subroutine sgemqr (SIDE, TRANS, M, N, K, A, LDA, T, TSIZE, C, LDC, WORK, LWORK, INFO)
Purpose:
SGEMQR 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 tall skinny QR factorization (SGEQR)
Parameters:
SIDE is CHARACTER*1
= 'L': apply Q or Q**T from the Left;
= 'R': apply Q or Q**T from the Right.
TRANS
TRANS is CHARACTER*1
= 'N': No transpose, apply Q;
= 'T': Transpose, apply Q**T.
M
M is INTEGER
The number of rows of the matrix A. M >=0.
N
N is INTEGER
The number of columns of the matrix C. N >= 0.
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.
A
A is REAL array, dimension (LDA,K)
Part of the data structure to represent Q as returned by SGEQR.
LDA
LDA is INTEGER
The leading dimension of the array A.
If SIDE = 'L', LDA >= max(1,M);
if SIDE = 'R', LDA >= max(1,N).
T
T is REAL array, dimension (MAX(5,TSIZE)).
Part of the data structure to represent Q as returned by SGEQR.
TSIZE
TSIZE is INTEGER
The dimension of the array T. TSIZE >= 5.
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.
LDC
LDC is INTEGER
The leading dimension of the array C. LDC >= max(1,M).
WORK
(workspace) REAL array, dimension (MAX(1,LWORK))
LWORK
LWORK is INTEGER
The dimension of the array WORK.
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.
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
Author:
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 unlikely not 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 SLATSQR or SGEQRT
Depending on the matrix dimensions M and N, and row and column block sizes MB and NB returned by ILAENV, SGEQR will use either SLATSQR (if the matrix is tall-and-skinny) or SGEQRT to compute the QR factorization. This version of SGEMQR will use either SLAMTSQR or SGEMQRT to multiply matrix Q by another matrix. Further Details in SLAMTSQR or SGEMQRT.
Definition at line 171 of file sgemqr.f.
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