ZGEQP3  -  compute a QR factorization with column pivoting
       of a matrix A


SYNOPSIS

       SUBROUTINE ZGEQP3( M, N, A, LDA, JPVT, TAU,  WORK,  LWORK,
                          RWORK, INFO )

           INTEGER        INFO, LDA, LWORK, M, N

           INTEGER        JPVT( * )

           DOUBLE         PRECISION RWORK( * )

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


PURPOSE

       ZGEQP3 computes a QR factorization with column pivoting of
       a matrix A: A*P = Q*R using Level 3 BLAS.


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 trapezoidal 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(J).ne.0, the J-th column of A is
               permuted to the front of A*P (a  leading  column);
               if  JPVT(J)=0, the J-th column of A is a free col­
               umn.  On exit, if JPVT(J)=K, then the J-th  column
               of A*P was the the K-th column of A.

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

       WORK    (workspace/output) COMPLEX*16 array, dimension
               (LWORK)
               On exit, if INFO=0, WORK(1)  returns  the  optimal
               LWORK.

               The  dimension  of  the  array WORK. LWORK >= N+1.
               For optimal performance LWORK >= ( N+1 )*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
               related to LWORK is issued by XERBLA.

       RWORK   (workspace) DOUBLE PRECISION array, dimension
               (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(k), where k = min(m,n).

       Each H(i) has the form

          H(i) = I - tau * v * v'

       where tau is a real/complex scalar, and v is  a  real/com­
       plex  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).

       Based on contributions by
         G. Quintana-Orti,  Depto.  de  Informatica,  Universidad
       Jaime I, Spain
         X. Sun, Computer Science Dept., Duke University, USA


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