zgbrfs(3)

NAME

ZGBRFS - improve the computed solution to a system of lin

ear equations when the coefficient matrix is banded, and provides

error bounds and backward error estimates for the solution

SYNOPSIS

SUBROUTINE ZGBRFS( TRANS, N, KL, KU, NRHS, AB, LDAB,  AFB,
LDAFB, IPIV, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO )
    CHARACTER      TRANS
    INTEGER        INFO, KL, KU, LDAB, LDAFB, LDB, LDX, N,
NRHS
    INTEGER        IPIV( * )
    DOUBLE         PRECISION BERR( * ), FERR( * ),  RWORK(
* )
    COMPLEX*16     AB( LDAB, * ), AFB( LDAFB, * ), B( LDB,
* ), WORK( * ), X( LDX, * )

PURPOSE

ZGBRFS improves the computed solution to a system of lin

ear equations when the coefficient matrix is banded, and provides

error bounds and backward error estimates for the solution.

ARGUMENTS

TRANS (input) CHARACTER*1

Specifies the form of the system of equations:
= 'N': A * X = B (No transpose)
= 'T': A**T * X = B (Transpose)
= 'C': A**H * X = B (Conjugate transpose)

N (input) INTEGER

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

KL (input) INTEGER

The number of subdiagonals within the band of A.

KL >= 0.

KU (input) INTEGER

The number of superdiagonals within the band of A.

KU >= 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*16 array, dimension (LDAB,N)

The original band matrix A, stored in rows 1 to

KL+KU+1. The j-th column of A is stored in the j-th column of

the array AB as follows: AB(ku+1+i-j,j) = A(i,j) for max(1,j

ku)<=i<=min(n,j+kl).

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >=

KL+KU+1.

AFB (input) COMPLEX*16 array, dimension (LDAFB,N)

Details of the LU factorization of the band matrix

A, as computed by ZGBTRF. U is stored as an upper triangular

band matrix with KL+KU superdiagonals in rows 1 to KL+KU+1, and

the multipliers used during the factorization are stored in rows

KL+KU+2 to 2*KL+KU+1.

LDAFB (input) INTEGER

The leading dimension of the array AFB. LDAFB >=

2*KL*KU+1.

IPIV (input) INTEGER array, dimension (N)

The pivot indices from ZGBTRF; for 1<=i<=N, row i

of the matrix was interchanged with row IPIV(i).

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

ZGBTRS. 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 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) 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 (2*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

ZGBRFS(3)