GGES3: computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized real Schur form (S,T), optionally, the left and/or right matrices of Schur vectors (VSL and VSR). This gives the generalized Schur factorization (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T.The leading columns of VSL and VSR then form an orthonormal basis for the corresponding left and right eigenspaces (deflating subspaces). (If only the generalized eigenvalues are needed, use the driver GGEV instead, which is faster.) A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0 or both being zero. A pair of matrices (S,T) is in generalized real Schur form if T is upper triangular with non-negative diagonal and S is block upper triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond to real generalized eigenvalues, while 2-by-2 blocks of S will be "standardized" by making the corresponding elements of T have the form: [ a 0 ] [ 0 b ] and the pair of corresponding 2-by-2 blocks in S and T will have a complex conjugate pair of generalized eigenvalues.
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GGES3: computes for a pair of N-by-N real nonsymmetric matrices (A,B), the generalized eigenvalues, the generalized real Schur form (S,T), optionally, the left and/or right matrices of Schur vectors (VSL and VSR). This gives the generalized Schur factorization (A,B) = ( (VSL)*S*(VSR)**T, (VSL)*T*(VSR)**T ) Optionally, it also orders the eigenvalues so that a selected cluster of eigenvalues appears in the leading diagonal blocks of the upper quasi-triangular matrix S and the upper triangular matrix T.The leading columns of VSL and VSR then form an orthonormal basis for the corresponding left and right eigenspaces (deflating subspaces). (If only the generalized eigenvalues are needed, use the driver GGEV instead, which is faster.) A generalized eigenvalue for a pair of matrices (A,B) is a scalar w or a ratio alpha/beta = w, such that A - w*B is singular. It is usually represented as the pair (alpha,beta), as there is a reasonable interpretation for beta=0 or both being zero. A pair of matrices (S,T) is in generalized real Schur form if T is upper triangular with non-negative diagonal and S is block upper triangular with 1-by-1 and 2-by-2 blocks. 1-by-1 blocks correspond to real generalized eigenvalues, while 2-by-2 blocks of S will be "standardized" by making the corresponding elements of T have the form: [ a 0 ] [ 0 b ] and the pair of corresponding 2-by-2 blocks in S and T will have a complex conjugate pair of generalized eigenvalues.
◆ la_cgges3()
| la_lapack::gges3::la_cgges3 |
◆ la_dgges3()
| la_lapack::gges3::la_dgges3 |
◆ la_qgges3()
| la_lapack::gges3::la_qgges3 |
◆ la_sgges3()
| la_lapack::gges3::la_sgges3 |
◆ la_wgges3()
| la_lapack::gges3::la_wgges3 |
◆ la_zgges3()
| la_lapack::gges3::la_zgges3 |
The documentation for this interface was generated from the following file:
1.13.2