STREXC(3F) STREXC(3F)
STREXC - 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
SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO )
CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
STREXC 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
transformation 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-diagonal
elements of opposite sign.
COMPQ (input) CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) REAL array, dimension (LDT,N)
On entry, the upper quasi-triangular matrix T, in Schur Schur
canonical form. On exit, the reordered upper quasi-triangular
matrix, again in Schur canonical form.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) REAL array, dimension (LDQ,N)
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.
Page 1
STREXC(3F) STREXC(3F)
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IFST (input/output) INTEGER
ILST (input/output) INTEGER 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 differ from its input value by +1 or -1). 1 <= IFST
<= N; 1 <= ILST <= N.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 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.
STREXC(3F) STREXC(3F)
STREXC - 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
SUBROUTINE STREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, INFO )
CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
REAL Q( LDQ, * ), T( LDT, * ), WORK( * )
STREXC 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
transformation 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-diagonal
elements of opposite sign.
COMPQ (input) CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N (input) INTEGER
The order of the matrix T. N >= 0.
T (input/output) REAL array, dimension (LDT,N)
On entry, the upper quasi-triangular matrix T, in Schur Schur
canonical form. On exit, the reordered upper quasi-triangular
matrix, again in Schur canonical form.
LDT (input) INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q (input/output) REAL array, dimension (LDQ,N)
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.
Page 1
STREXC(3F) STREXC(3F)
LDQ (input) INTEGER
The leading dimension of the array Q. LDQ >= max(1,N).
IFST (input/output) INTEGER
ILST (input/output) INTEGER 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 differ from its input value by +1 or -1). 1 <= IFST
<= N; 1 <= ILST <= N.
WORK (workspace) REAL array, dimension (N)
INFO (output) INTEGER
= 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.
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