zungrq(3F)

NAME
     ZUNGRQ - generate an M-by-N complex matrix Q with orthonormal 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 elementary reflector
             H(i), as returned by ZGERQF.

     WORK    (workspace/output) 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