CGELQ2(3f)               LAPACK routine (version 3.1)               CGELQ2(3f)



NAME
       CGELQ2 - an LQ factorization of a complex m by n matrix A

SYNOPSIS
       SUBROUTINE CGELQ2( M, N, A, LDA, TAU, WORK, INFO )

           INTEGER        INFO, LDA, M, N

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

PURPOSE
       CGELQ2 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 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
               dimension of the array A.  LDA >= max(1,M).

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

       WORK    (workspace) COMPLEX array, dimension (M)

       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                      CGELQ2(3f)
