strexc(3P) Sun Performance Library strexc(3P)NAMEstrexc - reorder the real Schur factorization of a real matrix A =
Q*T*Q**T, so that the diagonal block of T with row index IFST is moved
to row ILST
SYNOPSIS
SUBROUTINE STREXC(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO)
CHARACTER * 1 COMPQ
INTEGER N, LDT, LDQ, IFST, ILST, INFO
REAL T(LDT,*), Q(LDQ,*), WORK(*)
SUBROUTINE STREXC_64(COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK,
INFO)
CHARACTER * 1 COMPQ
INTEGER*8 N, LDT, LDQ, IFST, ILST, INFO
REAL T(LDT,*), Q(LDQ,*), WORK(*)
F95 INTERFACE
SUBROUTINE TREXC(COMPQ, N, T, [LDT], Q, [LDQ], IFST, ILST, [WORK],
[INFO])
CHARACTER(LEN=1) :: COMPQ
INTEGER :: N, LDT, LDQ, IFST, ILST, INFO
REAL, DIMENSION(:) :: WORK
REAL, DIMENSION(:,:) :: T, Q
SUBROUTINE TREXC_64(COMPQ, N, T, [LDT], Q, [LDQ], IFST, ILST, [WORK],
[INFO])
CHARACTER(LEN=1) :: COMPQ
INTEGER(8) :: N, LDT, LDQ, IFST, ILST, INFO
REAL, DIMENSION(:) :: WORK
REAL, DIMENSION(:,:) :: T, Q
C INTERFACE
#include <sunperf.h>
void strexc(char compq, int n, float *t, int ldt, float *q, int ldq,
int *ifst, int *ilst, int *info);
void strexc_64(char compq, long n, float *t, long ldt, float *q, long
ldq, long *ifst, long *ilst, long *info);
PURPOSEstrexc reorders the real Schur factorization of a real matrix A =
Q*T*Q**T, so that the diagonal block of T with row index IFST is moved
to row ILST.
The real Schur form T is reordered by an orthogonal similarity trans‐
formation Z**T*T*Z, and optionally the matrix Q of Schur vectors is
updated by postmultiplying it with Z.
T must be in Schur canonical form (as returned by SHSEQR), that is,
block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each
2-by-2 diagonal block has its diagonal elements equal and its off-diag‐
onal elements of opposite sign.
ARGUMENTS
COMPQ (input)
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N (input) The order of the matrix T. N >= 0.
T (input/output)
On entry, the upper quasi-triangular matrix T, in Schur Schur
canonical form. On exit, the reordered upper quasi-triangu‐
lar matrix, again in Schur canonical form.
LDT (input)
The leading dimension of the array T. LDT >= max(1,N).
Q (input) On entry, if COMPQ = 'V', the matrix Q of Schur vectors. On
exit, if COMPQ = 'V', Q has been postmultiplied by the
orthogonal transformation matrix Z which reorders T. If
COMPQ = 'N', Q is not referenced.
LDQ (input)
The leading dimension of the array Q. LDQ >= max(1,N).
IFST (input/output)
Specify the reordering of the diagonal blocks of T. The
block with row index IFST is moved to row ILST, by a sequence
of transpositions between adjacent blocks. On exit, if IFST
pointed on entry to the second row of a 2-by-2 block, 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 dif‐
fer from its input value by +1 or -1). 1 <= IFST <= N; 1 <=
ILST <= N.
ILST (input/output)
See the description of IFST.
WORK (workspace)
dimension(N)
INFO (output)
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
= 1: two adjacent blocks were too close to swap (the problem
is very ill-conditioned); T may have been partially
reordered, and ILST points to the first row of the current
position of the block being moved.
6 Mar 2009 strexc(3P)