version 1.8, 2010/12/21 13:53:40
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version 1.16, 2017/06/17 10:54:05
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*> \brief \b DTGEXC |
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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 DTGEXC + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtgexc.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/dtgexc.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/dtgexc.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 DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
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* LDZ, IFST, ILST, WORK, LWORK, 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, LWORK, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION A( LDA, * ), B( LDB, * ), Q( LDQ, * ), |
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* $ WORK( * ), 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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*> DTGEXC reorders the generalized real Schur decomposition of a real |
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*> matrix pair (A,B) using an orthogonal equivalence transformation |
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*> |
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*> (A, B) = Q * (A, B) * Z**T, |
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*> |
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*> so that the diagonal block of (A, B) with row index IFST is moved |
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*> to row ILST. |
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*> |
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*> (A, B) must be in generalized real Schur canonical form (as returned |
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*> by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 |
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*> diagonal blocks. B is 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)**T = Q(out) * A(out) * Z(out)**T |
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*> Q(in) * B(in) * Z(in)**T = Q(out) * B(out) * Z(out)**T |
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*> |
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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 DOUBLE PRECISION array, dimension (LDA,N) |
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*> On entry, the matrix A in generalized real Schur canonical |
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*> form. |
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*> On exit, the updated matrix A, again in generalized |
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*> real Schur canonical form. |
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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 DOUBLE PRECISION array, dimension (LDB,N) |
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*> On entry, the matrix B in generalized real Schur canonical |
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*> form (A,B). |
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*> On exit, the updated matrix B, again in generalized |
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*> real Schur canonical form (A,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 DOUBLE PRECISION array, dimension (LDQ,N) |
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*> On entry, if WANTQ = .TRUE., the orthogonal 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 DOUBLE PRECISION array, dimension (LDZ,N) |
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*> On entry, if WANTZ = .TRUE., the orthogonal 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,out] 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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*> On exit, if IFST pointed on entry to the second row of |
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*> a 2-by-2 block, it is changed to point to the first row; |
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*> ILST always points to the first row of the block in its |
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*> final position (which may differ from its input value by |
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*> +1 or -1). 1 <= IFST, ILST <= N. |
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*> \endverbatim |
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*> |
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*> \param[out] WORK |
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*> \verbatim |
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*> WORK is DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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*> On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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*> \endverbatim |
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*> |
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*> \param[in] LWORK |
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*> \verbatim |
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*> LWORK is INTEGER |
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*> The dimension of the array WORK. |
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*> LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. |
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*> |
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*> If LWORK = -1, then a workspace query is assumed; the routine |
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*> only calculates the optimal size of the WORK array, returns |
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*> this value as the first entry of the WORK array, and no error |
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*> message related to LWORK is issued by XERBLA. |
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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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*> \date December 2016 |
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* |
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*> \ingroup doubleGEcomputational |
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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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*> \verbatim |
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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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*> \endverbatim |
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*> |
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* ===================================================================== |
SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
SUBROUTINE DTGEXC( WANTQ, WANTZ, N, A, LDA, B, LDB, Q, LDQ, Z, |
$ LDZ, IFST, ILST, WORK, LWORK, INFO ) |
$ LDZ, IFST, ILST, WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2.2) -- |
* -- LAPACK computational routine (version 3.7.0) -- |
* -- 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..-- |
* June 2010 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
LOGICAL WANTQ, WANTZ |
LOGICAL WANTQ, WANTZ |
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$ WORK( * ), Z( LDZ, * ) |
$ WORK( * ), Z( LDZ, * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
|
* |
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* DTGEXC reorders the generalized real Schur decomposition of a real |
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* matrix pair (A,B) using an orthogonal equivalence transformation |
|
* |
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* (A, B) = Q * (A, B) * Z', |
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* |
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* so that the diagonal block of (A, B) with row index IFST is moved |
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* to row ILST. |
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* |
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* (A, B) must be in generalized real Schur canonical form (as returned |
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* by DGGES), i.e. A is block upper triangular with 1-by-1 and 2-by-2 |
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* diagonal blocks. B is 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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* |
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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) DOUBLE PRECISION array, dimension (LDA,N) |
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* On entry, the matrix A in generalized real Schur canonical |
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* form. |
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* On exit, the updated matrix A, again in generalized |
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* real Schur canonical form. |
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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) DOUBLE PRECISION array, dimension (LDB,N) |
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* On entry, the matrix B in generalized real Schur canonical |
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* form (A,B). |
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* On exit, the updated matrix B, again in generalized |
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* real Schur canonical form (A,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) DOUBLE PRECISION array, dimension (LDQ,N) |
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* On entry, if WANTQ = .TRUE., the orthogonal 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) DOUBLE PRECISION array, dimension (LDZ,N) |
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* On entry, if WANTZ = .TRUE., the orthogonal 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/output) 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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* On exit, if IFST pointed on entry to the second row of |
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* a 2-by-2 block, it is changed to point to the first row; |
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* ILST always points to the first row of the block in its |
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* final position (which may differ from its input value by |
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* +1 or -1). 1 <= IFST, ILST <= N. |
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* |
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* WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) |
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* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. |
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* |
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* LWORK (input) INTEGER |
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* The dimension of the array WORK. |
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* LWORK >= 1 when N <= 1, otherwise LWORK >= 4*N + 16. |
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* |
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* If LWORK = -1, then a workspace query is assumed; the routine |
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* only calculates the optimal size of the WORK array, returns |
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* this value as the first entry of the WORK array, and no error |
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* message related to LWORK is issued by XERBLA. |
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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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* 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 |
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* Real-Time Applications, Kluwer Academic Publ. 1993, pp 195-218. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |