SPTRFS(3)      LAPACK routine of NEC Numeric Library Collection      SPTRFS(3)



NAME
       SPTRFS

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



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

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

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

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

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

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

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

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

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

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

           FERR      (output)
                     FERR is REAL 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).

           BERR      (output)
                     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      (output)
                     WORK is REAL array, dimension (2*N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                      SPTRFS(3)