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sgtrfs

 NAME
      SGTRFS - improve the computed solution to a system of linear
      equations when the coefficient matrix is tridiagonal, and
      provides error bounds and backward error estimates for the
      solution

 SYNOPSIS
      SUBROUTINE SGTRFS( TRANS, N, NRHS, DL, D, DU, DLF, DF, DUF,
                         DU2, IPIV, B, LDB, X, LDX, FERR, BERR,
                         WORK, IWORK, INFO )

          CHARACTER      TRANS

          INTEGER        INFO, LDB, LDX, N, NRHS

          INTEGER        IPIV( * ), IWORK( * )

          REAL           B( LDB, * ), BERR( * ), D( * ), DF( * ),
                         DL( * ), DLF( * ), DU( * ), DU2( * ),
                         DUF( * ), FERR( * ), WORK( * ), X( LDX, *
                         )

 PURPOSE
      SGTRFS improves the computed solution to a system of linear
      equations when the coefficient matrix is tridiagonal, and
      provides error bounds and backward error estimates for the
      solution.

 ARGUMENTS
      TRANS   (input) CHARACTER*1
              Specifies the form of the system of equations:
              = 'N':  A * X = B     (No transpose)
              = 'T':  A**T * X = B  (Transpose)
              = 'C':  A**H * X = B  (Conjugate transpose = Tran-
              spose)

      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.

      DL      (input) REAL array, dimension (N-1)
              The (n-1) subdiagonal elements of A.

      D       (input) REAL array, dimension (N)
              The diagonal elements of A.

      DU      (input) REAL array, dimension (N-1)
              The (n-1) superdiagonal elements of A.

      DLF     (input) REAL array, dimension (N-1)
              The (n-1) multipliers that define the matrix L from
              the LU factorization of A as computed by SGTTRF.

      DF      (input) REAL array, dimension (N)
              The n diagonal elements of the upper triangular
              matrix U from the LU factorization of A.

      DUF     (input) REAL array, dimension (N-1)
              The (n-1) elements of the first superdiagonal of U.

      DU2     (input) REAL array, dimension (N-2)
              The (n-2) elements of the second superdiagonal of U.

      IPIV    (input) INTEGER array, dimension (N)
              The pivot indices; for 1 <= i <= n, row i of the
              matrix was interchanged with row IPIV(i).  IPIV(i)
              will always be either i or i+1; IPIV(i) = i indi-
              cates a row interchange was not required.

      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
              SGTTRS.  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 (3*N)

      IWORK   (workspace) INTEGER array, dimension (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.