Eigen教程(5)

整理下Eigen库的教程,参考:http://eigen.tuxfamily.org/dox/index.html

块操作

块是matrix或array中的矩形子部分。

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

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

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

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);
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