zptrfs(3)

NAME

ZPTRFS - improve the computed solution to a system of lin

ear equations when the coefficient 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 lin

ear equations when the coefficient matrix is Hermitian positive

definite and tridiagonal, and provides error bounds and backward

error estimates for the solution.

ARGUMENTS

UPLO (input) CHARACTER*1

Specifies whether the superdiagonal or the subdi

agonal 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 equivalent 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 (N-1)

The (n-1) off-diagonal 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 (N-1)

The (n-1) off-diagonal elements of the unit bidi

agonal factor U or L from the factorization 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 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) COMPLEX*16 array, dimension (N)

RWORK (workspace) DOUBLE PRECISION array, dimension (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

ZPTRFS(3)