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dpbsv

 NAME
      DPBSV - compute 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 equa-
      tions
         A * X = B, where A is an N-by-N symmetric positive defin-
      ite 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 matrix, and L is a lower tri-
      angular 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 sym-
              metric 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.

 (LDB,NRHS)
      B       (input/output) DOUBLE PRECISION array, dimension
              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 com-
              puted.

 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.