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NAME

        ZGEQRF - compute a QR factorization of a complex M-by-N matrix A
 

SYNOPSIS

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

PURPOSE

        ZGEQRF  computes a QR factorization of a complex M-by-N matrix A: A = Q
        * R.
 

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
                above the diagonal of the array contain the min(M,N)-by-N upper
                trapezoidal matrix R (R is upper triangular if  m  >=  n);  the
                elements  below the diagonal, with the array TAU, represent the
                unitary matrix Q as a product of min(m,n) elementary reflectors
                (see Further Details).
 
        LDA     (input) INTEGER
                The leading dimension 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(2) . . . H(k), 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; v(i+1:m) is stored on exit in A(i+1:m,i), and tau  in
        TAU(i).
 

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