zgelqf(l) [redhat man page]

ZGELQF(l)								 )								 ZGELQF(l)

NAME

       ZGELQF - compute an LQ factorization of a complex M-by-N matrix A

SYNOPSIS

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

	   INTEGER	  INFO, LDA, LWORK, M, N

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

PURPOSE

       ZGELQF computes an LQ factorization of a complex M-by-N matrix A: A = L * Q.

ARGUMENTS

       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       A       (input/output) COMPLEX*16 array, dimension (LDA,N)
	       On entry, the M-by-N matrix A.  On exit, the elements on and below the diagonal of the array contain the m-by-min(m,n) lower trape-
	       zoidal matrix L (L is lower triangular if m <= n); the elements above the diagonal, with  the  array  TAU,  represent  the  unitary
	       matrix  Q  as a product of elementary reflectors (see Further Details).	LDA	(input) INTEGER The leading dimension of the array
	       A.  LDA >= max(1,M).

       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
	       The scalar factors of the elementary reflectors (see Further Details).

       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.

	       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 had an illegal value

FURTHER DETAILS

       The matrix Q is represented as a product of elementary reflectors

	  Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).

       Each H(i) has the form

	  H(i) = I - tau * v * v'

       where  tau  is a complex scalar, and v is a complex vector with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in A(i,i+1:n),
       and tau in TAU(i).

LAPACK version 3.0						   15 June 2000 							 ZGELQF(l)