C++_Eigen函数库用法笔记——Block Operations

• Using block operations
  • rvalue, i.e. it was only read from
  • lvalues, i.e. you can assign to a block

• Columns and rows

• Corner-related operations

• Block operations for vectors

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• Using block operations

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);

 

• • rvalue, i.e. it was only read from

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

• • lvalues, i.e. you can assign to a block

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

 

• Columns and rows

Block operation	Method
ith row *	matrix.row(i);
jth column *	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;

}

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

 

• Corner-related operations

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<q>();
Block containing the last q rows *	matrix.bottomRows(q);	matrix.bottomRows<q>();
Block containing the first p columns *	matrix.leftCols(p);	matrix.leftCols<p>();
Block containing the last q columns *	matrix.rightCols(q);	matrix.rightCols<q>();

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  820:37:13
 9 10 11 12
13 14 15 16

 

• Block operations for vectors

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

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