ctbrfs(3)

NAME

CTBRFS - provide error bounds and backward error estimates

for the solution to a system of linear equations with a triangu

lar band coefficient matrix

SYNOPSIS

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

PURPOSE

CTBRFS provides error bounds and backward error estimates

for the solution to a system of linear equations with a triangu

lar band coefficient matrix. The solution matrix X must be com

puted by CTBTRS or some other means before entering this routine.

CTBRFS does not do iterative refinement because doing so cannot

improve the backward error.

ARGUMENTS

UPLO (input) CHARACTER*1

= 'U': A is upper triangular;
= 'L': A is lower triangular.

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)

DIAG (input) CHARACTER*1

= 'N': A is non-unit triangular;
= 'U': A is unit triangular.

N (input) INTEGER

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

KD (input) INTEGER

The number of superdiagonals or subdiagonals of

the triangular band matrix A. 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 triangular 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 follows: 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). If DIAG =

'U', the diagonal elements of A are not referenced and are as

sumed to be 1.

LDAB (input) INTEGER

The leading dimension of the array AB. LDAB >=

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) COMPLEX array, dimension (LDX,NRHS)

The 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

LAPACK version 3.0 15 June 2000

CTBRFS(3)