 DPTRFS(3) 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

## 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 backward 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 (N-1)
The (n-1) 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 (N-1)
The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization 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 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) DOUBLE PRECISION array, dimension (2*N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

## PARAMETERS

ITMAX is the maximum number of steps of iterative refinement.