.TH  SPTRFS 1 "November 2006" " LAPACK routine (version 3.1) " " LAPACK routine (version 3.1) " 
.SH NAME
SPTRFS - 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
.SH SYNOPSIS
.TP 19
SUBROUTINE SPTRFS(
N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR,
BERR, WORK, INFO )
.TP 19
.ti +4
INTEGER
INFO, LDB, LDX, N, NRHS
.TP 19
.ti +4
REAL
B( LDB, * ), BERR( * ), D( * ), DF( * ),
E( * ), EF( * ), FERR( * ), WORK( * ),
X( LDX, * )
.SH 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.

.SH ARGUMENTS
.TP 8
N       (input) INTEGER
The order of the matrix A.  N >= 0.
.TP 8
NRHS    (input) INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B.  NRHS >= 0.
.TP 8
D       (input) REAL array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.
.TP 8
E       (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.
.TP 8
DF      (input) REAL array, dimension (N)
The n diagonal elements of the diagonal matrix D from the
factorization computed by SPTTRF.
.TP 8
EF      (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit bidiagonal factor
L from the factorization computed by SPTTRF.
.TP 8
B       (input) REAL array, dimension (LDB,NRHS)
The right hand side matrix B.
.TP 8
LDB     (input) INTEGER
The leading dimension of the array B.  LDB >= max(1,N).
.TP 8
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.
.TP 8
LDX     (input) INTEGER
The leading dimension of the array X.  LDX >= max(1,N).
.TP 8
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).
.TP 8
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).
.TP 8
WORK    (workspace) REAL array, dimension (2*N)
.TP 8
INFO    (output) INTEGER
= 0:  successful exit
.br
< 0:  if INFO = -i, the i-th argument had an illegal value
.SH PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.
