dptrfs(3)

NAME

DPTRFS - improve the computed solution to a system of lin

ear 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 lin

ear 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 bidiag

onal 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 up

per 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 ille

gal value

PARAMETERS

ITMAX is the maximum number of steps of iterative refine

ment.

LAPACK version 3.0 15 June 2000

DPTRFS(3)