ZGELQF(3)                  MathKeisan LAPACK routine                 ZGELQF(3)



NAME
       ZGELQF - 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
               trapezoidal 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 dimen-
               sion 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 (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,M).  For opti-
               mum performance LWORK >= M*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 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 routine (version 3.1)    November 2006                       ZGELQF(3)