
DPTRFS(l) ) DPTRFS(l)
NAME
DPTRFS  improve the computed solution to a system of linear equations when the coeffi
cient matrix is symmetric positive definite and tridiagonal, and provides error bounds and
backward error estimates for the solution
SYNOPSIS
SUBROUTINE DPTRFS( N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO )
INTEGER INFO, LDB, LDX, N, NRHS
DOUBLE PRECISION B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ),
FERR( * ), WORK( * ), X( LDX, * )
PURPOSE
DPTRFS 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 back
ward 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) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
E (input) DOUBLE PRECISION array, dimension (N1)
The (n1) subdiagonal elements of the tridiagonal matrix A.
DF (input) DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the diagonal matrix D from the factorization computed
by DPTTRF.
EF (input) DOUBLE PRECISION array, dimension (N1)
The (n1) subdiagonal elements of the unit bidiagonal factor L from the factoriza
tion computed by DPTTRF.
B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPTTRS. 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) DOUBLE PRECISION array, dimension (2*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 DPTRFS(l) 
