SGBTRF(l)		LAPACK routine (version	1.1)		    SGBTRF(l)

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

SYNOPSIS

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

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

      INTEGER	     IPIV( * )

      REAL	     AB( LDAB, * )

PURPOSE
  SGBTRF computes an LU	factorization of a real	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) 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 tri-
	  angular band matrix with KL+KU superdiagonals	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 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	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; elements	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.