cpbrfs(3)

NAME

CPBRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is Hermitian positive

definite and banded, and provides error bounds and backward error

estimates for the solution

SYNOPSIS

SUBROUTINE  CPBRFS(  UPLO,  N,  KD,  NRHS,  AB, LDAB, AFB,
LDAFB, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
    CHARACTER      UPLO
    INTEGER        INFO, KD, LDAB,  LDAFB,  LDB,  LDX,  N,
NRHS
    REAL           BERR( * ), FERR( * ), RWORK( * )
    COMPLEX        AB( LDAB, * ), AFB( LDAFB, * ), B( LDB,
* ), WORK( * ), X( LDX, * )

PURPOSE

CPBRFS improves the computed solution to a system of lin

ear equations when the coefficient matrix is Hermitian positive

definite and banded, and provides error bounds and backward error

estimates for the solution.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': Upper triangle of A is stored;
= 'L': Lower triangle of A is stored.

N (input) INTEGER

The order of the matrix A. N >= 0.

KD (input) INTEGER

The number of superdiagonals of the matrix A if

UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KD >=

0.

NRHS (input) INTEGER

The number of right hand sides, i.e., the number

of columns of the matrices B and X. NRHS >= 0.

AB (input) COMPLEX array, dimension (LDAB,N)

The upper or lower triangle of the Hermitian band

matrix A, stored in the first KD+1 rows of the array. The j-th

column of A is stored in the j-th column of the array AB as fol

lows: if UPLO = 'U', AB(kd+1+i-j,j) = A(i,j) for max(1,j

kd)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for

j<=i<=min(n,j+kd).

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >=

KD+1.

AFB (input) COMPLEX array, dimension (LDAFB,N)

The triangular factor U or L from the Cholesky

factorization A = U**H*U or A = L*L**H of the band matrix A as

computed by CPBTRF, in the same storage format as A (see AB).

LDAFB (input) INTEGER

The leading dimension of the array AFB. LDAFB >=

KD+1.

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

CPBTRS. 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 estimated forward error bound for each solu

tion 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). The estimate is as reliable as the estimate for RCOND, and

is almost always a slight overestimate of the true error.

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 (2*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

CPBRFS(3)