DGBSV(l)	     LAPACK driver routine (version 1.1)	     DGBSV(l)

NAME
  DGBSV	- compute the solution to a real system	of linear equations A *	X =
  B, where A is	a band matrix of order N with KL subdiagonals and KU superdi-
  agonals, and X and B are N-by-NRHS matrices

SYNOPSIS

  SUBROUTINE DGBSV( N, KL, KU, NRHS, AB, LDAB, IPIV, B,	LDB, INFO )

      INTEGER	    INFO, KL, KU, LDAB,	LDB, N,	NRHS

      INTEGER	    IPIV( * )

      DOUBLE	    PRECISION AB( LDAB,	* ), B(	LDB, * )

PURPOSE
  DGBSV	computes the solution to a real	system of linear equations A * X = B,
  where	A is a band matrix of order N with KL subdiagonals and KU superdiago-
  nals,	and X and B are	N-by-NRHS matrices.

  The LU decomposition with partial pivoting and row interchanges is used to
  factor A as A	= L * U, where L is a product of permutation and unit lower
  triangular matrices with KL subdiagonals, and	U is upper triangular with
  KL+KU	superdiagonals.	 The factored form of A	is then	used to	solve the
  system of equations A	* X = B.

ARGUMENTS

  N	  (input) INTEGER
	  The number of	linear equations, i.e.,	the order 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.

  NRHS	  (input) INTEGER
	  The number of	right hand sides, i.e.,	the number of columns of the
	  matrix B.  NRHS >= 0.

  AB	  (input/output) DOUBLE	PRECISION 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(N,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
	  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 (N)
	  The pivot indices that define	the permutation	matrix P; row i	of
	  the matrix was interchanged with row IPIV(i).

  B	  (input/output) DOUBLE	PRECISION array, dimension (LDB,NRHS)
	  On entry, the	N-by-NRHS right	hand side matrix B.  On	exit, if INFO
	  = 0, the N-by-NRHS solution matrix X.

  LDB	  (input) INTEGER
	  The leading dimension	of the array B.	 LDB >=	max(1,N).

  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 the	solu-
	  tion has not been computed.

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.