Visible to Intel only — GUID: GUID-CAFC1A46-A123-4D82-8515-01E92CE63CAA
Visible to Intel only — GUID: GUID-CAFC1A46-A123-4D82-8515-01E92CE63CAA
?trexc
Reorders the Schur factorization of a general matrix.
Syntax
call strexc(compq, n, t, ldt, q, ldq, ifst, ilst, work, info)
call dtrexc(compq, n, t, ldt, q, ldq, ifst, ilst, work, info)
call ctrexc(compq, n, t, ldt, q, ldq, ifst, ilst, info)
call ztrexc(compq, n, t, ldt, q, ldq, ifst, ilst, info)
call trexc(t, ifst, ilst [,q] [,info])
Include Files
- mkl.fi, lapack.f90
Description
The routine reorders the Schur factorization of a general matrix A = Q*T*QH, so that the diagonal element or block of T with row index ifst is moved to row ilst.
The reordered Schur form S is computed by an unitary (or, for real flavors, orthogonal) similarity transformation: S = ZH*T*Z. Optionally the updated matrix P of Schur vectors is computed as P = Q*Z, giving A = P*S*PH.
Input Parameters
- compq
-
CHARACTER*1. Must be 'V' or 'N'.
If compq = 'V', then the Schur vectors (Q) are updated.
If compq = 'N', then no Schur vectors are updated.
- n
-
INTEGER. The order of the matrix T (n≥ 0).
- t, q
-
REAL for strexc
DOUBLE PRECISION for dtrexc
COMPLEX for ctrexc
DOUBLE COMPLEX for ztrexc.
Arrays:
t(ldt,*) contains the n-by-n matrix T.
The second dimension of t must be at least max(1, n).
q(ldq,*)
If compq = 'V', then q must contain Q (Schur vectors).
If compq = 'N', then q is not referenced.
The second dimension of q must be at least max(1, n) if compq = 'V' and at least 1 if compq = 'N'.
- ldt
-
INTEGER. The leading dimension of t; at least max(1, n).
- ldq
-
INTEGER. The leading dimension of q;
If compq = 'N', then ldq≥ 1.
If compq = 'V', then ldq≥ max(1, n).
- ifst, ilst
-
INTEGER. 1 ≤ifst≤n; 1 ≤ilst≤n.
Must specify the reordering of the diagonal elements (or blocks, which is possible for real flavors) of the matrix T. The element (or block) with row index ifst is moved to row ilst by a sequence of exchanges between adjacent elements (or blocks).
- work
-
REAL for strexc
DOUBLE PRECISION for dtrexc.
Array, size at least max (1, n).
Output Parameters
- t
-
Overwritten by the updated matrix S.
- q
-
If compq = 'V', q contains the updated matrix of Schur vectors.
- 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.
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 trexc interface are the following:
- t
-
Holds the matrix T of size (n,n).
- q
-
Holds the matrix Q of size (n,n).
- compq
-
Restored based on the presence of the argument q as follows:
compq = 'V', if q is present,
compq = 'N', if q is omitted.
Application Notes
The computed matrix S is exactly similar to a matrix T+E, where ||E||2 = O(ε)*||T||2, and ε is the machine precision.
Note that if a 2 by 2 diagonal block is involved in the re-ordering, its off-diagonal elements are in general changed; the diagonal elements and the eigenvalues of the block are unchanged unless the block is sufficiently ill-conditioned, in which case they may be noticeably altered. It is possible for a 2 by 2 block to break into two 1 by 1 blocks, that is, for a pair of complex eigenvalues to become purely real.
The approximate number of floating-point operations is
for real flavors: |
6n(ifst-ilst) if compq = 'N'; 12n(ifst-ilst) if compq = 'V'; |
for complex flavors: |
20n(ifst-ilst) if compq = 'N'; 40n(ifst-ilst) if compq = 'V'. |