version 1.4, 2010/08/06 15:32:52
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version 1.17, 2023/08/07 08:39:44
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*> \brief \b ZUNMBR |
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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 ZUNMBR + dependencies |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/zunmbr.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/zunmbr.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/zunmbr.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 ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, |
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* LDC, WORK, LWORK, INFO ) |
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* |
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* .. Scalar Arguments .. |
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* CHARACTER SIDE, TRANS, VECT |
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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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*> If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C |
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*> with |
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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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*> If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C |
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*> with |
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*> SIDE = 'L' SIDE = 'R' |
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*> TRANS = 'N': P * C C * P |
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*> TRANS = 'C': P**H * C C * P**H |
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*> |
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*> Here Q and P**H are the unitary matrices determined by ZGEBRD when |
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*> reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q |
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*> and P**H are defined as products of elementary reflectors H(i) and |
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*> G(i) respectively. |
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*> |
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*> Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the |
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*> order of the unitary matrix Q or P**H that is applied. |
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*> |
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*> If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: |
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*> if nq >= k, Q = H(1) H(2) . . . H(k); |
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*> if nq < k, Q = H(1) H(2) . . . H(nq-1). |
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*> |
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*> If VECT = 'P', A is assumed to have been a K-by-NQ matrix: |
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*> if k < nq, P = G(1) G(2) . . . G(k); |
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*> if k >= nq, P = G(1) G(2) . . . G(nq-1). |
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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] VECT |
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*> \verbatim |
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*> VECT is CHARACTER*1 |
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*> = 'Q': apply Q or Q**H; |
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*> = 'P': apply P or P**H. |
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*> \endverbatim |
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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, Q**H, P or P**H from the Left; |
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*> = 'R': apply Q, Q**H, P or P**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 or P; |
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*> = 'C': Conjugate transpose, apply Q**H or P**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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*> If VECT = 'Q', the number of columns in the original |
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*> matrix reduced by ZGEBRD. |
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*> If VECT = 'P', the number of rows in the original |
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*> matrix reduced by ZGEBRD. |
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*> 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,min(nq,K)) if VECT = 'Q' |
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*> (LDA,nq) if VECT = 'P' |
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*> The vectors which define the elementary reflectors H(i) and |
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*> G(i), whose products determine the matrices Q and P, as |
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*> returned by ZGEBRD. |
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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. |
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*> If VECT = 'Q', LDA >= max(1,nq); |
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*> if VECT = 'P', LDA >= max(1,min(nq,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 (min(nq,K)) |
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*> TAU(i) must contain the scalar factor of the elementary |
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*> reflector H(i) or G(i) which determines Q or P, as returned |
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*> by ZGEBRD in the array argument TAUQ or TAUP. |
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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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*> or P*C or P**H*C or C*P or C*P**H. |
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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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*> if N = 0 or M = 0, LWORK >= 1. |
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*> For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', |
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*> and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the |
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*> optimal blocksize. (NB = 0 if M = 0 or N = 0.) |
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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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*> \ingroup complex16OTHERcomputational |
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* |
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* ===================================================================== |
SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, |
SUBROUTINE ZUNMBR( VECT, SIDE, TRANS, M, N, K, A, LDA, TAU, C, |
$ LDC, WORK, LWORK, INFO ) |
$ LDC, WORK, LWORK, 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 .. |
CHARACTER SIDE, TRANS, VECT |
CHARACTER SIDE, TRANS, VECT |
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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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* If VECT = 'Q', ZUNMBR overwrites the general complex M-by-N matrix C |
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* with |
