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NAME

        ZGEQL2 - compute a QL factorization of a complex m by n matrix A
 

SYNOPSIS

        SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )
 
            INTEGER        INFO, LDA, M, N
 
            COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )
 

PURPOSE

        ZGEQL2  computes a QL factorization of a complex m by n matrix A: A = Q
        * L.
 

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, if m >= n,  the  lower
                triangle  of  the  subarray  A(m-n+1:m,1:n) contains the n by n
                lower triangular matrix L; if m <= n, the elements on and below
                the (n-m)-th superdiagonal contain the m by n lower trapezoidal
                matrix L; the remaining elements, 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) COMPLEX*16 array, dimension (N)
 
        INFO    (output) INTEGER
                = 0: successful exit
                < 0: if INFO = -i, the i-th argument had an illegal value
        The matrix Q is represented as a product of elementary reflectors
 
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(m-
        k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is stored on exit in A(1:m-
        k+i-1,n-k+i), and tau in TAU(i).
 

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