c++ Eigen之block

最新推荐文章于 2024-07-11 11:47:58 发布

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最新推荐文章于 2024-07-11 11:47:58 发布

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这篇博客详细介绍了Eigen库中矩阵块操作的方法，包括动态大小和固定大小的块选择，以及各种特殊位置的块如行、列、角块等的访问。通过示例展示了如何进行块赋值和拷贝，以及对数组中的块进行操作。内容涵盖了矩阵的切片、复制和重组，是理解Eigen库高效使用的关键。

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块 block

定义

Block of size (p,q), starting at (i,j)

动态大小

matrix.block(i,j,p,q);

固定大小

matrix.block<p,q>(i,j)

示例

右值

#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;
  }
}

左值

#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 2x3 block:" << endl << a << endl << endl;
}

特殊的block: column 和row

第i行 matrix.row(i)
j列： 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;
}

特殊位置的块

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();
Block containing the q columns starting from i	matrix.middleCols(i,q);	matrix.middleCols(i);
Block containing the q rows starting from i	matrix.middleRows(i,q);	matrix.middleRows(i);

#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;
}

数组中的块操作

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();
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;
}