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.

Definition at line 125 of file ctrexc.f.

  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.

Definition at line 146 of file dtrexc.f.

  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.

Definition at line 146 of file strexc.f.

  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.

Definition at line 125 of file ztrexc.f.

Author

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