C++_Eigen函数库用法笔记——Advanced Initialization

The comma initializer
- a simple example
- join and block initialize
  - join two row vectors together
  - initialize metrics with block structure
  - fill block expression
Special metrics and arrays
- Zero();
  - Array33f::Zero();
  - ArrayXf::Zero(3);
  - ArrayXXf::Zero(3,4);
- Constant(rows,cols,value);
- Identity();
- LinSpaced
- 3 ways to construct the matrix
Usage as temporary objects

The comma initializer
1. a simple example
  Matrix3f m;
  
  m << 1, 2, 3,
  
  4, 5, 6,
  
  7, 8, 9;
  
  std::cout << m;
2. join and block initialize
  - join two row vectors together
    
    RowVectorXd vec1(3);
    
    vec1 << 1, 2, 3;
    
    std::cout << "vec1 = " << vec1 << std::endl;
    
    RowVectorXd vec2(4);
    
    vec2 << 1, 4, 9, 16;;
    
    std::cout << "vec2 = " << vec2 << std::endl;
    
    RowVectorXd joined(7);
    
    joined << vec1, vec2;
    
    std::cout << "joined = " << joined << std::endl;
    vec1 = 1 2 3
    vec2 = 1 4 9 16
    joined = 1 2 3 1 4 9 16
  - initialize metrics with block structure
    MatrixXf matA(2, 2);
    
    matA << 1, 2, 3, 4;
    
    MatrixXf matB(4, 4);
    
    matB << matA, matA/10, matA/10, matA;
    
    std::cout << matB << std::endl;
    1 2 0.1 0.2
    3 4 0.3 0.4
    0.1 0.2 1 2
    0.3 0.4 3 4
  - fill block expression
    Matrix3f m;
    
    m.row(0) << 1, 2, 3;
    
    m.block(1,0,2,2) << 4, 5, 7, 8;
    
    m.col(2).tail(2) << 6, 9;
    
    std::cout << m;
    1 2 3
    4 5 6
    7 8 9
Special metrics and arrays
1. Zero()
  - Array33f::Zero();
  - ArrayXf::Zero(3);
  - ArrayXXf::Zero(3,4);
    std::cout << "A fixed-size array:\n";
    
    Array33f a1 = Array33f::Zero();
    
    std::cout << a1 << "\n\n";
    
    std::cout << "A one-dimensional dynamic-size array:\n";
    
    ArrayXf a2 = ArrayXf::Zero(3);
    
    std::cout << a2 << "\n\n";
    
    std::cout << "A two-dimensional dynamic-size array:\n";
    
    ArrayXXf a3 = ArrayXXf::Zero(3, 4);
    
    std::cout << a3 << "\n";
    A fixed-size array:
    0 0 0
    0 0 0
    0 0 0
    A one-dimensional dynamic-size array:
    0
    0
    0
    
    A two-dimensional dynamic-size array:
    0 0 0 0
    0 0 0 0
    0 0 0 0
2. Constant(rows,cols,value);
3. Identity();
4. LinSpaced
  ArrayXXf table(10, 4);
  
  table.col(0) = ArrayXf::LinSpaced(10, 0, 90);
  
  table.col(1) = M_PI / 180 * table.col(0);
  
  table.col(2) = table.col(1).sin();
  
  table.col(3) = table.col(1).cos();
  
  std::cout << " Degrees Radians Sine Cosine\n";
  
  std::cout << table << std::endl;
  Degrees Radians Sine Cosine
  0 0 0 1
  10 0.175 0.174 0.985
  20 0.349 0.342 0.94
  30 0.524 0.5 0.866
  40 0.698 0.643 0.766
  50 0.873 0.766 0.643
  60 1.05 0.866 0.5
  70 1.22 0.94 0.342
  80 1.4 0.985 0.174
  90 1.57 1 -4.37e-08
5. 3 ways to construct the matrix
  const int size = 6;
  
  MatrixXd mat1(size, size);
  
  mat1.topLeftCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);
  
  mat1.topRightCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2);
  
  mat1.bottomLeftCorner(size/2, size/2) = MatrixXd::Identity(size/2, size/2);
  
  mat1.bottomRightCorner(size/2, size/2) = MatrixXd::Zero(size/2, size/2);
  
  std::cout << mat1 << std::endl << std::endl;
  MatrixXd mat2(size, size);
  
  mat2.topLeftCorner(size/2, size/2).setZero();
  
  mat2.topRightCorner(size/2, size/2).setIdentity();
  
  mat2.bottomLeftCorner(size/2, size/2).setIdentity();
  
  mat2.bottomRightCorner(size/2, size/2).setZero();
  
  std::cout << mat2 << std::endl << std::endl;
  MatrixXd mat3(size, size);
  
  mat3 << MatrixXd::Zero(size/2, size/2), MatrixXd::Identity(size/2, size/2),
  
  MatrixXd::Identity(size/2, size/2), MatrixXd::Zero(size/2, size/2);
  std::cout << mat3 << std::endl;
  0 0 0 1 0 0
  0 0 0 0 1 0
  0 0 0 0 0 1
  1 0 0 0 0 0
  0 1 0 0 0 0
  0 0 1 0 0 0 0 0 0 1 0 0
  0 0 0 0 1 0
  0 0 0 0 0 1
  1 0 0 0 0 0
  0 1 0 0 0 0
  0 0 1 0 0 0 0 0 0 1 0 0
  0 0 0 0 1 0
  0 0 0 0 0 1
  1 0 0 0 0 0
  0 1 0 0 0 0
  0 0 1 0 0 0
Usage as temporary objects
MatrixXf mat = MatrixXf::Random(2, 3);

std::cout << mat << std::endl << std::endl;

mat = (MatrixXf(2,2) << 0, 1, 1, 0).finished() * mat;

std::cout << mat << std::endl;
0.68 0.566 0.823
-0.211 0.597 -0.605
-0.211 0.597 -0.605
0.68 0.566 0.823

The finished() method is necessary here to get the actual matrix object once the comma initialization of our temporary submatrix is done.

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C++_Eigen函数库用法笔记——Advanced Initialization

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