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419 lines
12 KiB
419 lines
12 KiB
2 years ago
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*> \brief \b ZLAMTSQR
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE ZLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
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* $ LDT, C, LDC, WORK, LWORK, INFO )
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*
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*
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* .. Scalar Arguments ..
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* CHARACTER SIDE, TRANS
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* INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
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* ..
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* .. Array Arguments ..
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* COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
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* $ T( LDT, * )
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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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*> ZLAMTSQR overwrites the general complex M-by-N matrix C with
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*>
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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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*> where Q is a complex unitary matrix defined as the product
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*> of blocked elementary reflectors computed by tall skinny
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*> QR factorization (ZLATSQR)
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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 A. 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. M >= K >= 0;
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*>
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*> \endverbatim
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*>
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*> \param[in] MB
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*> \verbatim
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*> MB is INTEGER
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*> The block size to be used in the blocked QR.
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*> MB > N. (must be the same as ZLATSQR)
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*> \endverbatim
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*>
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*> \param[in] NB
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*> \verbatim
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*> NB is INTEGER
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*> The column block size to be used in the blocked QR.
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*> N >= NB >= 1.
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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 (LDA,K)
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*> The i-th column must contain the vector which defines the
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*> blockedelementary reflector H(i), for i = 1,2,...,k, as
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*> returned by ZLATSQR in the first k columns of
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*> 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.
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*> If SIDE = 'L', LDA >= max(1,M);
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*> if SIDE = 'R', LDA >= max(1,N).
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*> \endverbatim
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*>
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*> \param[in] T
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*> \verbatim
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*> T is COMPLEX*16 array, dimension
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*> ( N * Number of blocks(CEIL(M-K/MB-K)),
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*> The blocked upper triangular block reflectors stored in compact form
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*> as a sequence of upper triangular blocks. See below
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*> for further details.
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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 >= NB.
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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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*> (workspace) COMPLEX*16 array, dimension (MAX(1,LWORK))
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*>
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*> \endverbatim
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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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*>
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*> If SIDE = 'L', LWORK >= max(1,N)*NB;
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*> if SIDE = 'R', LWORK >= max(1,MB)*NB.
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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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*> \endverbatim
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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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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*> Tall-Skinny QR (TSQR) performs QR by a sequence of unitary transformations,
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*> representing Q as a product of other unitary matrices
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*> Q = Q(1) * Q(2) * . . . * Q(k)
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*> where each Q(i) zeros out subdiagonal entries of a block of MB rows of A:
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*> Q(1) zeros out the subdiagonal entries of rows 1:MB of A
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*> Q(2) zeros out the bottom MB-N rows of rows [1:N,MB+1:2*MB-N] of A
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*> Q(3) zeros out the bottom MB-N rows of rows [1:N,2*MB-N+1:3*MB-2*N] of A
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*> . . .
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*>
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*> Q(1) is computed by GEQRT, which represents Q(1) by Householder vectors
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*> stored under the diagonal of rows 1:MB of A, and by upper triangular
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*> block reflectors, stored in array T(1:LDT,1:N).
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*> For more information see Further Details in GEQRT.
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*>
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*> Q(i) for i>1 is computed by TPQRT, which represents Q(i) by Householder vectors
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*> stored in rows [(i-1)*(MB-N)+N+1:i*(MB-N)+N] of A, and by upper triangular
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*> block reflectors, stored in array T(1:LDT,(i-1)*N+1:i*N).
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*> The last Q(k) may use fewer rows.
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*> For more information see Further Details in TPQRT.
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*>
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*> For more details of the overall algorithm, see the description of
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*> Sequential TSQR in Section 2.2 of [1].
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*>
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*> [1] “Communication-Optimal Parallel and Sequential QR and LU Factorizations,”
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*> J. Demmel, L. Grigori, M. Hoemmen, J. Langou,
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*> SIAM J. Sci. Comput, vol. 34, no. 1, 2012
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE ZLAMTSQR( SIDE, TRANS, M, N, K, MB, NB, A, LDA, T,
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$ LDT, C, LDC, WORK, LWORK, INFO )
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*
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* -- LAPACK computational routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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CHARACTER SIDE, TRANS
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INTEGER INFO, LDA, M, N, K, MB, NB, LDT, LWORK, LDC
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* ..
