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  ele­
               ments  on and above the diagonal of the array con­
               tain 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) ele­
               mentary 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)
               On  exit, if INFO = 0, WORK(1) returns the optimal
               LWORK.

       LWORK   (input) INTEGER
               The  dimension  of  the  array  WORK.   LWORK   >=
               max(1,N).   For optimum performance LWORK >= N*NB,
               where NB is the optimal blocksize.

               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


       INFO    (output) INTEGER
               = 0:  successful exit
               < 0:  if INFO = -i, the i-th argument had an ille­
               gal value


FURTHER DETAILS

       The  matrix  Q  is  represented as a product of elementary
       reflectors

          Q = H(1) 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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