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

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