SORGRQ - generate an M-by-N real matrix Q with orthonormal
rows,
SYNOPSIS
SUBROUTINE SORGRQ( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
)
INTEGER INFO, K, LDA, LWORK, M, N
REAL A( LDA, * ), TAU( * ), WORK( * )
PURPOSE
SORGRQ generates an M-by-N real matrix Q with orthonormal
rows, which is defined as the last M rows of a product of
K elementary reflectors of order N
Q = H(1) H(2) . . . H(k)
as returned by SGERQF.
ARGUMENTS
M (input) INTEGER
The number of rows of the matrix Q. M >= 0.
N (input) INTEGER
The number of columns of the matrix Q. N >= M.
K (input) INTEGER
The number of elementary reflectors whose product
defines the matrix Q. M >= K >= 0.
A (input/output) REAL array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vec
tor which defines the elementary reflector H(i),
for i = 1,2,...,k, as returned by SGERQF in the
last k rows of its array argument A. On exit, the
M-by-N matrix Q.
LDA (input) INTEGER
The first dimension of the array A. LDA >=
max(1,M).
TAU (input) REAL array, dimension (K)
TAU(i) must contain the scalar factor of the ele
mentary reflector H(i), as returned by SGERQF.
WORK (workspace/output) REAL array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >=
where NB is the optimal blocksize.
If LWORK = -1, then a workspace query is assumed;
the routine only calculates the optimal size of
the WORK array, returns this value as the first
entry of the WORK array, and no error message
related to LWORK is issued by XERBLA.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument has an ille
gal value
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