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# zungrq

```
NAME
ZUNGRQ - generate an M-by-N complex matrix Q with orthonor-
mal rows,

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

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

COMPLEX*16     A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE
ZUNGRQ generates an M-by-N complex 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 ZGERQF.

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) COMPLEX*16 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 ZGERQF 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) COMPLEX*16 array, dimension (K)
TAU(i) must contain the scalar factor of the elemen-
tary reflector H(i), as returned by ZGERQF.

WORK    (workspace) COMPLEX*16 array, dimension (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.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument has an illegal
value
```