table of contents
| trexc(3) | LAPACK | trexc(3) |
NAME¶
trexc - trexc: reorder Schur form
SYNOPSIS¶
Functions¶
subroutine ctrexc (compq, n, t, ldt, q, ldq, ifst, ilst,
info)
CTREXC subroutine dtrexc (compq, n, t, ldt, q, ldq, ifst, ilst,
work, info)
DTREXC subroutine strexc (compq, n, t, ldt, q, ldq, ifst, ilst,
work, info)
STREXC subroutine ztrexc (compq, n, t, ldt, q, ldq, ifst, ilst,
info)
ZTREXC
Detailed Description¶
Function Documentation¶
subroutine ctrexc (character compq, integer n, complex, dimension( ldt, * ) t, integer ldt, complex, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info)¶
CTREXC
Purpose:
CTREXC reorders the Schur factorization of a complex matrix
A = Q*T*Q**H, so that the diagonal element of T with row index IFST
is moved to row ILST.
The Schur form T is reordered by a unitary similarity transformation
Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
postmultiplying it with Z.
Parameters
COMPQ
COMPQ is CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N
N is INTEGER
The order of the matrix T. N >= 0.
If N == 0 arguments ILST and IFST may be any value.
T
T is COMPLEX array, dimension (LDT,N)
On entry, the upper triangular matrix T.
On exit, the reordered upper triangular matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q
Q is COMPLEX 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
unitary transformation matrix Z which reorders T.
If COMPQ = 'N', Q is not referenced.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = 'V', LDQ >= max(1,N).
IFST
IFST is INTEGER
ILST
ILST is INTEGER
Specify the reordering of the diagonal elements of T:
The element with row index IFST is moved to row ILST by a
sequence of transpositions between adjacent elements.
1 <= IFST <= N; 1 <= ILST <= N.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine dtrexc (character compq, integer n, double precision, dimension( ldt, * ) t, integer ldt, double precision, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, double precision, dimension( * ) work, integer info)¶
DTREXC
Purpose:
DTREXC 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 DHSEQR), 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.
Parameters
COMPQ
COMPQ is CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N
N is INTEGER
The order of the matrix T. N >= 0.
If N == 0 arguments ILST and IFST may be any value.
T
T is DOUBLE PRECISION 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
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q
Q is DOUBLE PRECISION 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.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = 'V', LDQ >= max(1,N).
IFST
IFST is INTEGER
ILST
ILST is 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
WORK is DOUBLE PRECISION array, dimension (N)
INFO
INFO is 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine strexc (character compq, integer n, real, dimension( ldt, * ) t, integer ldt, real, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, real, dimension( * ) work, integer info)¶
STREXC
Purpose:
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.
Parameters
COMPQ
COMPQ is CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N
N is INTEGER
The order of the matrix T. N >= 0.
If N == 0 arguments ILST and IFST may be any value.
T
T is 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
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q
Q is 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.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = 'V', LDQ >= max(1,N).
IFST
IFST is INTEGER
ILST
ILST is 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
WORK is REAL array, dimension (N)
INFO
INFO is 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.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
subroutine ztrexc (character compq, integer n, complex*16, dimension( ldt, * ) t, integer ldt, complex*16, dimension( ldq, * ) q, integer ldq, integer ifst, integer ilst, integer info)¶
ZTREXC
Purpose:
ZTREXC reorders the Schur factorization of a complex matrix
A = Q*T*Q**H, so that the diagonal element of T with row index IFST
is moved to row ILST.
The Schur form T is reordered by a unitary similarity transformation
Z**H*T*Z, and optionally the matrix Q of Schur vectors is updated by
postmultiplying it with Z.
Parameters
COMPQ
COMPQ is CHARACTER*1
= 'V': update the matrix Q of Schur vectors;
= 'N': do not update Q.
N
N is INTEGER
The order of the matrix T. N >= 0.
If N == 0 arguments ILST and IFST may be any value.
T
T is COMPLEX*16 array, dimension (LDT,N)
On entry, the upper triangular matrix T.
On exit, the reordered upper triangular matrix.
LDT
LDT is INTEGER
The leading dimension of the array T. LDT >= max(1,N).
Q
Q is COMPLEX*16 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
unitary transformation matrix Z which reorders T.
If COMPQ = 'N', Q is not referenced.
LDQ
LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = 'V', LDQ >= max(1,N).
IFST
IFST is INTEGER
ILST
ILST is INTEGER
Specify the reordering of the diagonal elements of T:
The element with row index IFST is moved to row ILST by a
sequence of transpositions between adjacent elements.
1 <= IFST <= N; 1 <= ILST <= N.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Author¶
Generated automatically by Doxygen for LAPACK from the source code.
| Wed Feb 7 2024 11:30:40 | Version 3.12.0 |