zungql man page on Scientific

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ZUNGQL(1)		 LAPACK routine (version 3.2)		     ZUNGQL(1)

NAME
       ZUNGQL - generates an M-by-N complex matrix Q with orthonormal columns,

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

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

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

PURPOSE
       ZUNGQL  generates  an M-by-N complex matrix Q with orthonormal columns,
       which is defined as the last N columns of a  product  of	 K  elementary
       reflectors of order M
	     Q	=  H(k) . . . H(2) H(1)
       as returned by ZGEQLF.

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) COMPLEX*16 array, dimension (LDA,N)
	       On entry, the (n-k+i)-th column must contain the	 vector	 which
	       defines	the  elementary	 reflector H(i), for i = 1,2,...,k, as
	       returned by ZGEQLF in the last 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) COMPLEX*16 array, dimension (K)
	       TAU(i) must contain the scalar factor of the elementary reflec‐
	       tor H(i), as returned by ZGEQLF.

       WORK    (workspace/output) COMPLEX*16 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,N).  For	 opti‐
	       mum  performance	 LWORK >= N*NB, where NB is the optimal block‐
	       size.  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

 LAPACK routine (version 3.2)	 November 2008			     ZUNGQL(1)
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