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NAME
     sgbtf2 - compute an LU factorization of a real  m-by-n  band
     matrix A using partial pivoting with row interchanges

SYNOPSIS
     SUBROUTINE SGBTF2( M, N, KL, KU, AB, LDAB, IPIV, INFO )

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

     INTEGER IPIV( * )

     REAL AB( LDAB, * )



     #include <sunperf.h>

     void sgbtf2(int m, int n, int kl, int ku,  float  *sab,  int
               ldab, int *ipivot, int *info) ;

PURPOSE
     SGBTF2 computes an LU factorization of a  real  m-by-n  band
     matrix A using partial pivoting with row interchanges.

     This is the unblocked  version  of  the  algorithm,  calling
     Level 2 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) REAL 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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