SGERFS improves the computed solution to a system of linear
 equations and provides error bounds and backward error estimates for
 the solution.

          TRANS is 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 = Transpose)

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

          NRHS is INTEGER
          The number of right hand sides, i.e., the number of columns
          of the matrices B and X.  NRHS >= 0.

          A is REAL array, dimension (LDA,N)
          The original N-by-N matrix A.

          LDA is INTEGER
          The leading dimension of the array A.  LDA >= max(1,N).

          AF is REAL array, dimension (LDAF,N)
          The factors L and U from the factorization A = P*L*U
          as computed by SGETRF.

          LDAF is INTEGER
          The leading dimension of the array AF.  LDAF >= max(1,N).

          IPIV is INTEGER array, dimension (N)
          The pivot indices from SGETRF; for 1<=i<=N, row i of the
          matrix was interchanged with row IPIV(i).

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

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

          X is REAL array, dimension (LDX,NRHS)
          On entry, the solution matrix X, as computed by SGETRS.
          On exit, the improved solution matrix X.

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

          FERR is REAL array, dimension (NRHS)
          The estimated 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).  The estimate is as reliable as
          the estimate for RCOND, and is almost always a slight
          overestimate of the true error.

          BERR is REAL 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).

          WORK is REAL array, dimension (3*N)

          IWORK is INTEGER array, dimension (N)

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

  ITMAX is the maximum number of steps of iterative refinement.