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

Posted 2020-06-20 一鸣先森

• 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

 

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1. 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
2. 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
      

       
3. 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.