sgemlq()

subroutine sgemlq	(	character	side,
		character	trans,
		integer	m,
		integer	n,
		integer	k,
		real, dimension( lda, * )	a,
		integer	lda,
		real, dimension( * )	t,
		integer	tsize,
		real, dimension( ldc, * )	c,
		integer	ldc,
		real, dimension( * )	work,
		integer	lwork,
		integer	info )

SGEMLQ

Purpose:

!>
!>     SGEMLQ overwrites the general real M-by-N matrix C with
!>
!>                    SIDE = 'L'     SIDE = 'R'
!>    TRANS = 'N':      Q * C          C * Q
!>    TRANS = 'T':      Q**T * C       C * Q**T
!>    where Q is a real orthogonal matrix defined as the product
!>    of blocked elementary reflectors computed by short wide LQ
!>    factorization (SGELQ)
!>
!> 

Parameters

[in]	SIDE	!> SIDE is CHARACTER*1 !> = 'L': apply Q or Q**T from the Left; !> = 'R': apply Q or Q**T from the Right. !>
[in]	TRANS	!> TRANS is CHARACTER*1 !> = 'N': No transpose, apply Q; !> = 'T': Transpose, apply Q**T. !>
[in]	M	!> M is INTEGER !> The number of rows of the matrix A. M >=0. !>
[in]	N	!> N is INTEGER !> The number of columns of the matrix C. N >= 0. !>
[in]	K	!> K is INTEGER !> The number of elementary reflectors whose product defines !> the matrix Q. !> If SIDE = 'L', M >= K >= 0; !> if SIDE = 'R', N >= K >= 0. !>
[in]	A	!> A is REAL array, dimension !> (LDA,M) if SIDE = 'L', !> (LDA,N) if SIDE = 'R' !> Part of the data structure to represent Q as returned by SGELQ. !>
[in]	LDA	!> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,K). !>
[in]	T	!> T is REAL array, dimension (MAX(5,TSIZE)). !> Part of the data structure to represent Q as returned by SGELQ. !>
[in]	TSIZE	!> TSIZE is INTEGER !> The dimension of the array T. TSIZE >= 5. !>
[in,out]	C	!> C is REAL array, dimension (LDC,N) !> On entry, the M-by-N matrix C. !> On exit, C is overwritten by Q*C or Q**T*C or C*Q**T or C*Q. !>
[in]	LDC	!> LDC is INTEGER !> The leading dimension of the array C. LDC >= max(1,M). !>
[out]	WORK	!> (workspace) DOUBLE PRECISION array, dimension (MAX(1,LWORK)) !> On exit, if INFO = 0, WORK(1) returns the minimal LWORK. !>
[in]	LWORK	!> LWORK is INTEGER !> The dimension of the array WORK. LWORK >= 1. !> If LWORK = -1, then a workspace query is assumed. The routine !> only calculates the size of the WORK array, returns this !> value as WORK(1), and no error message related to WORK !> is issued by XERBLA. !>
[out]	INFO	!> INFO is INTEGER !> = 0: successful exit !> < 0: if INFO = -i, the i-th argument had an illegal value !>

Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Further Details

!>
!> These details are particular for this LAPACK implementation. Users should not
!> take them for granted. These details may change in the future, and are not likely
!> true for another LAPACK implementation. These details are relevant if one wants
!> to try to understand the code. They are not part of the interface.
!>
!> In this version,
!>
!>          T(2): row block size (MB)
!>          T(3): column block size (NB)
!>          T(6:TSIZE): data structure needed for Q, computed by
!>                           SLASWLQ or SGELQT
!>
!>  Depending on the matrix dimensions M and N, and row and column
!>  block sizes MB and NB returned by ILAENV, SGELQ will use either
!>  SLASWLQ (if the matrix is wide-and-short) or SGELQT to compute
!>  the LQ factorization.
!>  This version of SGEMLQ will use either SLAMSWLQ or SGEMLQT to
!>  multiply matrix Q by another matrix.
!>  Further Details in SLAMSWLQ or SGEMLQT.
!>