1. 块操作

    块是matrix或array中的矩形子部分。

2. 使用块

    函数.block()，有两种形式

operation	构建一个动态尺寸的block	构建一个固定尺寸的block
起点(i,j)块大小(p,q)	.block(i,j,p,q)	.block< p,q >(i,j)

    Eigen中，索引从0开始。

    两个版本都可以用于固定尺寸和动态尺寸的matrix/array。功能是等价的，只是固定尺寸的版本在block较小时速度更快一些。

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;}}

输出

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

作为左值

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;}

输出

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

3. 行和列

Operation	Method
ith row	matrix.row(i)
jth colum	matrix.col(j)

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;}

输出

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

4. 角相关操作

operation	dynamic-size block	fixed-size block
左上角p\*q	matrix.topLeftCorner(p,q);	matrix.topLeftCorner< p,q >();
左下角p\*q	matrix.bottomLeftCorner(p,q);	matrix.bottomLeftCorner< p,q >();
右上角p\*q	matrix.topRightCorner(p,q);	matrix.topRightCorner< p,q >();
右下角p\*q	matrix.bottomRightCorner(p,q);	matrix.bottomRightCorner< p,q >();
前q行	matrix.topRows(q);	matrix.topRows< q >();
后q行	matrix.bottomRows(q);	matrix.bottomRows< q >();
左p列	matrix.leftCols(p);	matrix.leftCols< p >();
右p列	matrix.rightCols(p);	matrix.rightCols< p >();

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;}

输出

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

5. vectors的块操作

operation	dynamic-size block	fixed-size block
前n个	vector.head(n);	vector.head< n >();
后n个	vector.tail(n);	vector.tail< n >();
i起始的n个元素	vector.segment(i,n);	vector.segment< n >(i);