version 1.5, 2010/08/07 13:22:28
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version 1.8, 2011/11/21 20:43:06
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*> \brief \b DTREXC |
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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 DTREXC + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dtrexc.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/dtrexc.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/dtrexc.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 DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, |
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* INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER COMPQ |
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* INTEGER IFST, ILST, INFO, LDQ, LDT, N |
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* .. |
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* .. Array Arguments .. |
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* DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) |
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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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*> DTREXC reorders the real Schur factorization of a real matrix |
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*> A = Q*T*Q**T, so that the diagonal block of T with row index IFST is |
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*> moved to row ILST. |
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*> |
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*> The real Schur form T is reordered by an orthogonal similarity |
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*> transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors |
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*> is updated by postmultiplying it with Z. |
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*> |
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*> T must be in Schur canonical form (as returned by DHSEQR), that is, |
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*> block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each |
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*> 2-by-2 diagonal block has its diagonal elements equal and its |
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*> off-diagonal elements of opposite sign. |
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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] COMPQ |
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*> \verbatim |
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*> COMPQ is CHARACTER*1 |
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*> = 'V': update the matrix Q of Schur vectors; |
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*> = 'N': do not update Q. |
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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 matrix T. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in,out] T |
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*> \verbatim |
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*> T is DOUBLE PRECISION array, dimension (LDT,N) |
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*> On entry, the upper quasi-triangular matrix T, in Schur |
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*> Schur canonical form. |
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*> On exit, the reordered upper quasi-triangular matrix, again |
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*> in Schur canonical form. |
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*> \endverbatim |
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*> |
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*> \param[in] LDT |
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*> \verbatim |
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*> LDT is INTEGER |
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*> The leading dimension of the array T. LDT >= 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 COMPQ = 'V', the matrix Q of Schur vectors. |
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*> On exit, if COMPQ = 'V', Q has been postmultiplied by the |
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*> orthogonal transformation matrix Z which reorders T. |
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*> If COMPQ = 'N', 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 >= max(1,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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*> |
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*> Specify the reordering of the diagonal blocks of T. |
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*> The block with row index IFST is moved to row ILST, by a |
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*> sequence of transpositions between adjacent blocks. |
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*> On exit, if IFST pointed on entry to the second row of a |
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*> 2-by-2 block, it is changed to point to the first row; ILST |
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*> always points to the first row of the block in its final |
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*> position (which may differ from its input value by +1 or -1). |
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*> 1 <= IFST <= N; 1 <= 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 (N) |
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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: two adjacent blocks were too close to swap (the problem |
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*> is very ill-conditioned); T may have been partially |
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*> reordered, and ILST points to the first row of the |
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*> current 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 November 2011 |
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* |
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*> \ingroup doubleOTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, |
SUBROUTINE DTREXC( COMPQ, N, T, LDT, Q, LDQ, IFST, ILST, WORK, |
$ INFO ) |
$ INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- LAPACK computational routine (version 3.4.0) -- |
* -- 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..-- |
* November 2006 |
* November 2011 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER COMPQ |
CHARACTER COMPQ |
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DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) |
DOUBLE PRECISION Q( LDQ, * ), T( LDT, * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* DTREXC reorders the real Schur factorization of a real matrix |
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* A = Q*T*Q**T, so that the diagonal block of T with row index IFST is |
|
* moved to row ILST. |
|
* |
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* The real Schur form T is reordered by an orthogonal similarity |
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* transformation Z**T*T*Z, and optionally the matrix Q of Schur vectors |
|
* is updated by postmultiplying it with Z. |
|
* |
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* T must be in Schur canonical form (as returned by DHSEQR), that is, |
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* block upper triangular with 1-by-1 and 2-by-2 diagonal blocks; each |
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* 2-by-2 diagonal block has its diagonal elements equal and its |
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* off-diagonal elements of opposite sign. |
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* |
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* Arguments |
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* ========= |
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* |
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* COMPQ (input) CHARACTER*1 |
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* = 'V': update the matrix Q of Schur vectors; |
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* = 'N': do not update Q. |
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* |
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* N (input) INTEGER |
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* The order of the matrix T. N >= 0. |
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* |
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* T (input/output) DOUBLE PRECISION array, dimension (LDT,N) |
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* On entry, the upper quasi-triangular matrix T, in Schur |
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* Schur canonical form. |
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* On exit, the reordered upper quasi-triangular matrix, again |
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* in Schur canonical form. |
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* |
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* LDT (input) INTEGER |
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* The leading dimension of the array T. LDT >= 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 COMPQ = 'V', the matrix Q of Schur vectors. |
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* On exit, if COMPQ = 'V', Q has been postmultiplied by the |
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* orthogonal transformation matrix Z which reorders T. |
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* If COMPQ = 'N', 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 >= max(1,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 T. |
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* The block with row index IFST is moved to row ILST, by a |
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* sequence of transpositions between adjacent blocks. |
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* On exit, if IFST pointed on entry to the second row of a |
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* 2-by-2 block, it is changed to point to the first row; ILST |
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* always points to the first row of the block in its final |
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* position (which may differ from its input value by +1 or -1). |
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* 1 <= IFST <= N; 1 <= ILST <= N. |
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* |
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* WORK (workspace) DOUBLE PRECISION array, dimension (N) |
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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: two adjacent blocks were too close to swap (the problem |
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* is very ill-conditioned); T may have been partially |
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* reordered, and ILST points to the first row of the |
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* current position of the block being moved. |
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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |