version 1.5, 2010/08/07 13:22:47
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version 1.17, 2017/06/17 10:54:34
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*> \brief \b ZUNMLQ |
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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 ZUNMLQ + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmlq.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/zunmlq.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/zunmlq.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 ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
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* WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER SIDE, TRANS |
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* INTEGER INFO, K, LDA, LDC, LWORK, M, N |
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* .. |
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* .. Array Arguments .. |
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* COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), 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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*> ZUNMLQ overwrites the general complex M-by-N matrix C with |
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*> |
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*> SIDE = 'L' SIDE = 'R' |
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*> TRANS = 'N': Q * C C * Q |
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*> TRANS = 'C': Q**H * C C * Q**H |
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*> |
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*> where Q is a complex unitary matrix defined as the product of k |
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*> elementary reflectors |
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*> |
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*> Q = H(k)**H . . . H(2)**H H(1)**H |
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*> |
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*> as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N |
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*> if SIDE = 'R'. |
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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] SIDE |
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*> \verbatim |
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*> SIDE is CHARACTER*1 |
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*> = 'L': apply Q or Q**H from the Left; |
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*> = 'R': apply Q or Q**H from the Right. |
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*> \endverbatim |
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*> |
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*> \param[in] TRANS |
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*> \verbatim |
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*> TRANS is CHARACTER*1 |
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*> = 'N': No transpose, apply Q; |
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*> = 'C': Conjugate transpose, apply Q**H. |
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*> \endverbatim |
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*> |
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*> \param[in] M |
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*> \verbatim |
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*> M is INTEGER |
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*> The number of rows of the matrix C. M >= 0. |
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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 number of columns of the matrix C. N >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] K |
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*> \verbatim |
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*> K is INTEGER |
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*> The number of elementary reflectors whose product defines |
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*> the matrix Q. |
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*> If SIDE = 'L', M >= K >= 0; |
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*> if SIDE = 'R', N >= K >= 0. |
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*> \endverbatim |
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*> |
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*> \param[in] A |
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*> \verbatim |
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*> A is COMPLEX*16 array, dimension |
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*> (LDA,M) if SIDE = 'L', |
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*> (LDA,N) if SIDE = 'R' |
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*> The i-th row must contain the vector which defines the |
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*> elementary reflector H(i), for i = 1,2,...,k, as returned by |
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*> ZGELQF in the first k rows of its array argument 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,K). |
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*> \endverbatim |
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*> |
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*> \param[in] TAU |
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*> \verbatim |
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*> TAU is COMPLEX*16 array, dimension (K) |
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*> TAU(i) must contain the scalar factor of the elementary |
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*> reflector H(i), as returned by ZGELQF. |
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*> \endverbatim |
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*> |
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*> \param[in,out] C |
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*> \verbatim |
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*> C is COMPLEX*16 array, dimension (LDC,N) |
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*> On entry, the M-by-N matrix C. |
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*> On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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*> \endverbatim |
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*> |
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*> \param[in] LDC |
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*> \verbatim |
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*> LDC is INTEGER |
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*> The leading dimension of the array C. LDC >= max(1,M). |
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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 COMPLEX*16 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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*> If SIDE = 'L', LWORK >= max(1,N); |
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*> if SIDE = 'R', LWORK >= max(1,M). |
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*> For good performance, LWORK should generally be larger. |
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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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*> \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 complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
SUBROUTINE ZUNMLQ( SIDE, TRANS, M, N, K, A, LDA, TAU, C, LDC, |
$ WORK, LWORK, INFO ) |
$ WORK, LWORK, INFO ) |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* -- 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..-- |
* November 2006 |
* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
CHARACTER SIDE, TRANS |
CHARACTER SIDE, TRANS |
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COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
COMPLEX*16 A( LDA, * ), C( LDC, * ), TAU( * ), WORK( * ) |
* .. |
* .. |
* |
* |
* Purpose |
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* ======= |
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* |
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* ZUNMLQ overwrites the general complex M-by-N matrix C with |
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* |
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* SIDE = 'L' SIDE = 'R' |
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* TRANS = 'N': Q * C C * Q |
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* TRANS = 'C': Q**H * C C * Q**H |
