix或array中的矩形子部分。块区域可以被用作 左值 和 右值。

# 1. 使用块

Block operation Version constructing a dynamic-size block expression Version constructing a fixed-size block expression
Block of size (p,q), starting at (i,j) matrix.block(i,j,p,q); matrix.block<p,q>(i,j);

Eigen中，索引从0开始。

``````#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

``````

block也可以被用作左值，即block可以进行赋值操作。

``````#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;
}
``````

``````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. 行和列

Block operation Method
ith row matrix.row(i);
jth colum matrix.col(j);

``````#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
``````

# 3. 角块相关的操作

Eigen提供了一些方法实现对角块和边的提取。

Block operation Version constructing a dynamic-size block expression Version constructing a fixed-size block expression
Top-left p by q block * matrix.topLeftCorner(p,q); matrix.topLeftCorner<p,q>();
Bottom-left p by q block * matrix.bottomLeftCorner(p,q); matrix.bottomLeftCorner<p,q>();
Top-right p by q block * matrix.topRightCorner(p,q); matrix.topRightCorner<p,q>();
Bottom-right p by q block * matrix.bottomRightCorner(p,q); matrix.bottomRightCorner<p,q>();
Block containing the first q rows * matrix.topRows(q); matrix.topRows();
Block containing the last q rows * matrix.bottomRows(q); matrix.bottomRows();
Block containing the first p columns * matrix.leftCols§; matrix.leftCols

();

Block containing the last q columns * matrix.rightCols(q); matrix.rightCols();

``````#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;
}
``````

``````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. Vector相关的块操作

Block operation Version constructing a dynamic-size block expression Version constructing a fixed-size block expression
Block containing the last n elements * vector.tail(n); vector.tail();
Block containing n elements, starting at position i * vector.segment(i,n); vector.segment(i);

``````#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
``````