ZGEQPF  -  routine  is deprecated and has been replaced by
       routine ZGEQP3


SYNOPSIS

       SUBROUTINE ZGEQPF( M, N, A, LDA, JPVT, TAU,  WORK,  RWORK,
                          INFO )

           INTEGER        INFO, LDA, M, N

           INTEGER        JPVT( * )

           DOUBLE         PRECISION RWORK( * )

           COMPLEX*16     A( LDA, * ), TAU( * ), WORK( * )


PURPOSE

       This  routine  is deprecated and has been replaced by rou­
       tine ZGEQP3.  ZGEQPF computes a QR factorization with col­
       umn pivoting of a complex M-by-N matrix A: A*P = 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 upper
               triangle  of  the array contains the min(M,N)-by-N
               upper triangular matrix R; the elements below  the
               diagonal,  together  with the array TAU, represent
               the unitary matrix Q as a product of min(m,n) ele­
               mentary reflectors.

       LDA     (input) INTEGER
               The  leading  dimension  of  the  array  A. LDA >=
               max(1,M).

       JPVT    (input/output) INTEGER array, dimension (N)
               On entry, if JPVT(i) .ne. 0, the i-th column of  A
               is  permuted  to  the front of A*P (a leading col­
               umn); if JPVT(i) = 0, the i-th column of  A  is  a
               free column.  On exit, if JPVT(i) = k, then the i-
               th column of A*P was the k-th column of A.

       TAU     (output) COMPLEX*16 array, dimension (min(M,N))
               The scalar factors of the elementary reflectors.

       WORK    (workspace) COMPLEX*16 array, dimension (N)

               (2*N)

       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(n)

       Each H(i) has the form

          H = 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).

       The matrix P is represented in jpvt as follows: If
          jpvt(j) = i
       then the jth column of P is the ith canonical unit vector.


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