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dpbsv.f(3)				      LAPACK				       dpbsv.f(3)

NAME
       dpbsv.f -

SYNOPSIS
   Functions/Subroutines
       subroutine dpbsv (UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO)
	    DPBSV computes the solution to system of linear equations A * X = B for OTHER
	   matrices

Function/Subroutine Documentation
   subroutine dpbsv (characterUPLO, integerN, integerKD, integerNRHS, double precision,
       dimension( ldab, * )AB, integerLDAB, double precision, dimension( ldb, * )B, integerLDB,
       integerINFO)
	DPBSV computes the solution to system of linear equations A * X = B for OTHER matrices

       Purpose:

	    DPBSV computes the solution to a real system of linear equations
	       A * X = B,
	    where A is an N-by-N symmetric positive definite band matrix and X
	    and B are N-by-NRHS matrices.

	    The Cholesky decomposition is used to factor A as
	       A = U**T * U,  if UPLO = 'U', or
	       A = L * L**T,  if UPLO = 'L',
	    where U is an upper triangular band matrix, and L is a lower
	    triangular band matrix, with the same number of superdiagonals or
	    subdiagonals as A.	The factored form of A is then used to solve the
	    system of equations A * X = B.

       Parameters:
	   UPLO

		     UPLO is CHARACTER*1
		     = 'U':  Upper triangle of A is stored;
		     = 'L':  Lower triangle of A is stored.

	   N

		     N is INTEGER
		     The number of linear equations, i.e., the order of the
		     matrix A.	N >= 0.

	   KD

		     KD is INTEGER
		     The number of superdiagonals of the matrix A if UPLO = 'U',
		     or the number of subdiagonals if UPLO = 'L'.  KD >= 0.

	   NRHS

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

	   AB

		     AB is DOUBLE PRECISION array, dimension (LDAB,N)
		     On entry, the upper or lower triangle of the symmetric band
		     matrix A, stored in the first KD+1 rows of the array.  The
		     j-th column of A is stored in the j-th column of the array AB
		     as follows:
		     if UPLO = 'U', AB(KD+1+i-j,j) = A(i,j) for max(1,j-KD)<=i<=j;
		     if UPLO = 'L', AB(1+i-j,j)    = A(i,j) for j<=i<=min(N,j+KD).
		     See below for further details.

		     On exit, if INFO = 0, the triangular factor U or L from the
		     Cholesky factorization A = U**T*U or A = L*L**T of the band
		     matrix A, in the same storage format as A.

	   LDAB

		     LDAB is INTEGER
		     The leading dimension of the array AB.  LDAB >= KD+1.

	   B

		     B is 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

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

	   INFO

		     INFO is INTEGER
		     = 0:  successful exit
		     < 0:  if INFO = -i, the i-th argument had an illegal value
		     > 0:  if INFO = i, the leading minor of order i of A is not
			   positive definite, so the factorization could not be
			   completed, and the solution has not been computed.

       Author:
	   Univ. of Tennessee

	   Univ. of California Berkeley

	   Univ. of Colorado Denver

	   NAG Ltd.

       Date:
	   November 2011

       Further Details:

	     The band storage scheme is illustrated by the following example, when
	     N = 6, KD = 2, and UPLO = 'U':

	     On entry:			     On exit:

		 *    *   a13  a24  a35  a46	  *    *   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

	     Similarly, if UPLO = 'L' the format of A is as follows:

	     On entry:			     On exit:

		a11  a22  a33  a44  a55  a66	 l11  l22  l33	l44  l55  l66
		a21  a32  a43  a54  a65   *	 l21  l32  l43	l54  l65   *
		a31  a42  a53  a64   *	  *	 l31  l42  l53	l64   *    *

	     Array elements marked * are not used by the routine.

       Definition at line 165 of file dpbsv.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

Version 3.4.2				 Tue Sep 25 2012			       dpbsv.f(3)
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