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version 1.19, 2023/08/07 08:39:40
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*> \brief \b ZTGEXC |
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* |
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* =========== DOCUMENTATION =========== |
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* |
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* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
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* |
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*> \htmlonly |
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*> Download ZTGEXC + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/ztgexc.f"> |
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*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/ztgexc.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/ztgexc.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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* SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
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* LDZ, IFST, ILST, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* LOGICAL WANTQ, WANTZ |
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* INTEGER IFST, ILST, INFO, LDA, LDB, LDQ, LDZ, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( LDA, * ), B( LDB, * ), Q( LDQ, * ), |
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* $ Z( LDZ, * ) |
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* .. |
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* |
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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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*> |
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*> ZTGEXC reorders the generalized Schur decomposition of a complex |
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*> matrix pair (A,B), using an unitary equivalence transformation |
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*> (A, B) := Q * (A, B) * Z**H, so that the diagonal block of (A, B) with |
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*> row index IFST is moved to row ILST. |
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*> |
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*> (A, B) must be in generalized Schur canonical form, that is, A and |
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*> B are both upper triangular. |
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*> |
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*> Optionally, the matrices Q and Z of generalized Schur vectors are |
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*> updated. |
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*> |
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*> Q(in) * A(in) * Z(in)**H = Q(out) * A(out) * Z(out)**H |
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*> Q(in) * B(in) * Z(in)**H = Q(out) * B(out) * Z(out)**H |
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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] WANTQ |
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*> \verbatim |
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*> WANTQ is LOGICAL |
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*> .TRUE. : update the left transformation matrix Q; |
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*> .FALSE.: do not update Q. |
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*> \endverbatim |
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*> |
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*> \param[in] WANTZ |
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*> \verbatim |
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*> WANTZ is LOGICAL |
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*> .TRUE. : update the right transformation matrix Z; |
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*> .FALSE.: do not update Z. |
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*> \endverbatim |
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*> |
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*> \param[in] N |
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*> \verbatim |
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*> N is INTEGER |
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*> The order of the matrices A and B. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension (LDA,N) |
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*> On entry, the upper triangular matrix A in the pair (A, B). |
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*> On exit, the updated matrix A. |
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*> \endverbatim |
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*> |
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*> \param[in] LDA |
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*> \verbatim |
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*> LDA is INTEGER |
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*> The leading dimension of the array A. LDA >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in,out] B |
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*> \verbatim |
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*> B is COMPLEX*16 array, dimension (LDB,N) |
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*> On entry, the upper triangular matrix B in the pair (A, B). |
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*> On exit, the updated matrix B. |
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*> \endverbatim |
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*> |
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*> \param[in] LDB |
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*> \verbatim |
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*> LDB is INTEGER |
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*> The leading dimension of the array B. LDB >= max(1,N). |
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*> \endverbatim |
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*> |
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*> \param[in,out] Q |
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*> \verbatim |
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*> Q is COMPLEX*16 array, dimension (LDQ,N) |
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*> On entry, if WANTQ = .TRUE., the unitary matrix Q. |
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*> On exit, the updated matrix Q. |
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*> If WANTQ = .FALSE., Q is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDQ |
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*> \verbatim |
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*> LDQ is INTEGER |
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*> The leading dimension of the array Q. LDQ >= 1; |
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*> If WANTQ = .TRUE., LDQ >= N. |
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*> \endverbatim |
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*> |
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*> \param[in,out] Z |
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*> \verbatim |
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*> Z is COMPLEX*16 array, dimension (LDZ,N) |
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*> On entry, if WANTZ = .TRUE., the unitary matrix Z. |
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*> On exit, the updated matrix Z. |
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*> If WANTZ = .FALSE., Z is not referenced. |
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*> \endverbatim |
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*> |
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*> \param[in] LDZ |
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*> \verbatim |
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*> LDZ is INTEGER |
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*> The leading dimension of the array Z. LDZ >= 1; |
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*> If WANTZ = .TRUE., LDZ >= N. |
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*> \endverbatim |
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*> |
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*> \param[in] IFST |
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*> \verbatim |
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*> IFST is INTEGER |
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*> \endverbatim |
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*> |
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*> \param[in,out] ILST |
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*> \verbatim |
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*> ILST is INTEGER |
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*> Specify the reordering of the diagonal blocks of (A, B). |
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*> The block with row index IFST is moved to row ILST, by a |
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*> sequence of swapping between adjacent blocks. |
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*> \endverbatim |
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*> |
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*> \param[out] INFO |
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*> \verbatim |
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*> INFO is INTEGER |
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*> =0: Successful exit. |
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*> <0: if INFO = -i, the i-th argument had an illegal value. |
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*> =1: The transformed matrix pair (A, B) would be too far |
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*> from generalized Schur form; the problem is ill- |
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*> conditioned. (A, B) may have been partially reordered, |
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*> and ILST points to the first row of the current |
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*> position of the block being moved. |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
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* |
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*> \ingroup complex16GEcomputational |
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* |
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*> \par Contributors: |
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* ================== |
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*> |
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*> Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
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*> Umea University, S-901 87 Umea, Sweden. |
