 DORGRQ(3) generates an M-by-N real matrix Q with orthonormal rows,

## SYNOPSIS

SUBROUTINE DORGRQ(
M, N, K, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER INFO, K, LDA, LWORK, M, N

DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )

## PURPOSE

DORGRQ 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 DGERQF.

## 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) DOUBLE PRECISION array, dimension (LDA,N)
On entry, the (m-k+i)-th row must contain the vector which defines the elementary reflector H(i), for i = 1,2,...,k, as returned by DGERQF 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) DOUBLE PRECISION array, dimension (K)
TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by DGERQF.
WORK (workspace/output) DOUBLE PRECISION array, dimension (MAX(1,LWORK))
On exit, if INFO = 0, WORK(1) returns the optimal LWORK.
LWORK (input) INTEGER
The dimension of the array WORK. LWORK >= max(1,M). For optimum performance LWORK >= M*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 illegal value