Overload List
| # | Signature | Description |
|---|---|---|
| 1 | void EigGen(TMtx B, TVec DAlpha, TVec DBeta, TBalanceType Balance, TEigBalancing BInfo, TVec rconde, TVec rcondv, TMtx VL, TMtx VR) | Computes generalized eigenvalues and eigenvectors of a non-symmetric matrix. |
| 2 | void EigGen(TMtx B, TVec DAlpha, TVec DBeta, TMtx VL, TMtx VR) | Computes generalized eigenvalues and eigenvectors of a non-symmetric matrix. |
Overload 1: void EigGen(TMtx B, TVec DAlpha, TVec DBeta, TBalanceType Balance, TEigBalancing BInfo, TVec rconde, TVec rcondv, TMtx VL, TMtx VR)
Computes generalized eigenvalues and eigenvectors of a non-symmetric matrix.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | B | TMtx | source TMtx |
| 2 | DAlpha | TVec | source TVec |
| 3 | DBeta | TVec | source TVec |
| 4 | Balance | TBalanceType | |
| 5 | BInfo | TEigBalancing | |
| 6 | rconde | TVec | source TVec |
| 7 | rcondv | TVec | source TVec |
| 8 | VL | TMtx | source TMtx |
| 9 | VR | TMtx | source TMtx |
Result: stored in self (calling object)
Computes for a pair of N-by-N real nonsymmetric matrices (A = Self,B) the generalized eigenvalues, and optionally, the left and/or right generalized eigenvectors (VL and/or VR).
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). The individual eigevalues can be computed as:
lambda(j) = dAlpha(j) / dBeta(j) ;
Optionally also computes a balancing transformation to improve the conditioning of the eigenvalues and eigenvectors , reciprocal condition numbers for the eigenvalues (rconde), and reciprocal condition numbers for the right eigenvectors (rcondv).
Overload 2: void EigGen(TMtx B, TVec DAlpha, TVec DBeta, TMtx VL, TMtx VR)
Computes generalized eigenvalues and eigenvectors of a non-symmetric matrix.
| # | Name | Type | Description |
|---|---|---|---|
| 1 | B | TMtx | source TMtx |
| 2 | DAlpha | TVec | source TVec |
| 3 | DBeta | TVec | source TVec |
| 4 | VL | TMtx | source TMtx |
| 5 | VR | TMtx | source TMtx |
Result: stored in self (calling object)
A generalized eigenvalue for a pair of matrices (A = Self,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). The individual eigevalues can be computed as:
lambda(j) = dAlpha(j) / dBeta(j) ;