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

          M is INTEGER
          The number of rows of the matrix A. M >= 0.

          N is INTEGER
          The number of columns of the matrix A.  N >= 0.

          A is 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) elementary
          reflectors.

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

          JPVT is 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 column.
          On exit, if JPVT(J)=K, then the J-th column of A*P was the
          the K-th column of A.

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

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

          LWORK is INTEGER
          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 is DOUBLE PRECISION array, dimension (2*N)

          INFO is 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

     Q = H(1) H(2) . . . H(k), where k = min(m,n).

  Each H(i) has the form

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

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