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*> \brief \b ZTREXC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download ZTREXC + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztrexc.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztrexc.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztrexc.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* .. Scalar Arguments ..
* CHARACTER COMPQ
* INTEGER IFST, ILST, INFO, LDQ, LDT, N
* ..
* .. Array Arguments ..
* COMPLEX*16 Q( LDQ, * ), T( LDT, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> 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
*> postmultplying it with Z.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] COMPQ
*> \verbatim
*> COMPQ is CHARACTER*1
*> = 'V': update the matrix Q of Schur vectors;
*> = 'N': do not update Q.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrix T. N >= 0.
*> If N == 0 arguments ILST and IFST may be any value.
*> \endverbatim
*>
*> \param[in,out] T
*> \verbatim
*> T is COMPLEX*16 array, dimension (LDT,N)
*> On entry, the upper triangular matrix T.
*> On exit, the reordered upper triangular matrix.
*> \endverbatim
*>
*> \param[in] LDT
*> \verbatim
*> LDT is INTEGER
*> The leading dimension of the array T. LDT >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= 1, and if
*> COMPQ = 'V', LDQ >= max(1,N).
*> \endverbatim
*>
*> \param[in] IFST
*> \verbatim
*> IFST is INTEGER
*> \endverbatim
*>
*> \param[in] ILST
*> \verbatim
*> 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.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> = 0: successful exit
*> < 0: if INFO = -i, the i-th argument had an illegal value
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex16OTHERcomputational
*
* =====================================================================
SUBROUTINE ZTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, INFO )
*
* -- LAPACK computational routine (version 3.7.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* December 2016
*
* .. Scalar Arguments ..
CHARACTER COMPQ
INTEGER IFST, ILST, INFO, LDQ, LDT, N
* ..
* .. Array Arguments ..
COMPLEX*16 Q( LDQ, * ), T( LDT, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
LOGICAL WANTQ
INTEGER K, M1, M2, M3
DOUBLE PRECISION CS
COMPLEX*16 SN, T11, T22, TEMP
* ..
* .. External Functions ..
LOGICAL LSAME
EXTERNAL LSAME
* ..
* .. External Subroutines ..
EXTERNAL XERBLA, ZLARTG, ZROT
* ..
* .. Intrinsic Functions ..
INTRINSIC DCONJG, MAX
* ..
* .. Executable Statements ..
*
* Decode and test the input parameters.
*
INFO = 0
WANTQ = LSAME( COMPQ, 'V' )
IF( .NOT.LSAME( COMPQ, 'N' ) .AND. .NOT.WANTQ ) THEN
INFO = -1
ELSE IF( N.LT.0 ) THEN
INFO = -2
ELSE IF( LDT.LT.MAX( 1, N ) ) THEN
INFO = -4
ELSE IF( LDQ.LT.1 .OR. ( WANTQ .AND. LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -6
ELSE IF(( IFST.LT.1 .OR. IFST.GT.N ).AND.( N.GT.0 )) THEN
INFO = -7
ELSE IF(( ILST.LT.1 .OR. ILST.GT.N ).AND.( N.GT.0 )) THEN
INFO = -8
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZTREXC', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 .OR. IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
* Move the IFST-th diagonal element forward down the diagonal.
*
M1 = 0
M2 = -1
M3 = 1
ELSE
*
* Move the IFST-th diagonal element backward up the diagonal.
*
M1 = -1
M2 = 0
M3 = -1
END IF
*
DO 10 K = IFST + M1, ILST + M2, M3
*
* Interchange the k-th and (k+1)-th diagonal elements.
*
T11 = T( K, K )
T22 = T( K+1, K+1 )
*
* Determine the transformation to perform the interchange.
*
CALL ZLARTG( T( K, K+1 ), T22-T11, CS, SN, TEMP )
*
* Apply transformation to the matrix T.
*
IF( K+2.LE.N )
$ CALL ZROT( N-K-1, T( K, K+2 ), LDT, T( K+1, K+2 ), LDT, CS,
$ SN )
CALL ZROT( K-1, T( 1, K ), 1, T( 1, K+1 ), 1, CS,
$ DCONJG( SN ) )
*
T( K, K ) = T22
T( K+1, K+1 ) = T11
*
IF( WANTQ ) THEN
*
* Accumulate transformation in the matrix Q.
*
CALL ZROT( N, Q( 1, K ), 1, Q( 1, K+1 ), 1, CS,
$ DCONJG( SN ) )
END IF
*
10 CONTINUE
*
RETURN
*
* End of ZTREXC
*
END
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