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zgbtrf

 NAME
      ZGBTRF - compute an LU factorization of a complex m-by-n
      band matrix A using partial pivoting with row interchanges

 SYNOPSIS
      SUBROUTINE ZGBTRF( M, N, KL, KU, AB, LDAB, IPIV, INFO )

          INTEGER        INFO, KL, KU, LDAB, M, N

          INTEGER        IPIV( * )

          COMPLEX*16     AB( LDAB, * )

 PURPOSE
      ZGBTRF computes an LU factorization of a complex m-by-n band
      matrix A using partial pivoting with row interchanges.

      This is the blocked version of the algorithm, calling 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.

      KL      (input) INTEGER
              The number of subdiagonals within the band of A.  KL
              >= 0.

      KU      (input) INTEGER
              The number of superdiagonals within the band of A.
              KU >= 0.

      AB      (input/output) COMPLEX*16 array, dimension (LDAB,N)
              On entry, the matrix A in band storage, in rows KL+1
              to 2*KL+KU+1; rows 1 to KL of the array need not be
              set.  The j-th column of A is stored in the j-th
              column of the array AB as follows: AB(kl+ku+1+i-j,j)
              = A(i,j) for max(1,j-ku)<=i<=min(m,j+kl)

              On exit, details of the factorization: U is stored
              as an upper triangular band matrix with KL+KU super-
              diagonals in rows 1 to KL+KU+1, and the multipliers
              used during the factorization are stored in rows
              KL+KU+2 to 2*KL+KU+1.  See below for further
              details.

      LDAB    (input) INTEGER
              The leading dimension of the array AB.  LDAB >=

              2*KL+KU+1.

      IPIV    (output) INTEGER array, dimension (min(M,N))
              The pivot indices; for 1 <= i <= min(M,N), row i of
              the matrix was interchanged with row IPIV(i).

      INFO    (output) INTEGER
              = 0: successful exit
              < 0: if INFO = -i, the i-th argument had an illegal
              value
              > 0: if INFO = +i, U(i,i) is exactly zero. The fac-
              torization has been completed, but the factor U is
              exactly singular, and division by zero will occur if
              it is used to solve a system of equations.

 FURTHER DETAILS
      The band storage scheme is illustrated by the following
      example, when M = N = 6, KL = 2, KU = 1:

      On entry:                       On exit:

          *    *    *    +    +    +       *    *    *   u14  u25
      u36
          *    *    +    +    +    +       *    *   u13  u24  u35
      u46
          *   a12  a23  a34  a45  a56      *   u12  u23  u34  u45
      u56
         a11  a22  a33  a44  a55  a66     u11  u22  u33  u44  u55
      u66
         a21  a32  a43  a54  a65   *      m21  m32  m43  m54  m65
      *
         a31  a42  a53  a64   *    *      m31  m42  m53  m64   *
      *

      Array elements marked * are not used by the routine; ele-
      ments marked + need not be set on entry, but are required by
      the routine to store elements of U because of fill-in
      resulting from the row interchanges.