C++_Eigen函数库用法笔记——Matrix and Vector Arithmetic

• Addition and subtraction

• Scalar multiplication and division
• Transposition

• Matrix-matrix and matrix-vector multiplication

• Trace(求迹的和)

• Addition and subtraction
  • binary operator + as in a+b
  • binary operator - as in a-b
  • unary operator - as in -a
  • compound operator += as in a+=b
  • compound operator -= as in a-=b
    
    #include <iostream>

    #include <Eigen/Dense>

    using namespace Eigen;

    int main()

    {

    Matrix2d a;

    a << 1, 2,

    3, 4;

    MatrixXd b(2,2);

    b << 2, 3,

    1, 4;

    std::cout << "a + b =\n" << a + b << std::endl;

    std::cout << "a - b =\n" << a - b << std::endl;

    std::cout << "Doing a += b;" << std::endl;

    a += b;

    std::cout << "Now a =\n" << a << std::endl;

    Vector3d v(1,2,3);

    Vector3d w(1,0,0);

    std::cout << "-v + w - v =\n" << -v + w - v << std::endl;

    }

    a + b =
    3 5
    4 8
    a - b =
    -1 -1
     2  0
    Doing a += b;
    Now a =
    3 5
    4 8
    -v + w - v =
    -1
    -4
    -6

• Scalar multiplication and division
  • binary operator * as in matrix*scalar
  • binary operator * as in scalar*matrix
  • binary operator / as in matrix/scalar
  • compound operator *= as in matrix*=scalar
  • compound operator /= as in matrix/=scalar

    #include <iostream>

    #include <Eigen/Dense>

    using namespace Eigen;

    int main()

    {

    Matrix2d a;

    a << 1, 2,

    3, 4;

    Vector3d v(1,2,3);

    std::cout << "a * 2.5 =\n" << a * 2.5 << std::endl;

    std::cout << "0.1 * v =\n" << 0.1 * v << std::endl;

    std::cout << "Doing v *= 2;" << std::endl;

    v *= 2;

    std::cout << "Now v =\n" << v << std::endl;

    }

    a * 2.5 =
    2.5   5
    7.5  10
    0.1 * v =
    0.1
    0.2
    0.3
    Doing v *= 2;
    Now v =
    2
    4
    6

• Transposition

  MatrixXcf a = MatrixXcf::Random(2,2);

  cout << "Here is the matrix a\n" << a << endl;

  cout << "Here is the matrix a^T\n" << a.transpose() << endl;

  Here is the matrix a
   (-0.211,0.68) (-0.605,0.823)
   (0.597,0.566)  (0.536,-0.33)
  Here is the matrix a^T
   (-0.211,0.68)  (0.597,0.566)
  (-0.605,0.823)  (0.536,-0.33)

 the instruction a = a.transpose() does not replace a with its transpose

For in-place transposition,simply use the transposeInPlace()                

MatrixXf a(2,3); a << 1, 2, 3, 4, 5, 6;

cout << "Here is the initial matrix a:\n" << a << endl;

a.transposeInPlace();

cout << "and after being transposed:\n" << a << endl;

• Matrix-matrix and matrix-vector multiplication
  • binary operator * as in a*b
  • compound operator *= as in a*=b (this multiplies on the right: a*=b is equivalent to a = a*b
    
    #include <iostream>

    #include <Eigen/Dense>

    using namespace Eigen;

    int main()

    {

    Matrix2d mat;

    mat << 1, 2,

    3, 4;

    Vector2d u(-1,1), v(2,0);

    std::cout << "Here is mat*mat:\n" << mat*mat << std::endl;

    std::cout << "Here is mat*u:\n" << mat*u << std::endl;

    std::cout << "Here is u^T*mat:\n" << u.transpose()*mat << std::endl;

    std::cout << "Here is u^T*v:\n" << u.transpose()*v << std::endl;

    std::cout << "Here is u*v^T:\n" << u*v.transpose() << std::endl;

    std::cout << "Let‘s multiply mat by itself" << std::endl;

    mat = mat*mat;

    std::cout << "Now mat is mat:\n" << mat << std::endl;

    }

    Here is mat*mat:
     7 10
    15 22
    Here is mat*u:
    1
    1
    Here is u^T*mat:
    2 2
    Here is u^T*v:
    -2
    Here is u*v^T:
    -2 -0
     2  0
    Let‘s multiply mat by itself
    Now mat is mat:
     7 10
    15 22

• Trace(求迹的和)

  #include <iostream>

  #include <Eigen/Dense>

  using namespace std;

  int main()

  {

  Eigen::Matrix2d mat;

  mat << 1, 2,

  3, 4;

  cout << "Here is mat.trace(): " << mat.trace() << endl;

  }

  Here is mat.trace():     5