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329 lines
9.9 KiB
329 lines
9.9 KiB
2 years ago
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*> \brief \b DGELQ
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
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* INFO )
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*
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* .. Scalar Arguments ..
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* INTEGER INFO, LDA, M, N, TSIZE, LWORK
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), T( * ), 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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*> DGELQ computes an LQ factorization of a real M-by-N matrix A:
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*>
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*> A = ( L 0 ) * Q
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*>
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*> where:
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*>
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*> Q is a N-by-N orthogonal matrix;
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*> L is a lower-triangular M-by-M matrix;
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*> 0 is a M-by-(N-M) zero matrix, if M < N.
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*>
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] 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 A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the M-by-N matrix A.
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*> On exit, the elements on and below the diagonal of the array
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*> contain the M-by-min(M,N) lower trapezoidal matrix L
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*> (L is lower triangular if M <= N);
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*> the elements above the diagonal are used to store part of the
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*> data structure to represent Q.
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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,M).
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*> \endverbatim
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*>
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*> \param[out] T
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*> \verbatim
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*> T is DOUBLE PRECISION array, dimension (MAX(5,TSIZE))
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*> On exit, if INFO = 0, T(1) returns optimal (or either minimal
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*> or optimal, if query is assumed) TSIZE. See TSIZE for details.
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*> Remaining T contains part of the data structure used to represent Q.
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*> If one wants to apply or construct Q, then one needs to keep T
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*> (in addition to A) and pass it to further subroutines.
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*> \endverbatim
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*>
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*> \param[in] TSIZE
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*> \verbatim
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*> TSIZE is INTEGER
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*> If TSIZE >= 5, the dimension of the array T.
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*> If TSIZE = -1 or -2, then a workspace query is assumed. The routine
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*> only calculates the sizes of the T and WORK arrays, returns these
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*> values as the first entries of the T and WORK arrays, and no error
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*> message related to T or WORK is issued by XERBLA.
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*> If TSIZE = -1, the routine calculates optimal size of T for the
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*> optimum performance and returns this value in T(1).
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*> If TSIZE = -2, the routine calculates minimal size of T and
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*> returns this value in T(1).
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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) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
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*> On exit, if INFO = 0, WORK(1) contains optimal (or either minimal
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*> or optimal, if query was assumed) LWORK.
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*> See LWORK for details.
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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 LWORK = -1 or -2, then a workspace query is assumed. The routine
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*> only calculates the sizes of the T and WORK arrays, returns these
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*> values as the first entries of the T and WORK arrays, and no error
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*> message related to T or WORK is issued by XERBLA.
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*> If LWORK = -1, the routine calculates optimal size of WORK for the
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*> optimal performance and returns this value in WORK(1).
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*> If LWORK = -2, the routine calculates minimal size of WORK and
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*> returns this value in WORK(1).
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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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*> \par Further Details
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* ====================
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*>
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*> \verbatim
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*>
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*> The goal of the interface is to give maximum freedom to the developers for
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*> creating any LQ factorization algorithm they wish. The triangular
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*> (trapezoidal) L has to be stored in the lower part of A. The lower part of A
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*> and the array T can be used to store any relevant information for applying or
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*> constructing the Q factor. The WORK array can safely be discarded after exit.
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*>
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*> Caution: One should not expect the sizes of T and WORK to be the same from one
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*> LAPACK implementation to the other, or even from one execution to the other.
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*> A workspace query (for T and WORK) is needed at each execution. However,
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*> for a given execution, the size of T and WORK are fixed and will not change
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*> from one query to the next.
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*>
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*> \endverbatim
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*>
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*> \par Further Details particular to this LAPACK implementation:
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* ==============================================================
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*>
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*> \verbatim
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*>
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*> These details are particular for this LAPACK implementation. Users should not
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*> take them for granted. These details may change in the future, and are not likely
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*> true for another LAPACK implementation. These details are relevant if one wants
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*> to try to understand the code. They are not part of the interface.
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*>
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*> In this version,
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*>
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*> T(2): row block size (MB)
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*> T(3): column block size (NB)
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*> T(6:TSIZE): data structure needed for Q, computed by
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*> DLASWLQ or DGELQT
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*>
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*> Depending on the matrix dimensions M and N, and row and column
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*> block sizes MB and NB returned by ILAENV, DGELQ will use either
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*> DLASWLQ (if the matrix is short-and-wide) or DGELQT to compute
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*> the LQ factorization.
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DGELQ( M, N, A, LDA, T, TSIZE, WORK, LWORK,
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$ 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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INTEGER INFO, LDA, M, N, TSIZE, LWORK
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), T( * ), WORK( * )
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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 LQUERY, LMINWS, MINT, MINW
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INTEGER MB, NB, MINTSZ, NBLCKS, LWMIN, LWOPT, LWREQ
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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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* ..
