DTBRFS(3)
provides 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 follows:
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 elements 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 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) 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