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

```
ZHERFS(3F)							    ZHERFS(3F)

```

### NAME[Toc][Back]

```     ZHERFS - improve the computed solution to a system	of linear equations
when the coefficient matrix is Hermitian indefinite, and provides error
bounds and	backward error estimates for the solution
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZHERFS(	UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )

CHARACTER	UPLO

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

INTEGER	IPIV( *	)

DOUBLE		PRECISION BERR(	* ), FERR( * ),	RWORK( * )

COMPLEX*16	A( LDA,	* ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X(
LDX, * )
```

### PURPOSE[Toc][Back]

```     ZHERFS improves the computed solution to a	system of linear equations
when the coefficient matrix is Hermitian indefinite, and provides error
bounds and	backward error estimates for the solution.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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) COMPLEX*16	array, dimension (LDA,N)
The Hermitian matrix A.  If UPLO =	'U', the leading N-by-N	upper
triangular	part of	A contains the upper triangular	part of	the
matrix A, and the strictly	lower triangular part of A is not
referenced.  If UPLO = 'L', the leading N-by-N lower triangular
part of A contains	the lower triangular part of the matrix	A, and
the strictly upper	triangular part	of A is	not referenced.

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

AF	     (input) COMPLEX*16	array, dimension (LDAF,N)
The factored form of the matrix A.	 AF contains the block
diagonal matrix D and the multipliers used	to obtain the factor U

Page 1

ZHERFS(3F)							    ZHERFS(3F)

or	L from the factorization A = U*D*U**H or A = L*D*L**H as
computed by ZHETRF.

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

IPIV    (input) INTEGER array, dimension (N)
Details of	the interchanges and the block structure of D as
determined	by ZHETRF.

B	     (input) COMPLEX*16	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) COMPLEX*16 array, dimension	(LDX,NRHS)
On	entry, the solution matrix X, as computed by ZHETRS.  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) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE	PRECISION 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.
ZHERFS(3F)							    ZHERFS(3F)

```

### NAME[Toc][Back]

```     ZHERFS - improve the computed solution to a system	of linear equations
when the coefficient matrix is Hermitian indefinite, and provides error
bounds and	backward error estimates for the solution
```

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZHERFS(	UPLO, N, NRHS, A, LDA, AF, LDAF, IPIV, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )

CHARACTER	UPLO

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

INTEGER	IPIV( *	)

DOUBLE		PRECISION BERR(	* ), FERR( * ),	RWORK( * )

COMPLEX*16	A( LDA,	* ), AF( LDAF, * ), B( LDB, * ), WORK( * ), X(
LDX, * )
```

### PURPOSE[Toc][Back]

```     ZHERFS improves the computed solution to a	system of linear equations
when the coefficient matrix is Hermitian indefinite, and provides error
bounds and	backward error estimates for the solution.

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
= 'U':  Upper triangle of A is stored;
= 'L':  Lower triangle of A is stored.

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) COMPLEX*16	array, dimension (LDA,N)
The Hermitian matrix A.  If UPLO =	'U', the leading N-by-N	upper
triangular	part of	A contains the upper triangular	part of	the
matrix A, and the strictly	lower triangular part of A is not
referenced.  If UPLO = 'L', the leading N-by-N lower triangular
part of A contains	the lower triangular part of the matrix	A, and
the strictly upper	triangular part	of A is	not referenced.

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

AF	     (input) COMPLEX*16	array, dimension (LDAF,N)
The factored form of the matrix A.	 AF contains the block
diagonal matrix D and the multipliers used	to obtain the factor U

Page 1

ZHERFS(3F)							    ZHERFS(3F)

or	L from the factorization A = U*D*U**H or A = L*D*L**H as
computed by ZHETRF.

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

IPIV    (input) INTEGER array, dimension (N)
Details of	the interchanges and the block structure of D as
determined	by ZHETRF.

B	     (input) COMPLEX*16	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) COMPLEX*16 array, dimension	(LDX,NRHS)
On	entry, the solution matrix X, as computed by ZHETRS.  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) COMPLEX*16 array, dimension (2*N)

RWORK   (workspace) DOUBLE	PRECISION 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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