stgex2 (l) - Linux Manuals
stgex2: swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation
NAME
STGEX2 - swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformationSYNOPSIS
- SUBROUTINE STGEX2(
- WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ, J1, N1, N2, WORK, LWORK, INFO )
- LOGICAL WANTQ, WANTZ
- INTEGER INFO, J1, LDA, LDB, LDQ, LDZ, LWORK, N, N1, N2
- REAL A( LDA, * ), B( LDB, * ), Q( LDQ, * ), WORK( * ), Z( LDZ, * )
PURPOSE
STGEX2 swaps adjacent diagonal blocks (A11, B11) and (A22, B22) of size 1-by-1 or 2-by-2 in an upper (quasi) triangular matrix pair (A, B) by an orthogonal equivalence transformation. (A, B) must be in generalized real Schur canonical form (as returned by SGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks. B is upper triangular.Optionally, the matrices Q and Z of generalized Schur vectors are updated.
ARGUMENTS
- WANTQ (input) LOGICAL .TRUE. : update the left transformation matrix Q;
-
- WANTZ (input) LOGICAL
-
- N (input) INTEGER
- The order of the matrices A and B. N >= 0.
- A (input/output) REAL arrays, dimensions (LDA,N)
- On entry, the matrix A in the pair (A, B). On exit, the updated matrix A.
- LDA (input) INTEGER
- The leading dimension of the array A. LDA >= max(1,N).
- B (input/output) REAL arrays, dimensions (LDB,N)
- On entry, the matrix B in the pair (A, B). On exit, the updated matrix B.
- LDB (input) INTEGER
- The leading dimension of the array B. LDB >= max(1,N).
- Q (input/output) REAL array, dimension (LDZ,N)
- On entry, if WANTQ = .TRUE., the orthogonal matrix Q. On exit, the updated matrix Q. Not referenced if WANTQ = .FALSE..
- LDQ (input) INTEGER
- The leading dimension of the array Q. LDQ >= 1. If WANTQ = .TRUE., LDQ >= N.
- Z (input/output) REAL array, dimension (LDZ,N)
- On entry, if WANTZ =.TRUE., the orthogonal matrix Z. On exit, the updated matrix Z. Not referenced if WANTZ = .FALSE..
- LDZ (input) INTEGER
- The leading dimension of the array Z. LDZ >= 1. If WANTZ = .TRUE., LDZ >= N.
- J1 (input) INTEGER
- The index to the first block (A11, B11). 1 <= J1 <= N.
- N1 (input) INTEGER
- The order of the first block (A11, B11). N1 = 0, 1 or 2.
- N2 (input) INTEGER
- The order of the second block (A22, B22). N2 = 0, 1 or 2.
- WORK (workspace) REAL array, dimension (MAX(1,LWORK)).
- LWORK (input) INTEGER
- The dimension of the array WORK. LWORK >= MAX( N*(N2+N1), (N2+N1)*(N2+N1)*2 )
- INFO (output) INTEGER
-
=0: Successful exit
>0: If INFO = 1, the transformed matrix (A, B) would be too far from generalized Schur form; the blocks are not swapped and (A, B) and (Q, Z) are unchanged. The problem of swapping is too ill-conditioned. <0: If INFO = -16: LWORK is too small. Appropriate value for LWORK is returned in WORK(1).
FURTHER DETAILS
Based on contributions byBo Kagstrom and Peter Poromaa, Department of Computing Science,
Umea University, S-901 87 Umea, Sweden.
In the current code both weak and strong stability tests are performed. The user can omit the strong stability test by changing the internal logical parameter WANDS to .FALSE.. See ref. [2] for details.
[1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the