
ZPTRFS(l) ) ZPTRFS(l)
NAME
ZPTRFS  improve the computed solution to a system of linear equations when the coeffi
cient 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, * )
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 back
ward 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 equiva
lent 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 fac
torization 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 solu
tion).
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.
LAPACK version 3.0 15 June 2000 ZPTRFS(l) 
