C++使用eigen庫做本征分解

Eigendecomposition的概念可見https://en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

這里貼一段厄米矩陣的代碼,見https://eigen.tuxfamily.org/dox/group__TutorialLinearAlgebra.html

注意,不同本征值的本征向量是正交的,這是我們可以直接用矩陣共軛來取代矩陣求逆的原因。

 1 #include <iostream>  2 #include <eigen3/Eigen/Dense>  3 using namespace std;  4 using namespace Eigen;  5  6 int main ()  7 {  8  Matrix2cd A;  9 A<<complex<double>(1,0), complex<double>(0,1), 10 complex<double>(0,-1), complex<double>(1,0); 11 12 SelfAdjointEigenSolver<Matrix2cd> solver(A); 13 if (solver.info() != Success) 14  { 15 cerr<<"Eigen solver failed."<<endl; 16  abort (); 17  } 18 Matrix2cd lambda = Matrix2cd::Zero(); 19 for (int i = 0; i < lambda.cols(); ++i) 20 lambda(i,i) = solver.eigenvalues()(i); 21 Matrix2cd Q = solver.eigenvectors(); 22 cout<<"Matrix A:n"<<A<<endl<<endl; 23 cout<<"Matrix lambda:n"<<lambda<<endl<<endl; 24 cout<<"Matrix Q:n"<<Q<<endl<<endl; 25 cout<<"Q*Q^dagger:n"<<Q*Q.adjoint()<<endl<<endl; 26 cout<<"Q*lambda*Q^dagger:n"<<Q*lambda*Q.adjoint()<<endl<<endl; 27 28 return 0; 29 }

輸出結果為

 1 Matrix A:  2 (1,0) (0,1)  3 (0,-1) (1,0)  4  5 Matrix lambda:  6 (0,0) (0,0)  7 (0,0) (2,0)  8  9 Matrix Q: 10 (0.707107,0) (0.707107,0) 11 (0,0.707107) (0,-0.707107) 12 13 Q*Q^dagger: 14 (1,0) (0,0) 15 (0,0) (1,0) 16 17 Q*lambda*Q^dagger: 18 (1,0) (0,1) 19 (0,-1) (1,0)

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