DORGQR - generate an M-by-N real matrix Q with orthonormal
columns,
SYNOPSIS
SUBROUTINE DORGQR( M, N, K, A, LDA, TAU, WORK, LWORK, INFO
)
INTEGER INFO, K, LDA, LWORK, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK(
* )
PURPOSE
DORGQR generates an M-by-N real matrix Q with orthonormal
columns, which is defined as the first N columns of a
product of K elementary reflectors of order M
Q = H(1) H(2) . . . H(k)
as returned by DGEQRF.
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. M >= N >=
0.
K (input) INTEGER
The number of elementary reflectors whose product
defines the matrix Q. N >= K >= 0.
A (input/output) DOUBLE PRECISION array, dimension
(LDA,N)
On entry, the i-th column must contain the vector
which defines the elementary reflector H(i), for i
= 1,2,...,k, as returned by DGEQRF in the first k
columns 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) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the ele
mentary reflector H(i), as returned by DGEQRF.
WORK (workspace/output) DOUBLE PRECISION array,
dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >=
max(1,N). For optimum performance LWORK >= N*NB,
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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