- QuantLib
- SymmetricSchurDecomposition
 
symmetric threshold Jacobi algorithm. More...
#include <ql/math/matrixutilities/symmetricschurdecomposition.hpp>
| Public Member Functions | |
| SymmetricSchurDecomposition (const Matrix &s) | |
| const Array & | eigenvalues () const | 
| const Matrix & | eigenvectors () const | 
symmetric threshold Jacobi algorithm.
Given a real symmetric matrix S, the Schur decomposition finds the eigenvalues and eigenvectors of S. If D is the diagonal matrix formed by the eigenvalues and U the unitarian matrix of the eigenvectors we can write the Schur decomposition as
![\[ S = U \cdot D \cdot U^T \, ,\]](form_214.png) 
 where  is the standard matrix product and
 is the standard matrix product and  is the transpose operator. This class implements the Schur decomposition using the symmetric threshold Jacobi algorithm. For details on the different Jacobi transfomations see "Matrix computation," second edition, by Golub and Van Loan, The Johns Hopkins University Press
 is the transpose operator. This class implements the Schur decomposition using the symmetric threshold Jacobi algorithm. For details on the different Jacobi transfomations see "Matrix computation," second edition, by Golub and Van Loan, The Johns Hopkins University Press
| SymmetricSchurDecomposition | ( | const Matrix & | s | ) |