DPBSV(3)              LAPACK driver routine (version 3.1)             DPBSV(3)



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

SYNOPSIS
       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, * )

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  equa-
       tions 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.




 LAPACK driver routine (version 3.N1o)vember 2006                        DPBSV(3)