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## dptrfs()

subroutine dptrfs | ( | integer | n,
|  | integer | nrhs,
|  | double precision, dimension( * ) | d,
|  | double precision, dimension( * ) | e,
|  | double precision, dimension( * ) | df,
|  | double precision, dimension( * ) | ef,
|  | double precision, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | double precision, dimension( ldx, * ) | x,
|  | integer | ldx,
|  | double precision, dimension( * ) | ferr,
|  | double precision, dimension( * ) | berr,
|  | double precision, dimension( * ) | work,
|  | integer | info )

DPTRFS

Download DPTRFS + dependencies [TGZ] [ZIP] [TXT]

Purpose:

      !>
      !> DPTRFS improves the computed solution to a system of linear
      !> equations when the coefficient matrix is symmetric positive definite
      !> and tridiagonal, and provides error bounds and backward error
      !> estimates for the solution.
      !>

Parameters

  [in]

  N

      !>          N is INTEGER
      !>          The order of the matrix A.  N >= 0.
      !>

  [in]

  NRHS

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

  [in]

  D

      !>          D is DOUBLE PRECISION array, dimension (N)
      !>          The n diagonal elements of the tridiagonal matrix A.
      !>

  [in]

  E

      !>          E is DOUBLE PRECISION array, dimension (N-1)
      !>          The (n-1) subdiagonal elements of the tridiagonal matrix A.
      !>

  [in]

  DF

      !>          DF is DOUBLE PRECISION array, dimension (N)
      !>          The n diagonal elements of the diagonal matrix D from the
      !>          factorization computed by DPTTRF.
      !>

  [in]

  EF

      !>          EF is DOUBLE PRECISION array, dimension (N-1)
      !>          The (n-1) subdiagonal elements of the unit bidiagonal factor
      !>          L from the factorization computed by DPTTRF.
      !>

  [in]

  B

      !>          B is DOUBLE PRECISION array, dimension (LDB,NRHS)
      !>          The right hand side matrix B.
      !>

  [in]

  LDB

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

  [in,out]

  X

      !>          X is DOUBLE PRECISION array, dimension (LDX,NRHS)
      !>          On entry, the solution matrix X, as computed by DPTTRS.
      !>          On exit, the improved solution matrix X.
      !>

  [in]

  LDX

      !>          LDX is INTEGER
      !>          The leading dimension of the array X.  LDX >= max(1,N).
      !>

  [out]

  FERR

      !>          FERR is DOUBLE PRECISION array, dimension (NRHS)
      !>          The forward error bound for each solution vector
      !>          X(j) (the j-th column of the solution matrix X).
      !>          If XTRUE is the true solution corresponding to X(j), FERR(j)
      !>          is an estimated upper bound for the magnitude of the largest
      !>          element in (X(j) - XTRUE) divided by the magnitude of the
      !>          largest element in X(j).
      !>

  [out]

  BERR

      !>          BERR is DOUBLE PRECISION array, dimension (NRHS)
      !>          The componentwise relative backward error of each solution
      !>          vector X(j) (i.e., the smallest relative change in
      !>          any element of A or B that makes X(j) an exact solution).
      !>

  [out]

  WORK

      !>          WORK is DOUBLE PRECISION array, dimension (2*N)
      !>

  [out]

  INFO

      !>          INFO is INTEGER
      !>          = 0:  successful exit
      !>          < 0:  if INFO = -i, the i-th argument had an illegal value
      !>

Internal Parameters:

      !>  ITMAX is the maximum number of steps of iterative refinement.
      !>

Author
  Univ. of Tennessee
  Univ. of California Berkeley
  Univ. of Colorado Denver
  NAG Ltd.