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* |
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* where Q is a complex unitary matrix defined as the product of k |
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* elementary reflectors |
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* |
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* Q = H(k)' . . . H(2)' H(1)' |
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* |
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* as returned by ZGELQF. Q is of order M if SIDE = 'L' and of order N |
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* if SIDE = 'R'. |
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* |
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* Arguments |
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* ========= |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': apply Q or Q**H from the Left; |
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* = 'R': apply Q or Q**H from the Right. |
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* |
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* TRANS (input) CHARACTER*1 |
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* = 'N': No transpose, apply Q; |
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* = 'C': Conjugate transpose, apply Q**H. |
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* |
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* M (input) INTEGER |
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* The number of rows of the matrix C. M >= 0. |
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* |
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* N (input) INTEGER |
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* The number of columns of the matrix C. N >= 0. |
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* |
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* K (input) INTEGER |
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* The number of elementary reflectors whose product defines |
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* the matrix Q. |
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* If SIDE = 'L', M >= K >= 0; |
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* if SIDE = 'R', N >= K >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension |
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* (LDA,M) if SIDE = 'L', |
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* (LDA,N) if SIDE = 'R' |
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* The i-th row must contain the vector which defines the |
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* elementary reflector H(i), for i = 1,2,...,k, as returned by |
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* ZGELQF in the first k rows of its array argument A. |
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* A is modified by the routine but restored on exit. |
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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,K). |
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* |
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* TAU (input) COMPLEX*16 array, dimension (K) |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i), as returned by ZGELQF. |
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* |
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* C (input/output) COMPLEX*16 array, dimension (LDC,N) |
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* On entry, the M-by-N matrix C. |
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* On exit, C is overwritten by Q*C or Q**H*C or C*Q**H or C*Q. |
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* |
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* LDC (input) INTEGER |
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* The leading dimension of the array C. LDC >= max(1,M). |
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* |
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* WORK (workspace/output) COMPLEX*16 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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* If SIDE = 'L', LWORK >= max(1,N); |
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* if SIDE = 'R', LWORK >= max(1,M). |
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* For optimum performance LWORK >= N*NB if SIDE 'L', and |
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* LWORK >= M*NB if SIDE = 'R', where NB is the optimal |
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* blocksize. |
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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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* |
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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameters .. |
* .. Parameters .. |
INTEGER NBMAX, LDT |
INTEGER NBMAX, LDT, TSIZE |
PARAMETER ( NBMAX = 64, LDT = NBMAX+1 ) |
PARAMETER ( NBMAX = 64, LDT = NBMAX+1, |
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$ TSIZE = LDT*NBMAX ) |
* .. |
* .. |
* .. Local Scalars .. |
* .. Local Scalars .. |
LOGICAL LEFT, LQUERY, NOTRAN |
LOGICAL LEFT, LQUERY, NOTRAN |
CHARACTER TRANST |
CHARACTER TRANST |
INTEGER I, I1, I2, I3, IB, IC, IINFO, IWS, JC, LDWORK, |
INTEGER I, I1, I2, I3, IB, IC, IINFO, IWT, JC, LDWORK, |
$ LWKOPT, MI, NB, NBMIN, NI, NQ, NW |
$ LWKOPT, MI, NB, NBMIN, NI, NQ, NW |
* .. |
* .. |
* .. Local Arrays .. |
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COMPLEX*16 T( LDT, NBMAX ) |
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* .. |
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* .. External Functions .. |
* .. External Functions .. |
LOGICAL LSAME |
LOGICAL LSAME |
INTEGER ILAENV |
INTEGER ILAENV |
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* |
* |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |
* |
* |
* Determine the block size. NB may be at most NBMAX, where NBMAX |
* Compute the workspace requirements |
* is used to define the local array T. |
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* |
* |
NB = MIN( NBMAX, ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N, K, |
NB = MIN( NBMAX, ILAENV( 1, 'ZUNMLQ', SIDE // TRANS, M, N, K, |
$ -1 ) ) |
$ -1 ) ) |
LWKOPT = MAX( 1, NW )*NB |
LWKOPT = MAX( 1, NW )*NB + TSIZE |
WORK( 1 ) = LWKOPT |
WORK( 1 ) = LWKOPT |
END IF |
END IF |
* |
* |
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NBMIN = 2 |
NBMIN = 2 |
LDWORK = NW |
LDWORK = NW |
IF( NB.GT.1 .AND. NB.LT.K ) THEN |
IF( NB.GT.1 .AND. NB.LT.K ) THEN |
IWS = NW*NB |
IF( LWORK.LT.NW*NB+TSIZE ) THEN |
IF( LWORK.LT.IWS ) THEN |
NB = (LWORK-TSIZE) / LDWORK |
NB = LWORK / LDWORK |
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NBMIN = MAX( 2, ILAENV( 2, 'ZUNMLQ', SIDE // TRANS, M, N, K, |
NBMIN = MAX( 2, ILAENV( 2, 'ZUNMLQ', SIDE // TRANS, M, N, K, |
$ -1 ) ) |
$ -1 ) ) |
END IF |
END IF |
ELSE |
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IWS = NW |
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END IF |
END IF |
* |
* |
IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN |
IF( NB.LT.NBMIN .OR. NB.GE.K ) THEN |
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* |
* |
* Use blocked code |
* Use blocked code |
* |
* |
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IWT = 1 + NW*NB |
IF( ( LEFT .AND. NOTRAN ) .OR. |
IF( ( LEFT .AND. NOTRAN ) .OR. |
$ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN |
$ ( .NOT.LEFT .AND. .NOT.NOTRAN ) ) THEN |
I1 = 1 |
I1 = 1 |
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* H = H(i) H(i+1) . . . H(i+ib-1) |
* H = H(i) H(i+1) . . . H(i+ib-1) |
* |
* |
CALL ZLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), |
CALL ZLARFT( 'Forward', 'Rowwise', NQ-I+1, IB, A( I, I ), |
$ LDA, TAU( I ), T, LDT ) |
$ LDA, TAU( I ), WORK( IWT ), LDT ) |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
* |
* |
* H or H' is applied to C(i:m,1:n) |
* H or H**H is applied to C(i:m,1:n) |
* |
* |
MI = M - I + 1 |
MI = M - I + 1 |
IC = I |
IC = I |
ELSE |
ELSE |
* |
* |
* H or H' is applied to C(1:m,i:n) |
* H or H**H is applied to C(1:m,i:n) |
* |
* |
NI = N - I + 1 |
NI = N - I + 1 |
JC = I |
JC = I |
END IF |
END IF |
* |
* |
* Apply H or H' |
* Apply H or H**H |
* |
* |
CALL ZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, |
CALL ZLARFB( SIDE, TRANST, 'Forward', 'Rowwise', MI, NI, IB, |
$ A( I, I ), LDA, T, LDT, C( IC, JC ), LDC, WORK, |
$ A( I, I ), LDA, WORK( IWT ), LDT, |
$ LDWORK ) |
$ C( IC, JC ), LDC, WORK, LDWORK ) |
10 CONTINUE |
10 CONTINUE |
END IF |
END IF |
WORK( 1 ) = LWKOPT |
WORK( 1 ) = LWKOPT |