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## zptrfs()

subroutine zptrfs | ( | character | uplo,
|  | integer | n,
|  | integer | nrhs,
|  | double precision, dimension( * ) | d,
|  | complex*16, dimension( * ) | e,
|  | double precision, dimension( * ) | df,
|  | complex*16, dimension( * ) | ef,
|  | complex*16, dimension( ldb, * ) | b,
|  | integer | ldb,
|  | complex*16, dimension( ldx, * ) | x,
|  | integer | ldx,
|  | double precision, dimension( * ) | ferr,
|  | double precision, dimension( * ) | berr,
|  | complex*16, dimension( * ) | work,
|  | double precision, dimension( * ) | rwork,
|  | integer | info )

ZPTRFS

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

Purpose:

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

Parameters

  [in]

  UPLO

      !>          UPLO is CHARACTER*1
      !>          Specifies whether the superdiagonal or the subdiagonal of the
      !>          tridiagonal matrix A is stored and the form of the
      !>          factorization:
      !>          = 'U':  E is the superdiagonal of A, and A = U**H*D*U;
      !>          = 'L':  E is the subdiagonal of A, and A = L*D*L**H.
      !>          (The two forms are equivalent if A is real.)
      !>

  [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 real diagonal elements of the tridiagonal matrix A.
      !>

  [in]

  E

      !>          E is COMPLEX*16 array, dimension (N-1)
      !>          The (n-1) off-diagonal elements of the tridiagonal matrix A
      !>          (see UPLO).
      !>

  [in]

  DF

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

  [in]

  EF

      !>          EF is COMPLEX*16 array, dimension (N-1)
      !>          The (n-1) off-diagonal elements of the unit bidiagonal
      !>          factor U or L from the factorization computed by ZPTTRF
      !>          (see UPLO).
      !>

  [in]

  B

      !>          B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
      !>          On entry, the solution matrix X, as computed by ZPTTRS.
      !>          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 COMPLEX*16 array, dimension (N)
      !>

  [out]

  RWORK

      !>          RWORK is DOUBLE PRECISION array, dimension (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.