cgelq2(3F)

NAME
     CGELQ2 - compute 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).