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

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

     CHARACTER UPLO

     INTEGER INFO, LDB, LDX, N, NRHS

     DOUBLE PRECISION BERR( * ), D( * ), DF(  *  ),  FERR(  *  ),
               RWORK( * )

     COMPLEX*16 B( LDB, * ), E( * ), EF( * ), WORK( * ), X(  LDX,
               * )



     #include <sunperf.h>

     void zptrfs(char uplo, int n, int  nrhs,  double  *d,  doub-
               lecomplex *e, double *df, doublecomplex *ef, doub-
               lecomplex *zb, int  ldb,  doublecomplex  *zx,  int
               ldx, double *ferr, double *berr, int *info) ;

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


ARGUMENTS
     UPLO      (input) CHARACTER*1
               Specifies whether the superdiagonal or the  subdi-
               agonal  of  the tridiagonal matrix A is stored and
               the form of the factorization:
               = 'U':  E is the  superdiagonal  of  A,  and  A  =
               U**H*D*U;
               = 'L':  E  is  the  subdiagonal  of  A,  and  A  =
               L*D*L**H.   (The  two forms are equivalent if A is
               real.)

     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) DOUBLE PRECISION array, dimension (N)
               The n real diagonal elements  of  the  tridiagonal
               matrix A.

     E         (input) COMPLEX*16 array, dimension (N-1)
               The (n-1) off-diagonal elements of the tridiagonal
               matrix A (see UPLO).

     DF        (input) DOUBLE PRECISION array, dimension (N)
               The n diagonal elements of the diagonal  matrix  D
               from the factorization computed by ZPTTRF.

     EF        (input) COMPLEX*16 array, dimension (N-1)
               The (n-1) off-diagonal elements of the unit  bidi-
               agonal  factor  U or L from the factorization com-
               puted by ZPTTRF (see UPLO).

     B         (input) COMPLEX*16 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)   COMPLEX*16    array,    dimension
               (LDX,NRHS)
               On entry, the solution matrix X,  as  computed  by
               ZPTTRS.  On exit, the improved solution matrix X.

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

     FERR      (output) DOUBLE PRECISION 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) DOUBLE PRECISION 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) COMPLEX*16 array, dimension (N)

     RWORK     (workspace) DOUBLE PRECISION array, dimension (N)

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

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