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

```
DGERFS(3F)							    DGERFS(3F)

```

### NAME[Toc][Back]

```     DGERFS - improve the computed solution to a system	of linear equations
and provides error	bounds and backward error estimates for	the solution
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGERFS(	TRANS, N, NRHS,	A, LDA,	AF, LDAF, IPIV,	B, LDB,	X,
LDX, FERR, BERR, WORK, IWORK, INFO )

CHARACTER	TRANS

INTEGER	INFO, LDA, LDAF, LDB, LDX, N, NRHS

INTEGER	IPIV( *	), IWORK( * )

DOUBLE		PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, *	),
BERR( *	), FERR( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     DGERFS improves the computed solution to a	system of linear equations and
provides error bounds and backward	error estimates	for the	solution.

```

### ARGUMENTS[Toc][Back]

```     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)

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

NRHS    (input) INTEGER
The number	of right hand sides, i.e., the number of columns of
the matrices B and	X.  NRHS >= 0.

A	     (input) DOUBLE PRECISION array, dimension (LDA,N)
The original N-by-N matrix	A.

LDA     (input) INTEGER
The leading dimension of the array	A.  LDA	>= max(1,N).

AF	     (input) DOUBLE PRECISION array, dimension (LDAF,N)
The factors L and U from the factorization	A = P*L*U as computed
by	DGETRF.

LDAF    (input) INTEGER
The leading dimension of the array	AF.  LDAF >= max(1,N).

IPIV    (input) INTEGER array, dimension (N)
The pivot indices from DGETRF; for	1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).

Page 1

DGERFS(3F)							    DGERFS(3F)

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/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by DGETRS.  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	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) 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 i-th argument had an illegal value
```

### PARAMETERS[Toc][Back]

```     ITMAX is the maximum number of steps of iterative refinement.
DGERFS(3F)							    DGERFS(3F)

```

### NAME[Toc][Back]

```     DGERFS - improve the computed solution to a system	of linear equations
and provides error	bounds and backward error estimates for	the solution
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DGERFS(	TRANS, N, NRHS,	A, LDA,	AF, LDAF, IPIV,	B, LDB,	X,
LDX, FERR, BERR, WORK, IWORK, INFO )

CHARACTER	TRANS

INTEGER	INFO, LDA, LDAF, LDB, LDX, N, NRHS

INTEGER	IPIV( *	), IWORK( * )

DOUBLE		PRECISION A( LDA, * ), AF( LDAF, * ), B( LDB, *	),
BERR( *	), FERR( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     DGERFS improves the computed solution to a	system of linear equations and
provides error bounds and backward	error estimates	for the	solution.

```

### ARGUMENTS[Toc][Back]

```     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)

N	     (input) INTEGER
The order of the matrix A.	 N >= 0.

NRHS    (input) INTEGER
The number	of right hand sides, i.e., the number of columns of
the matrices B and	X.  NRHS >= 0.

A	     (input) DOUBLE PRECISION array, dimension (LDA,N)
The original N-by-N matrix	A.

LDA     (input) INTEGER
The leading dimension of the array	A.  LDA	>= max(1,N).

AF	     (input) DOUBLE PRECISION array, dimension (LDAF,N)
The factors L and U from the factorization	A = P*L*U as computed
by	DGETRF.

LDAF    (input) INTEGER
The leading dimension of the array	AF.  LDAF >= max(1,N).

IPIV    (input) INTEGER array, dimension (N)
The pivot indices from DGETRF; for	1<=i<=N, row i of the matrix
was interchanged with row IPIV(i).

Page 1

DGERFS(3F)							    DGERFS(3F)

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/output) DOUBLE PRECISION array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by DGETRS.  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	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) 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 i-th argument had an illegal value
```

### PARAMETERS[Toc][Back]

```     ITMAX is the maximum number of steps of iterative refinement.

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