*> \brief \b CTGEXC
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
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*
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*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
* LDZ, IFST, ILST, INFO )
*
* .. Scalar Arguments ..
* LOGICAL WANTQ, WANTZ
* INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
* ..
* .. Array Arguments ..
* COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
* $ Z( LDZ, * )
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> CTGEXC reorders the generalized Schur decomposition of a complex
*> matrix pair (A,B), using an unitary equivalence transformation
*> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with
*> row index IFST is moved to row ILST.
*>
*> (A, B) must be in generalized Schur canonical form, that is, A and
*> B are both upper triangular.
*>
*> Optionally, the matrices Q and Z of generalized Schur vectors are
*> updated.
*>
*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H
*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] WANTQ
*> \verbatim
*> WANTQ is LOGICAL
*> .TRUE. : update the left transformation matrix Q;
*> .FALSE.: do not update Q.
*> \endverbatim
*>
*> \param[in] WANTZ
*> \verbatim
*> WANTZ is LOGICAL
*> .TRUE. : update the right transformation matrix Z;
*> .FALSE.: do not update Z.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The order of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in,out] A
*> \verbatim
*> A is COMPLEX array, dimension (LDA,N)
*> On entry, the upper triangular matrix A in the pair (A, B).
*> On exit, the updated matrix A.
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the array A. LDA >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] B
*> \verbatim
*> B is COMPLEX array, dimension (LDB,N)
*> On entry, the upper triangular matrix B in the pair (A, B).
*> On exit, the updated matrix B.
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the array B. LDB >= max(1,N).
*> \endverbatim
*>
*> \param[in,out] Q
*> \verbatim
*> Q is COMPLEX array, dimension (LDQ,N)
*> On entry, if WANTQ = .TRUE., the unitary matrix Q.
*> On exit, the updated matrix Q.
*> If WANTQ = .FALSE., Q is not referenced.
*> \endverbatim
*>
*> \param[in] LDQ
*> \verbatim
*> LDQ is INTEGER
*> The leading dimension of the array Q. LDQ >= 1;
*> If WANTQ = .TRUE., LDQ >= N.
*> \endverbatim
*>
*> \param[in,out] Z
*> \verbatim
*> Z is COMPLEX array, dimension (LDZ,N)
*> On entry, if WANTZ = .TRUE., the unitary matrix Z.
*> On exit, the updated matrix Z.
*> If WANTZ = .FALSE., Z is not referenced.
*> \endverbatim
*>
*> \param[in] LDZ
*> \verbatim
*> LDZ is INTEGER
*> The leading dimension of the array Z. LDZ >= 1;
*> If WANTZ = .TRUE., LDZ >= N.
*> \endverbatim
*>
*> \param[in] IFST
*> \verbatim
*> IFST is INTEGER
*> \endverbatim
*>
*> \param[in,out] ILST
*> \verbatim
*> ILST is INTEGER
*> Specify the reordering of the diagonal blocks of (A, B).
*> The block with row index IFST is moved to row ILST, by a
*> sequence of swapping between adjacent blocks.
*> \endverbatim
*>
*> \param[out] INFO
*> \verbatim
*> INFO is INTEGER
*> =0: Successful exit.
*> <0: if INFO = -i, the i-th argument had an illegal value.
*> =1: The transformed matrix pair (A, B) would be too far
*> from generalized Schur form; the problem is ill-
*> conditioned. (A, B) may have been partially reordered,
*> and ILST points to the first row of the current
*> position of the block being moved.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup complexGEcomputational
*
*> \par Contributors:
* ==================
*>
*> Bo Kagstrom and Peter Poromaa, Department of Computing Science,
*> Umea University, S-901 87 Umea, Sweden.
*
*> \par References:
* ================
*>
*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the
*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in
*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and
*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218.
*> \n
*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified
*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition
*> Estimation: Theory, Algorithms and Software, Report
*> UMINF - 94.04, Department of Computing Science, Umea University,
*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87.
*> To appear in Numerical Algorithms, 1996.
*> \n
*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software
*> for Solving the Generalized Sylvester Equation and Estimating the
*> Separation between Regular Matrix Pairs, Report UMINF - 93.23,
*> Department of Computing Science, Umea University, S-901 87 Umea,
*> Sweden, December 1993, Revised April 1994, Also as LAPACK working
*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1,
*> 1996.
*>
* =====================================================================
SUBROUTINE CTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z,
$ LDZ, IFST, ILST, INFO )
*
* -- LAPACK computational routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
LOGICAL WANTQ, WANTZ
INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), B( LDB, * ), Q( LDQ, * ),
$ Z( LDZ, * )
* ..
*
* =====================================================================
*
* .. Local Scalars ..
INTEGER HERE
* ..
* .. External Subroutines ..
EXTERNAL CTGEX2, XERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Decode and test input arguments.
INFO = 0
IF( N.LT.0 ) THEN
INFO = -3
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -5
ELSE IF( LDB.LT.MAX( 1, N ) ) THEN
INFO = -7
ELSE IF( LDQ.LT.1 .OR. WANTQ .AND. ( LDQ.LT.MAX( 1, N ) ) ) THEN
INFO = -9
ELSE IF( LDZ.LT.1 .OR. WANTZ .AND. ( LDZ.LT.MAX( 1, N ) ) ) THEN
INFO = -11
ELSE IF( IFST.LT.1 .OR. IFST.GT.N ) THEN
INFO = -12
ELSE IF( ILST.LT.1 .OR. ILST.GT.N ) THEN
INFO = -13
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'CTGEXC', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.LE.1 )
$ RETURN
IF( IFST.EQ.ILST )
$ RETURN
*
IF( IFST.LT.ILST ) THEN
*
HERE = IFST
*
10 CONTINUE
*
* Swap with next one below
*
CALL CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE + 1
IF( HERE.LT.ILST )
$ GO TO 10
HERE = HERE - 1
ELSE
HERE = IFST - 1
*
20 CONTINUE
*
* Swap with next one above
*
CALL CTGEX2( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, LDZ,
$ HERE, INFO )
IF( INFO.NE.0 ) THEN
ILST = HERE
RETURN
END IF
HERE = HERE - 1
IF( HERE.GE.ILST )
$ GO TO 20
HERE = HERE + 1
END IF
ILST = HERE
RETURN
*
* End of CTGEXC
*
END