trexc - Man Page

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

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.

Definition at line 125 of file ctrexc.f.

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.

Definition at line 146 of file dtrexc.f.

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.

Definition at line 146 of file strexc.f.

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.

Definition at line 125 of file ztrexc.f.