SORGRQ(l)								 )								 SORGRQ(l)

NAME

       SORGRQ - generate an M-by-N real matrix Q with orthonormal rows,

SYNOPSIS

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

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

	   REAL 	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE

       SORGRQ 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 SGERQF.

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) REAL 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
	       SGERQF 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) REAL array, dimension (K)
	       TAU(i) must contain the scalar factor of the elementary reflector H(i), as returned by SGERQF.

       WORK    (workspace/output) REAL 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.

	       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 version 3.0						   15 June 2000 							 SORGRQ(l)