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DGBSV(l)			       )			      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
       superdiagonals, 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
       superdiagonals,	and X and B are N-by-NRHS matrices.  The LU decomposi‐
       tion 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 triangu‐
       lar matrices with KL subdiagonals, and U is upper triangular with KL+KU
       superdiagonals.	 The factored form of A is then used to solve the sys‐
       tem 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 superdiag‐
	       onals 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 solution 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 ele‐
       ments of U because of fill-in resulting from the row interchanges.

LAPACK version 3.0		 15 June 2000			      DGBSV(l)
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