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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, * )



     #include <sunperf.h>

     void zgbtrf(int m, int n,  int  kl,  int  ku,  doublecomplex
               *zab, int ldab, int *ipivot, int *info) ;

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
               superdiagonals in rows 1 to KL+KU+1, and the  mul-
               tipliers  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  ille-
               gal value
               > 0: if INFO = +i, U(i,i)  is  exactly  zero.  The
               factorization 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 equa-
               tions.

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.

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