5.4 KiB
EigenSolver2
Compute generalized eigenvalues and eigenvectors for a pair of ordinary square matrices (LAPACK function GGEV). Both matrices must be the same size.
Computing for type matrix
bool matrix::EigenSolver2(
matrix& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorc& alpha, // vector of computed eigenvalues
vector& beta, // vector of eigenvalue divisors
matrix& left_eigenvectors, // matrix of computed left vectors
matrix& right_eigenvectors // matrix of computed right vectors
);
Computing for type matrix
bool matrixf::EigenSolver2(
matrix& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorf& beta, // vector of eigenvalue divisors
matrixf& left_eigenvectors, // matrix of computed left vectors
matrixf& right_eigenvectors // matrix of computed right vectors
);
Computing for type matrix
bool matrixc::EigenSolver2(
matrixc& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorc& alpha, // vector of computed eigenvalues
vectorc& beta, // vector of eigenvalue divisors
matrixc& left_eigenvectors, // matrix of computed left vectors
matrixc& right_eigenvectors // matrix of computed right vectors
);
Computing for type matrix
bool matrixcf::EigenSolver2(
matrixcf& B, // second matrix in the pair
ENUM_EIG_VECTORS jobv, // method to compute right and left vectors
vectorcf& alpha, // vector of computed eigenvalues
vectorcf& beta, // vector of eigenvalue divisors
matrixcf& left_eigenvectors, // matrix of computed left vectors
matrixcf& right_eigenvectors // matrix of computed right vectors
);
Parameters
B
[in] The second matrix in the pair.
jobv
[in] ENUM_EIG_VECTORS enumeration value which determines the method for computing left and right eigenvectors.
alpha
[out] Vector of eigenvalues.
beta
[out] Vector of eigen value divisors.
left_eigenvectors
[out] Matrix of left eigenvectors.
right_eigenvectors
[out] Matrix of right eigenvectors.
Return Value
Return true if successful, otherwise false in case of an error.
Note
Computation depends on the value of the jobv parameter.
ENUM_EIG_VECTORS
An enumeration defining the need to compute eigenvectors.
| ID | Description |
|---|---|
| EIGVECTORS_N | Only eigenvalues are computed, without vectors. |
| EIGVECTORS_L | Only left eigenvectors are computed. |
| EIGVECTORS_R | Only right eigenvectors are computed. |
| EIGVECTORS_LR | Left and right eigenvectors are computed, eigenvalues are always computed. |
A generalized eigenvalue for a pair of matrices (A,B) is a scalar lambda or a ratio alpha/beta = lambda, such that A - lambda*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0, and even for both being zero.
The right eigenvector v(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies
A * v(j) = lambda(j) * B * v(j).
The left eigenvector u(j) corresponding to the eigenvalue lambda(j) of (A,B) satisfies
u(j)**H * A = lambda(j) * u(j)**H * B .
where u(j)**H is the conjugate-transpose of u(j).
Real (non-complex) matrices can have a complex solution. Therefore, the input vector of eigenvalues must be complex. In case of a complex solution, the error code is set to 4019 (ERR_MATH_OVERFLOW). Otherwise, only the real parts of the complex values of the eigenvalue vector should be used.