SPTRFS(3)                  MathKeisan LAPACK routine                 SPTRFS(3)



NAME
       SPTRFS - 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 tridiag-
       onal,  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 fac-
               torization computed by SPTTRF.

       EF      (input) REAL array, dimension (N-1)
               The (n-1) subdiagonal elements of the unit bidiagonal 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 forward error bound for each solution vector X(j) (the j-th
               column  of  the solution matrix X).  If XTRUE is the true solu-
               tion 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) REAL array, dimension (NRHS)
               The componentwise relative backward error of each solution vec-
               tor  X(j) (i.e., the smallest relative change in any element 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 refinement.



 LAPACK routine (version 3.1)    November 2006                       SPTRFS(3)