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* |
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*> \par References: |
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* ================ |
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*> |
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*> [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the |
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*> Generalized Real Schur Form of a Regular Matrix Pair (A, B), in |
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*> M.S. Moonen et al (eds), Linear Algebra for Large Scale and |
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*> Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. |
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*> \n |
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*> [2] B. Kagstrom and P. Poromaa; Computing Eigenspaces with Specified |
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*> Eigenvalues of a Regular Matrix Pair (A, B) and Condition |
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*> Estimation: Theory, Algorithms and Software, Report |
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*> UMINF - 94.04, Department of Computing Science, Umea University, |
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*> S-901 87 Umea, Sweden, 1994. Also as LAPACK Working Note 87. |
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*> To appear in Numerical Algorithms, 1996. |
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*> \n |
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*> [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software |
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*> for Solving the Generalized Sylvester Equation and Estimating the |
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*> Separation between Regular Matrix Pairs, Report UMINF - 93.23, |
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*> Department of Computing Science, Umea University, S-901 87 Umea, |
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*> Sweden, December 1993, Revised April 1994, Also as LAPACK working |
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*> Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, |
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*> 1996. |
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*> |
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* ===================================================================== |
SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
SUBROUTINE ZTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
$ LDZ, IFST, ILST, INFO ) |
$ LDZ, IFST, ILST, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* November 2006 |
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* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL WANTQ, WANTZ |
LOGICAL WANTQ, WANTZ |
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$ Z( LDZ, * ) |
$ Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZTGEXC reorders the generalized Schur decomposition of a complex |
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* matrix pair (A,B), using an unitary equivalence transformation |
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* (A, B) := Q * (A, B) * Z', so that the diagonal block of (A, B) with |
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* row index IFST is moved to row ILST. |
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* |
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* (A, B) must be in generalized Schur canonical form, that is, A and |
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* B are both upper triangular. |
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* |
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* Optionally, the matrices Q and Z of generalized Schur vectors are |
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* updated. |
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* |
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* Q(in) * A(in) * Z(in)' = Q(out) * A(out) * Z(out)' |
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* Q(in) * B(in) * Z(in)' = Q(out) * B(out) * Z(out)' |
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* |
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* Arguments |
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* ========= |
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* |
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* WANTQ (input) LOGICAL |
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* .TRUE. : update the left transformation matrix Q; |
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* .FALSE.: do not update Q. |
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* |
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* WANTZ (input) LOGICAL |
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* .TRUE. : update the right transformation matrix Z; |
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* .FALSE.: do not update Z. |
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* |
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* N (input) INTEGER |
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* The order of the matrices A and B. N >= 0. |
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* |
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* A (input/output) COMPLEX*16 array, dimension (LDA,N) |
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* On entry, the upper triangular matrix A in the pair (A, B). |
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* On exit, the updated matrix A. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. LDA >= max(1,N). |
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* |
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* B (input/output) COMPLEX*16 array, dimension (LDB,N) |
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* On entry, the upper triangular matrix B in the pair (A, B). |
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* On exit, the updated matrix B. |
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* |
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* LDB (input) INTEGER |
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* The leading dimension of the array B. LDB >= max(1,N). |
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* |
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* Q (input/output) COMPLEX*16 array, dimension (LDZ,N) |
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* On entry, if WANTQ = .TRUE., the unitary matrix Q. |
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* On exit, the updated matrix Q. |
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* If WANTQ = .FALSE., Q is not referenced. |
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* |
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* LDQ (input) INTEGER |
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* The leading dimension of the array Q. LDQ >= 1; |
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* If WANTQ = .TRUE., LDQ >= N. |
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* |
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* Z (input/output) COMPLEX*16 array, dimension (LDZ,N) |
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* On entry, if WANTZ = .TRUE., the unitary matrix Z. |
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* On exit, the updated matrix Z. |
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* If WANTZ = .FALSE., Z is not referenced. |
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* |
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* LDZ (input) INTEGER |
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* The leading dimension of the array Z. LDZ >= 1; |
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* If WANTZ = .TRUE., LDZ >= N. |
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* |
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* IFST (input) INTEGER |
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* ILST (input/output) INTEGER |
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* Specify the reordering of the diagonal blocks of (A, B). |
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* The block with row index IFST is moved to row ILST, by a |
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* sequence of swapping between adjacent blocks. |
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* |
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* INFO (output) INTEGER |
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* =0: Successful exit. |
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* <0: if INFO = -i, the i-th argument had an illegal value. |
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* =1: The transformed matrix pair (A, B) would be too far |
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* from generalized Schur form; the problem is ill- |
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* conditioned. (A, B) may have been partially reordered, |
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* and ILST points to the first row of the current |
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* position of the block being moved. |
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* |
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* |
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* Further Details |
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* =============== |
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* |
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* Based on contributions by |
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* Bo Kagstrom and Peter Poromaa, Department of Computing Science, |
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* Umea University, S-901 87 Umea, Sweden. |
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* |
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* [1] B. Kagstrom; A Direct Method for Reordering Eigenvalues in the |
|
* Generalized Real Schur Form of a Regular Matrix Pair (A, B), in |
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* M.S. Moonen et al (eds), Linear Algebra for Large Scale and |
|
* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. |
|
* |
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* [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. |
|
* |
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* [3] B. Kagstrom and P. Poromaa, LAPACK-Style Algorithms and Software |
|
* for Solving the Generalized Sylvester Equation and Estimating the |
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* 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 |
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* Note 75. To appear in ACM Trans. on Math. Software, Vol 22, No 1, |
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* 1996. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |