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man pages->IRIX man pages -> complib/stbrfs (3)
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### Contents

```
STBRFS(3F)							    STBRFS(3F)

```

### NAME[Toc][Back]

```     STBRFS - provide error bounds and backward	error estimates	for the
solution to a system of linear equations with a triangular	band
coefficient matrix
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	STBRFS(	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( * )

REAL		AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ),
WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     STBRFS 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 STBTRS or some other means
before entering this routine.  STBRFS does	not do iterative refinement
because doing so cannot improve the backward error.

```

### ARGUMENTS[Toc][Back]

```     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 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.

Page 1

STBRFS(3F)							    STBRFS(3F)

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) REAL 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 jth
column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,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 assumed to be 1.

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

B	     (input) REAL 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) REAL 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	solution 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) REAL array, dimension (3*N)

IWORK   (workspace) INTEGER array,	dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value
STBRFS(3F)							    STBRFS(3F)

```

### NAME[Toc][Back]

```     STBRFS - provide error bounds and backward	error estimates	for the
solution to a system of linear equations with a triangular	band
coefficient matrix
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	STBRFS(	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( * )

REAL		AB( LDAB, * ), B( LDB, * ), BERR( * ), FERR( * ),
WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     STBRFS 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 STBTRS or some other means
before entering this routine.  STBRFS does	not do iterative refinement
because doing so cannot improve the backward error.

```

### ARGUMENTS[Toc][Back]

```     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 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.

Page 1

STBRFS(3F)							    STBRFS(3F)

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) REAL 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 jth
column of the array AB as follows:  if UPLO = 'U', AB(kd+1+ij,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 assumed to be 1.

LDAB    (input) INTEGER
The leading dimension of the array	AB.  LDAB >= KD+1.

B	     (input) REAL 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) REAL 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	solution 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) REAL array, dimension (3*N)

IWORK   (workspace) INTEGER array,	dimension (N)

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value

PPPPaaaaggggeeee 2222```
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