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NAME

        ZGEQLF - compute a QL factorization of a complex M-by-N matrix A
 

SYNOPSIS

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

PURPOSE

        ZGEQLF  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/output) COMPLEX*16 array, dimension (LWORK)
WORK(1) returns the optimal LWORK.
 
        LWORK   (input) INTEGER
                The dimension of the array WORK.  LWORK >= max(1,N).  For opti‐
                mum  performance  LWORK >= N*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
        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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