cptrfs(3)

NAME

CPTRFS - 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 CPTRFS( UPLO, N, NRHS, D, E, DF, EF, B, LDB, X,
LDX, FERR, BERR, WORK, RWORK, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, LDB, LDX, N, NRHS
    REAL           BERR( * ), D( * ), DF( * ), FERR( *  ),
RWORK( * )
    COMPLEX         B(  LDB, * ), E( * ), EF( * ), WORK( *
), X( LDX, * )

PURPOSE

CPTRFS 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) REAL array, dimension (N)

The n real diagonal elements of the tridiagonal

matrix A.

E (input) COMPLEX array, dimension (N-1)

The (n-1) off-diagonal elements of the tridiagonal

matrix A (see UPLO).

DF (input) REAL array, dimension (N)

The n diagonal elements of the diagonal matrix D

from the factorization computed by CPTTRF.

EF (input) COMPLEX array, dimension (N-1)

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

agonal factor U or L from the factorization computed by CPTTRF

(see UPLO).

B (input) COMPLEX 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 array, dimension (LDX,NRHS)

On entry, the solution matrix X, as computed by

CPTTRS. On exit, the improved solution matrix X.

LDX (input) INTEGER

The leading dimension of the array X. LDX >=

max(1,N).

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 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) 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).

WORK (workspace) COMPLEX array, dimension (N)

RWORK (workspace) REAL 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

CPTRFS(3)