*> \brief \b CTGEXC * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * *> \htmlonly *> Download CTGEXC + dependencies *> *> [TGZ] *> *> [ZIP] *> *> [TXT] *> \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. * *> \date June 2017 * *> \ingroup complexGEcomputational * *> \par Contributors: * ================== *> *> Bo Kagstrom and Peter Poromaa, Department of Computing Science, *> Umea University, S-901 87 Umea, Sweden. * *> \par References: * ================ *> *>  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 *>  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 *>  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 (version 3.7.1) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * June 2017 * * .. 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