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DGBSV(3F)							     DGBSV(3F)

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 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.

									Page 1

DGBSV(3F)							     DGBSV(3F)

     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
     elements of U because of fill-in resulting from the row interchanges.

									Page 2

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