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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, * )



     #include <sunperf.h>

     void sptrfs(int n, int nrhs, float *d, float *e, float  *df,
               float *ef, float *sb, int ldb, float *sx, int ldx,
               float *ferr, float *berr, int *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) 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
               bidiagonal  factor  L  from the factorization com-
               puted 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  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) 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      (workspace) REAL array, dimension (2*N)

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

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