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, * )
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 subdiagonal 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 (N1)
 The (n1) offdiagonal 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 (N1)
 The (n1) offdiagonal elements of the unit bidiagonal factor U or L from the factorization computed 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 jth 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 ith argument had an illegal value
PARAMETERS
ITMAX is the maximum number of steps of iterative refinement.