
DTBRFS(l) ) DTBRFS(l)
NAME
DTBRFS  provide error bounds and backward error estimates for the solution to a system of
linear equations with a triangular band coefficient matrix
SYNOPSIS
SUBROUTINE DTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB, LDAB, B, LDB, X, LDX, FERR, BERR,
WORK, IWORK, INFO )
CHARACTER DIAG, TRANS, UPLO
INTEGER INFO, KD, LDAB, LDB, LDX, N, NRHS
INTEGER IWORK( * )
DOUBLE PRECISION AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ), WORK( * ),
X( LDX, * )
PURPOSE
DTBRFS provides error bounds and backward error estimates for the solution to a system of
linear equations with a triangular band coefficient matrix. The solution matrix X must be
computed by DTBTRS or some other means before entering this routine. DTBRFS 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 = Transpose)
DIAG (input) CHARACTER*1
= 'N': A is nonunit 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) DOUBLE PRECISION array, dimension (LDAB,N)
The upper or lower triangular band matrix A, stored in the first kd+1 rows of the
array. The jth column of A is stored in the jth column of the array AB as fol
lows: if UPLO = 'U', AB(kd+1+ij,j) = A(i,j) for max(1,jkd)<=i<=j; if UPLO = 'L',
AB(1+ij,j) = A(i,j) for j<=i<=min(n,j+kd). If DIAG = 'U', the diagonal ele
ments of A are not referenced and are assumed to be 1.
LDAB (input) INTEGER
The leading dimension of the array AB. LDAB >= KD+1.
B (input) DOUBLE PRECISION 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) DOUBLE PRECISION array, dimension (LDX,NRHS)
The 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 solution vector X(j) (the jth 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 esti
mate is as reliable as the estimate for RCOND, and is almost always a slight over
estimate 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 solu
tion).
WORK (workspace) DOUBLE PRECISION array, dimension (3*N)
IWORK (workspace) INTEGER array, dimension (N)
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
LAPACK version 3.0 15 June 2000 DTBRFS(l) 