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* .. External Subroutines ..
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EXTERNAL DGELQT, DLASWLQ, XERBLA
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, MOD
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* ..
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* .. External Functions ..
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INTEGER ILAENV
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EXTERNAL ILAENV
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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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INFO = 0
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*
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LQUERY = ( TSIZE.EQ.-1 .OR. TSIZE.EQ.-2 .OR.
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$ LWORK.EQ.-1 .OR. LWORK.EQ.-2 )
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*
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MINT = .FALSE.
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MINW = .FALSE.
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IF( TSIZE.EQ.-2 .OR. LWORK.EQ.-2 ) THEN
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IF( TSIZE.NE.-1 ) MINT = .TRUE.
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IF( LWORK.NE.-1 ) MINW = .TRUE.
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END IF
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*
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* Determine the block size
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*
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IF( MIN( M, N ).GT.0 ) THEN
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MB = ILAENV( 1, 'DGELQ ', ' ', M, N, 1, -1 )
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NB = ILAENV( 1, 'DGELQ ', ' ', M, N, 2, -1 )
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ELSE
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MB = 1
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NB = N
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END IF
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IF( MB.GT.MIN( M, N ) .OR. MB.LT.1 ) MB = 1
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IF( NB.GT.N .OR. NB.LE.M ) NB = N
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MINTSZ = M + 5
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IF ( NB.GT.M .AND. N.GT.M ) THEN
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IF( MOD( N - M, NB - M ).EQ.0 ) THEN
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NBLCKS = ( N - M ) / ( NB - M )
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ELSE
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NBLCKS = ( N - M ) / ( NB - M ) + 1
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END IF
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ELSE
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NBLCKS = 1
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END IF
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*
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* Determine if the workspace size satisfies minimal size
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*
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IF( ( N.LE.M ) .OR. ( NB.LE.M ) .OR. ( NB.GE.N ) ) THEN
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LWMIN = MAX( 1, N )
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LWOPT = MAX( 1, MB*N )
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ELSE
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LWMIN = MAX( 1, M )
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LWOPT = MAX( 1, MB*M )
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END IF
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LMINWS = .FALSE.
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IF( ( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 ) .OR. LWORK.LT.LWOPT )
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$ .AND. ( LWORK.GE.LWMIN ) .AND. ( TSIZE.GE.MINTSZ )
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$ .AND. ( .NOT.LQUERY ) ) THEN
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IF( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 ) ) THEN
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LMINWS = .TRUE.
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MB = 1
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NB = N
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END IF
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IF( LWORK.LT.LWOPT ) THEN
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LMINWS = .TRUE.
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MB = 1
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END IF
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END IF
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IF( ( N.LE.M ) .OR. ( NB.LE.M ) .OR. ( NB.GE.N ) ) THEN
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LWREQ = MAX( 1, MB*N )
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ELSE
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LWREQ = MAX( 1, MB*M )
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END IF
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*
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IF( M.LT.0 ) THEN
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INFO = -1
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ELSE IF( N.LT.0 ) THEN
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INFO = -2
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ELSE IF( LDA.LT.MAX( 1, M ) ) THEN
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INFO = -4
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ELSE IF( TSIZE.LT.MAX( 1, MB*M*NBLCKS + 5 )
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$ .AND. ( .NOT.LQUERY ) .AND. ( .NOT.LMINWS ) ) THEN
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INFO = -6
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ELSE IF( ( LWORK.LT.LWREQ ) .AND .( .NOT.LQUERY )
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$ .AND. ( .NOT.LMINWS ) ) THEN
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INFO = -8
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END IF
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*
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IF( INFO.EQ.0 ) THEN
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IF( MINT ) THEN
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T( 1 ) = MINTSZ
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ELSE
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T( 1 ) = MB*M*NBLCKS + 5
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END IF
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T( 2 ) = MB
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T( 3 ) = NB
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IF( MINW ) THEN
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WORK( 1 ) = LWMIN
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ELSE
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WORK( 1 ) = LWREQ
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END IF
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END IF
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IF( INFO.NE.0 ) THEN
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CALL XERBLA( 'DGELQ', -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 ).EQ.0 ) THEN
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RETURN
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END IF
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*
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* The LQ Decomposition
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*
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IF( ( N.LE.M ) .OR. ( NB.LE.M ) .OR. ( NB.GE.N ) ) THEN
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CALL DGELQT( M, N, MB, A, LDA, T( 6 ), MB, WORK, INFO )
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ELSE
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CALL DLASWLQ( M, N, MB, NB, A, LDA, T( 6 ), MB, WORK,
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$ LWORK, INFO )
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END IF
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*
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WORK( 1 ) = LWREQ
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*
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RETURN
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*
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* End of DGELQ
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*
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END
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