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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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* If VECT = 'P', ZUNMBR overwrites the general complex M-by-N matrix C |
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* with |
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* SIDE = 'L' SIDE = 'R' |
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* TRANS = 'N': P * C C * P |
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* TRANS = 'C': P**H * C C * P**H |
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* |
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* Here Q and P**H are the unitary matrices determined by ZGEBRD when |
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* reducing a complex matrix A to bidiagonal form: A = Q * B * P**H. Q |
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* and P**H are defined as products of elementary reflectors H(i) and |
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* G(i) respectively. |
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* |
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* Let nq = m if SIDE = 'L' and nq = n if SIDE = 'R'. Thus nq is the |
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* order of the unitary matrix Q or P**H that is applied. |
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* |
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* If VECT = 'Q', A is assumed to have been an NQ-by-K matrix: |
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* if nq >= k, Q = H(1) H(2) . . . H(k); |
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* if nq < k, Q = H(1) H(2) . . . H(nq-1). |
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* |
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* If VECT = 'P', A is assumed to have been a K-by-NQ matrix: |
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* if k < nq, P = G(1) G(2) . . . G(k); |
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* if k >= nq, P = G(1) G(2) . . . G(nq-1). |
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* |
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* Arguments |
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* ========= |
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* |
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* VECT (input) CHARACTER*1 |
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* = 'Q': apply Q or Q**H; |
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* = 'P': apply P or P**H. |
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* |
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* SIDE (input) CHARACTER*1 |
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* = 'L': apply Q, Q**H, P or P**H from the Left; |
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* = 'R': apply Q, Q**H, P or P**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 or P; |
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* = 'C': Conjugate transpose, apply Q**H or P**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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* If VECT = 'Q', the number of columns in the original |
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* matrix reduced by ZGEBRD. |
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* If VECT = 'P', the number of rows in the original |
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* matrix reduced by ZGEBRD. |
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* K >= 0. |
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* |
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* A (input) COMPLEX*16 array, dimension |
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* (LDA,min(nq,K)) if VECT = 'Q' |
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* (LDA,nq) if VECT = 'P' |
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* The vectors which define the elementary reflectors H(i) and |
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* G(i), whose products determine the matrices Q and P, as |
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* returned by ZGEBRD. |
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* |
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* LDA (input) INTEGER |
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* The leading dimension of the array A. |
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* If VECT = 'Q', LDA >= max(1,nq); |
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* if VECT = 'P', LDA >= max(1,min(nq,K)). |
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* |
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* TAU (input) COMPLEX*16 array, dimension (min(nq,K)) |
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* TAU(i) must contain the scalar factor of the elementary |
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* reflector H(i) or G(i) which determines Q or P, as returned |
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* by ZGEBRD in the array argument TAUQ or TAUP. |
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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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* or P*C or P**H*C or C*P or C*P**H. |
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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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* if N = 0 or M = 0, LWORK >= 1. |
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* For optimum performance LWORK >= max(1,N*NB) if SIDE = 'L', |
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* and LWORK >= max(1,M*NB) if SIDE = 'R', where NB is the |
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* optimal blocksize. (NB = 0 if M = 0 or N = 0.) |
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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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Local Scalars .. |
* .. Local Scalars .. |
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* |
* |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
NQ = M |
NQ = M |
NW = N |
NW = MAX( 1, N ) |
ELSE |
ELSE |
NQ = N |
NQ = N |
NW = M |
NW = MAX( 1, M ) |
END IF |
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IF( M.EQ.0 .OR. N.EQ.0 ) THEN |
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NW = 0 |
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END IF |
END IF |
IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN |
IF( .NOT.APPLYQ .AND. .NOT.LSAME( VECT, 'P' ) ) THEN |
INFO = -1 |
INFO = -1 |
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INFO = -8 |
INFO = -8 |
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
ELSE IF( LDC.LT.MAX( 1, M ) ) THEN |
INFO = -11 |
INFO = -11 |
ELSE IF( LWORK.LT.MAX( 1, NW ) .AND. .NOT.LQUERY ) THEN |
ELSE IF( LWORK.LT.NW .AND. .NOT.LQUERY ) THEN |
INFO = -13 |
INFO = -13 |
END IF |
END IF |
* |
* |
IF( INFO.EQ.0 ) THEN |
IF( INFO.EQ.0 ) THEN |
IF( NW.GT.0 ) THEN |
IF( M.GT.0 .AND. N.GT.0 ) THEN |
IF( APPLYQ ) THEN |
IF( APPLYQ ) THEN |
IF( LEFT ) THEN |
IF( LEFT ) THEN |
NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, |
NB = ILAENV( 1, 'ZUNMQR', SIDE // TRANS, M-1, N, M-1, |
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$ -1 ) |
$ -1 ) |
END IF |
END IF |
END IF |
END IF |
LWKOPT = MAX( 1, NW*NB ) |
LWKOPT = NW*NB |
ELSE |
ELSE |
LWKOPT = 1 |
LWKOPT = 1 |
END IF |
END IF |