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RedHat 9 (Linux i386) - man page for dgbsv (redhat section l)

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 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 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.

LAPACK version 3.0			   15 June 2000 				 DGBSV(l)


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