SymmetricSchurDecomposition Class Reference
#include <ql/math/matrixutilities/symmetricschurdecomposition.hpp>
Detailed Description
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
where 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
- Tests:
- the correctness of the returned values is tested by checking their properties.
Public Member Functions | |
SymmetricSchurDecomposition (const Matrix &s) | |
const Array & | eigenvalues () const |
const Matrix & | eigenvectors () const |
Constructor & Destructor Documentation
SymmetricSchurDecomposition | ( | const Matrix & | s | ) |
- Precondition:
- s must be symmetric