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* .. Array Arguments ..
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COMPLEX*16 A( LDA, * ), WORK( * ), C(LDC, * ),
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$ T( LDT, * )
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* ..
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*
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* =====================================================================
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*
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* ..
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* .. Local Scalars ..
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LOGICAL LEFT, RIGHT, TRAN, NOTRAN, LQUERY
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INTEGER I, II, KK, LW, CTR, Q
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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EXTERNAL LSAME
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* .. External Subroutines ..
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EXTERNAL ZGEMQRT, ZTPMQRT, XERBLA
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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LQUERY = LWORK.LT.0
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NOTRAN = LSAME( TRANS, 'N' )
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TRAN = LSAME( TRANS, 'C' )
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LEFT = LSAME( SIDE, 'L' )
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RIGHT = LSAME( SIDE, 'R' )
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IF (LEFT) THEN
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LW = N * NB
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Q = M
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ELSE
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LW = M * NB
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Q = N
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END IF
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*
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INFO = 0
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IF( .NOT.LEFT .AND. .NOT.RIGHT ) THEN
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INFO = -1
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ELSE IF( .NOT.TRAN .AND. .NOT.NOTRAN ) THEN
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INFO = -2
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ELSE IF( M.LT.K ) THEN
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INFO = -3
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ELSE IF( N.LT.0 ) THEN
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INFO = -4
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ELSE IF( K.LT.0 ) THEN
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INFO = -5
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ELSE IF( K.LT.NB .OR. NB.LT.1 ) THEN
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INFO = -7
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ELSE IF( LDA.LT.MAX( 1, Q ) ) THEN
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INFO = -9
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ELSE IF( LDT.LT.MAX( 1, NB) ) THEN
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INFO = -11
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ELSE IF( LDC.LT.MAX( 1, M ) ) THEN
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INFO = -13
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ELSE IF(( LWORK.LT.MAX(1,LW)).AND.(.NOT.LQUERY)) THEN
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INFO = -15
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END IF
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*
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* Determine the block size if it is tall skinny or short and wide
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*
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IF( INFO.EQ.0) THEN
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WORK(1) = LW
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END IF
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*
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'ZLAMTSQR', -INFO )
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RETURN
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ELSE IF (LQUERY) THEN
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RETURN
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END IF
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*
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* Quick return if possible
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*
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IF( MIN(M,N,K).EQ.0 ) THEN
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RETURN
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END IF
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*
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IF((MB.LE.K).OR.(MB.GE.MAX(M,N,K))) THEN
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CALL ZGEMQRT( SIDE, TRANS, M, N, K, NB, A, LDA,
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$ T, LDT, C, LDC, WORK, INFO)
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RETURN
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END IF
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*
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IF(LEFT.AND.NOTRAN) THEN
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*
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* Multiply Q to the last block of C
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*
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KK = MOD((M-K),(MB-K))
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CTR = (M-K)/(MB-K)
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IF (KK.GT.0) THEN
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II=M-KK+1
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CALL ZTPMQRT('L','N',KK , N, K, 0, NB, A(II,1), LDA,
