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LAPACK version 3.0
dpbsv(3)

PURPOSE
  DPBSV - compute the solution to a real system of linear equations A * X =
  B,

SYNTAX
  SUBROUTINE DPBSV( UPLO, N, KD, NRHS, AB, LDAB, B, LDB, INFO )

      CHARACTER	    UPLO

      INTEGER	    INFO, KD, LDAB, LDB, N, NRHS

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

DESCRIPTION
  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.

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

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

  KD	  (input) INTEGER
	  The number of superdiagonals of the matrix A if UPLO = 'U', or the
	  number of subdiagonals if UPLO = 'L'.	 KD >= 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 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	  (input) INTEGER
	  The leading dimension of the array AB.  LDAB >= KD+1.

  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, 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.

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.