Man page - trexc(3)

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Manual

trexc

NAME
SYNOPSIS
Functions
Detailed Description
Function Documentation
subroutine ctrexc (character compq, integer n, complex, dimension( ldt, * )t, integer ldt, complex, dimension( ldq, * ) q, integer ldq, integerifst, integer ilst, integer info)
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)
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)
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)
Author

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, integerifst, 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
= ā€™Vā€™: update the matrix Q of Schur vectors;
= ā€™Nā€™: 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 = ā€™Vā€™, the matrix Q of Schur vectors.
On exit, if COMPQ = ā€™Vā€™, Q has been postmultiplied by the
unitary transformation matrix Z which reorders T.
If COMPQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = ā€™Vā€™, 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
= ā€™Vā€™: update the matrix Q of Schur vectors;
= ā€™Nā€™: 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 = ā€™Vā€™, the matrix Q of Schur vectors.
On exit, if COMPQ = ā€™Vā€™, Q has been postmultiplied by the
orthogonal transformation matrix Z which reorders T.
If COMPQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = ā€™Vā€™, 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
= ā€™Vā€™: update the matrix Q of Schur vectors;
= ā€™Nā€™: 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 = ā€™Vā€™, the matrix Q of Schur vectors.
On exit, if COMPQ = ā€™Vā€™, Q has been postmultiplied by the
orthogonal transformation matrix Z which reorders T.
If COMPQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = ā€™Vā€™, 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
= ā€™Vā€™: update the matrix Q of Schur vectors;
= ā€™Nā€™: 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 = ā€™Vā€™, the matrix Q of Schur vectors.
On exit, if COMPQ = ā€™Vā€™, Q has been postmultiplied by the
unitary transformation matrix Z which reorders T.
If COMPQ = ā€™Nā€™, Q is not referenced.

LDQ

LDQ is INTEGER
The leading dimension of the array Q. LDQ >= 1, and if
COMPQ = ā€™Vā€™, 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

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