Visible to Intel only — GUID: GUID-4EF87F9E-03A1-4701-AF95-3BDA7FDD7F60
Visible to Intel only — GUID: GUID-4EF87F9E-03A1-4701-AF95-3BDA7FDD7F60
?tgexc
Reorders the generalized Schur decomposition of a pair of matrices (A,B) so that one diagonal block of (A,B) moves to another row index.
Syntax
call stgexc(wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)
call dtgexc(wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, work, lwork, info)
call ctgexc(wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)
call ztgexc(wantq, wantz, n, a, lda, b, ldb, q, ldq, z, ldz, ifst, ilst, info)
call tgexc(a, b [,ifst] [,ilst] [,z] [,q] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine reorders the generalized real-Schur/Schur decomposition of a real/complex matrix pair (A,B) using an orthogonal/unitary equivalence transformation
(A,B) = Q*(A,B)*ZH,
so that the diagonal block of (A, B) with row index ifst is moved to row ilst. Matrix pair (A, B) must be in a generalized real-Schur/Schur canonical form (as returned by gges), that is, A is block upper triangular with 1-by-1 and 2-by-2 diagonal blocks and B is upper triangular. Optionally, the matrices Q and Z of generalized Schur vectors are updated.
Qin*Ain*ZinT = Qout*Aout*ZoutT
Qin*Bin*ZinT = Qout*Bout*ZoutT.
Input Parameters
- wantq, wantz
-
LOGICAL.
If wantq = .TRUE., update the left transformation matrix Q;
If wantq = .FALSE., do not update Q;
If wantz = .TRUE., update the right transformation matrix Z;
If wantz = .FALSE., do not update Z.
- n
-
INTEGER. The order of the matrices A and B (n≥ 0).
- a, b, q, z
-
REAL for stgexc
DOUBLE PRECISION for dtgexc
COMPLEX for ctgexc
DOUBLE COMPLEX for ztgexc.
Arrays:
a(lda,*) contains the matrix A.
The second dimension of a must be at least max(1, n).
b(ldb,*) contains the matrix B. The second dimension of b must be at least max(1, n).
q(ldq,*)
If wantq = .FALSE., then q is not referenced.
If wantq = .TRUE., then q must contain the orthogonal/unitary matrix Q.
The second dimension of q must be at least max(1, n).
z(ldz,*)
If wantz = .FALSE., then z is not referenced.
If wantz = .TRUE., then z must contain the orthogonal/unitary matrix Z.
The second dimension of z must be at least max(1, n).
- lda
-
INTEGER. The leading dimension of a; at least max(1, n).
- ldb
-
INTEGER. The leading dimension of b; at least max(1, n).
- ldq
-
INTEGER. The leading dimension of q;
If wantq = .FALSE., then ldq≥ 1.
If wantq = .TRUE., then ldq≥ max(1, n).
- ldz
-
INTEGER. The leading dimension of z;
If wantz = .FALSE., then ldz≥ 1.
If wantz = .TRUE., then ldz≥ max(1, n).
- ifst, ilst
-
INTEGER. Specify the reordering of the diagonal blocks of (A, B). The block with row index ifst is moved to row ilst, by a sequence of swapping between adjacent blocks. Constraint: 1 ≤ifst, ilst≤n.
- work
-
REAL for stgexc;
DOUBLE PRECISION for dtgexc.
Workspace array, size (lwork). Used in real flavors only.
- lwork
-
INTEGER. The dimension of work; must be at least 4n +16.
If lwork = -1, then a workspace query is assumed; the routine only calculates the optimal size of the work array, returns this value as the first entry of the work array, and no error message related to lwork is issued by xerbla. See Application Notes for details.
Output Parameters
- a, b, q, z
-
Overwritten by the updated matrices A,B, Q, and Z respectively.
- ifst, ilst
-
Overwritten for real flavors only.
If ifst pointed to the second row of a 2 by 2 block on entry, it is changed to point to the first row; ilst always points to the first row of the block in its final position (which may differ from its input value by ±1).
- info
-
INTEGER.
If info = 0, the execution is successful.
If info = -i, the i-th parameter had an illegal value.
If info = 1, the transformed matrix pair (A, B) would be too far from generalized Schur form; the problem is ill-conditioned. (A, B) may have been partially reordered, and ilst points to the first row of the current position of the block being moved.
LAPACK 95 Interface Notes
Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or restorable arguments, see LAPACK 95 Interface Conventions.
Specific details for the routine tgexc interface are the following:
- a
-
Holds the matrix A of size (n,n).
- b
-
Holds the matrix B of size (n,n).
- z
-
Holds the matrix Z of size (n,n).
- q
-
Holds the matrix Q of size (n,n).
- wantq
-
Restored based on the presence of the argument q as follows:
wantq = .TRUE, if q is present,
wantq = .FALSE, if q is omitted.
- wantz
-
Restored based on the presence of the argument z as follows:
wantz = .TRUE, if z is present,
wantz = .FALSE, if z is omitted.
Application Notes
If it is not clear how much workspace to supply, use a generous value of lwork for the first run, or set lwork = -1.
In first case the routine completes the task, though probably not so fast as with a recommended workspace, and provides the recommended workspace in the first element of the corresponding array work on exit. Use this value (work(1)) for subsequent runs.
If lwork = -1, then the routine returns immediately and provides the recommended workspace in the first element of the corresponding array (work). This operation is called a workspace query.
Note that if lwork is less than the minimal required value and is not equal to -1, then the routine returns immediately with an error exit and does not provide any information on the recommended workspace.