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$ T(1, CTR * K + 1),LDT , C(1,1), LDC,
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$ C(II,1), LDC, WORK, INFO )
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ELSE
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II=M+1
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END IF
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*
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DO I=II-(MB-K),MB+1,-(MB-K)
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*
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* Multiply Q to the current block of C (I:I+MB,1:N)
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*
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CTR = CTR - 1
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CALL ZTPMQRT('L','N',MB-K , N, K, 0,NB, A(I,1), LDA,
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$ T(1,CTR * K + 1),LDT, C(1,1), LDC,
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$ C(I,1), LDC, WORK, INFO )
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END DO
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*
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* Multiply Q to the first block of C (1:MB,1:N)
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*
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CALL ZGEMQRT('L','N',MB , N, K, NB, A(1,1), LDA, T
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$ ,LDT ,C(1,1), LDC, WORK, INFO )
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*
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ELSE IF (LEFT.AND.TRAN) THEN
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*
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* Multiply Q to the first block of C
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*
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KK = MOD((M-K),(MB-K))
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II=M-KK+1
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CTR = 1
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CALL ZGEMQRT('L','C',MB , N, K, NB, A(1,1), LDA, T
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$ ,LDT ,C(1,1), LDC, WORK, INFO )
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*
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DO I=MB+1,II-MB+K,(MB-K)
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*
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* Multiply Q to the current block of C (I:I+MB,1:N)
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*
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CALL ZTPMQRT('L','C',MB-K , N, K, 0,NB, A(I,1), LDA,
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$ T(1,CTR * K + 1),LDT, C(1,1), LDC,
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$ C(I,1), LDC, WORK, INFO )
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CTR = CTR + 1
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*
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END DO
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IF(II.LE.M) THEN
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*
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* Multiply Q to the last block of C
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*
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CALL ZTPMQRT('L','C',KK , N, K, 0,NB, A(II,1), LDA,
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$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
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$ C(II,1), LDC, WORK, INFO )
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*
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END IF
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*
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ELSE IF(RIGHT.AND.TRAN) THEN
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*
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* Multiply Q to the last block of C
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*
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KK = MOD((N-K),(MB-K))
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CTR = (N-K)/(MB-K)
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IF (KK.GT.0) THEN
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II=N-KK+1
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CALL ZTPMQRT('R','C',M , KK, K, 0, NB, A(II,1), LDA,
|
||
|
|
$ T(1,CTR * K + 1), LDT, C(1,1), LDC,
|
||
|
|
$ C(1,II), LDC, WORK, INFO )
|
||
|
|
ELSE
|
||
|
|
II=N+1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
DO I=II-(MB-K),MB+1,-(MB-K)
|
||
|
|
*
|
||
|
|
* Multiply Q to the current block of C (1:M,I:I+MB)
|
||
|
|
*
|
||
|
|
CTR = CTR - 1
|
||
|
|
CALL ZTPMQRT('R','C',M , MB-K, K, 0,NB, A(I,1), LDA,
|
||
|
|
$ T(1, CTR * K + 1), LDT, C(1,1), LDC,
|
||
|
|
$ C(1,I), LDC, WORK, INFO )
|
||
|
|
|
||
|
|
END DO
|
||
|
|
*
|
||
|
|
* Multiply Q to the first block of C (1:M,1:MB)
|
||
|
|
*
|
||
|
|
CALL ZGEMQRT('R','C',M , MB, K, NB, A(1,1), LDA, T
|
||
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
||
|
|
*
|
||
|
|
ELSE IF (RIGHT.AND.NOTRAN) THEN
|
||
|
|
*
|
||
|
|
* Multiply Q to the first block of C
|
||
|
|
*
|
||
|
|
KK = MOD((N-K),(MB-K))
|
||
|
|
II=N-KK+1
|
||
|
|
CTR = 1
|
||
|
|
CALL ZGEMQRT('R','N', M, MB , K, NB, A(1,1), LDA, T
|
||
|
|
$ ,LDT ,C(1,1), LDC, WORK, INFO )
|
||
|
|
*
|
||
|
|
DO I=MB+1,II-MB+K,(MB-K)
|
||
|
|
*
|
||
|
|
* Multiply Q to the current block of C (1:M,I:I+MB)
|
||
|
|
*
|
||
|
|
CALL ZTPMQRT('R','N', M, MB-K, K, 0,NB, A(I,1), LDA,
|
||
|
|
$ T(1, CTR * K + 1),LDT, C(1,1), LDC,
|
||
|
|
$ C(1,I), LDC, WORK, INFO )
|
||
|
|
CTR = CTR + 1
|
||
|
|
*
|
||
|
|
END DO
|
||
|
|
IF(II.LE.N) THEN
|
||
|
|
*
|
||
|
|
* Multiply Q to the last block of C
|
||
|
|
*
|
||
|
|
CALL ZTPMQRT('R','N', M, KK , K, 0,NB, A(II,1), LDA,
|
||
|
|
$ T(1,CTR * K + 1),LDT, C(1,1), LDC,
|
||
|
|
$ C(1,II), LDC, WORK, INFO )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
WORK(1) = LW
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of ZLAMTSQR
|
||
|
|
*
|
||
|
|
END
|