Eigen 라 이브 러 리 특징 값 특징 벡터

http://eigen.tuxfamily.org/dox/classEigen_1_1EigenSolver.html
Eigen 의 행렬 유형 은 보통 Matrix XXX 와 유사 하 게 표시 되 는데 이 이름 에 따라 데이터 유형 을 판단 할 수 있 습 니 다. 예 를 들 어 'd' 는 double 을 대표 하 는 것 이 정 수 를 나타 내 는 것 이 아 닙 니 다. 'f '대표 float;'i '는 정 수 를 대표 한다.'c 'complex, 즉 복수' 를 대표 한다.d '는 dynamic 을 나타 낸다. 즉, 행렬 의 일부 비 수 는 불확실 하고 동태 적 인 것 을 나타 낸다. 예 를 들 어 Matrix2cd 는 2 * 2 차원 을 나타 내 고 모든 요 소 는 복수 이 며 복수 의 실제 부분 과 허 부 는 double 유형 이다.
EigenSolver
(
const MatrixType & 
matrix,
 
 
bool 
computeEigenvectors =  true  
 
)
 
 
inline
Constructor; computes eigendecomposition of given matrix.
Parameters
[in]
matrix
Square matrix whose eigendecomposition is to be computed.
[in]
computeEigenvectors
If true, both the eigenvectors and the eigenvalues are computed; if false, only the eigenvalues are computed.
This constructor calls compute() to compute the eigenvalues and eigenvectors.
Example:
MatrixXd A = MatrixXd::Random(6,6);
cout <<
"Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
EigenSolver es(A);
cout <<
"The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
cout <<
"The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
complex lambda = es.eigenvalues()[0];
cout <<
"Consider the first eigenvalue, lambda = " << lambda << endl;
VectorXcd v = es.eigenvectors().col(0);
cout <<
"If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
cout <<
"... and A * v = " << endl << A.cast >() * v << endl << endl;
MatrixXcd D = es.eigenvalues().asDiagonal();
MatrixXcd V = es.eigenvectors();
cout <<
"Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
Output:

Here is a random 6x6 matrix, A:
   0.68   -0.33   -0.27  -0.717  -0.687  0.0259
 -0.211   0.536  0.0268   0.214  -0.198   0.678
  0.566  -0.444   0.904  -0.967   -0.74   0.225
  0.597   0.108   0.832  -0.514  -0.782  -0.408
  0.823 -0.0452   0.271  -0.726   0.998   0.275
 -0.605   0.258   0.435   0.608  -0.563  0.0486

The eigenvalues of A are:
  (0.049,1.06)
 (0.049,-1.06)
     (0.967,0)
     (0.353,0)
 (0.618,0.129)
(0.618,-0.129)
The matrix of eigenvectors, V, is:
 (-0.292,-0.454)   (-0.292,0.454)      (-0.0607,0)       (-0.733,0)    (0.59,-0.122)     (0.59,0.122)
  (0.134,-0.104)    (0.134,0.104)       (-0.799,0)        (0.136,0)    (0.335,0.368)   (0.335,-0.368)
  (-0.422,-0.18)    (-0.422,0.18)        (0.192,0)       (0.0563,0)  (-0.335,-0.143)   (-0.335,0.143)
 (-0.589,0.0274) (-0.589,-0.0274)      (-0.0788,0)       (-0.627,0)   (0.322,-0.156)    (0.322,0.156)
  (-0.248,0.132)  (-0.248,-0.132)        (0.401,0)        (0.218,0)  (-0.335,-0.076)   (-0.335,0.076)
    (0.105,0.18)    (0.105,-0.18)       (-0.392,0)     (-0.00564,0)  (-0.0324,0.103) (-0.0324,-0.103)

Consider the first eigenvalue, lambda = (0.049,1.06)
If v is the corresponding eigenvector, then lambda * v = 
  (0.466,-0.331)
   (0.117,0.137)
   (0.17,-0.456)
(-0.0578,-0.622)
 (-0.152,-0.256)
   (-0.186,0.12)
... and A * v = 
  (0.466,-0.331)
   (0.117,0.137)
   (0.17,-0.456)
(-0.0578,-0.622)
 (-0.152,-0.256)
   (-0.186,0.12)

Finally, V * D * V^(-1) = 
     (0.68,1.9e-16)    (-0.33,4.82e-17)   (-0.27,-2.37e-16)    (-0.717,1.6e-16)   (-0.687,-2.2e-16)   (0.0259,2.72e-16)
  (-0.211,2.22e-16)    (0.536,4.16e-17)  (0.0268,-2.98e-16)           (0.214,0)   (-0.198,6.66e-16)    (0.678,6.66e-16)
   (0.566,1.22e-15)   (-0.444,1.11e-16)   (0.904,-4.61e-16)  (-0.967,-3.61e-16)    (-0.74,7.22e-16)    (0.225,8.88e-16)
    (0.597,1.6e-15)    (0.108,1.84e-16)    (0.832,-5.6e-16)  (-0.514,-4.44e-16)   (-0.782,1.28e-15)   (-0.408,9.44e-16)
  (0.823,-8.33e-16) (-0.0452,-2.71e-16)    (0.271,5.53e-16)   (-0.726,7.77e-16)   (0.998,-2.33e-15)   (0.275,-1.67e-15)
  (-0.605,1.03e-15)    (0.258,1.91e-16)    (0.435,-4.6e-16)   (0.608,-6.38e-16)   (-0.563,1.69e-15)   (0.0486,1.25e-15)