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sptrfs

 NAME
      SPTRFS - improve 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

 SYNOPSIS
      SUBROUTINE SPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX,
                         FERR, BERR, WORK, INFO )

          INTEGER        INFO, LDB, LDX, N, NRHS

          REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ),
                         E( * ), EF( * ), FERR( * ), WORK( * ), X(
                         LDX, * )

 PURPOSE
      SPTRFS 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.

 ARGUMENTS
      N       (input) INTEGER
              The order of the matrix A.  N >= 0.

      NRHS    (input) INTEGER
              The number of right hand sides, i.e., the number of
              columns of the matrix B.  NRHS >= 0.

      D       (input) REAL array, dimension (N)
              The n diagonal elements of the tridiagonal matrix A.

      E       (input) REAL array, dimension (N-1)
              The (n-1) subdiagonal elements of the tridiagonal
              matrix A.

      DF      (input) REAL array, dimension (N)
              The n diagonal elements of the diagonal matrix D
              from the factorization computed by SPTTRF.

      EF      (input) REAL array, dimension (N-1)
              The (n-1) subdiagonal elements of the unit bidiago-
              nal factor L from the factorization computed by
              SPTTRF.

      B       (input) REAL array, dimension (LDB,NRHS)
              The right hand side matrix B.

      LDB     (input) INTEGER
              The leading dimension of the array B.  LDB >=

              max(1,N).

      X       (input/output) REAL array, dimension (LDX,NRHS)
              On entry, the solution matrix X, as computed by
              SPTTRS.  On exit, the improved solution matrix X.

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

      FERR    (output) REAL array, dimension (NRHS)
              The estimated forward error bounds for each solution
              vector X(j) (the j-th column of the solution matrix
              X).  If XTRUE is the true solution, FERR(j) bounds
              the magnitude of the largest entry in (X(j) - XTRUE)
              divided by the magnitude of the largest entry in
              X(j).  The quality of the error bound depends on the
              quality of the estimate of norm(inv(A)) computed in
              the code; if the estimate of norm(inv(A)) is accu-
              rate, the error bound is guaranteed.

      BERR    (output) REAL array, dimension (NRHS)
              The componentwise relative backward error of each
              solution vector X(j) (i.e., the smallest relative
              change in any entry of A or B that makes X(j) an
              exact solution).

      WORK    (workspace) REAL array, dimension (2*N)

      INFO    (output) INTEGER
              = 0:  successful exit
              < 0:  if INFO = -i, the i-th argument had an illegal
              value

 PARAMETERS
      ITMAX is the maximum number of steps of iterative refine-
      ment.