C++_eigen function Library usage Note--matrix and Vector arithmetic

• Addition and subtraction

• Scalar Multiplication and division
• Transposition

• Matrix-matrix and Matrix-vector multiplication

• Trace (the and of traces)

 

• addition and subtraction
  • Binary operator + as ina+b
  • Binary Operator-as ina-b
  • Unary Operator-as in-a
  • Compound operator + = as ina+=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-=\n "<< A-B << std::endl;std::cout <<" Doing A + + +; "<< std::endl;a + = B;std::cout <&L T "Now a =\n" << a << Std::endl; Vector3D V (n/a); 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 inmatrix*scalar
  • Binary operator * as inscalar*matrix
  • Binary Operator/as inmatrix/scalar
  • Compound operator *= as inmatrix*=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 (n/a);  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's The Matrix a\n" << a << endl;cout << "Here I s 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 With its a 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 ina*b
  • Compound operator *= as ina*=b(This multiplies in the right:a*=bis equivalent toa = 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 << "H Ere is mat*u:\n "<< mat*u << std::endl;std::cout <<" Here's u^t*mat:\n "<< u.transpose () *mat < < Std::endl;std::cout << "Here's 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 (tracing and)#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

C++_eigen function Library usage Note--matrix and Vector arithmetic