·  Home
+   man pages
 -> Linux -> FreeBSD -> OpenBSD -> NetBSD -> Tru64 Unix -> HP-UX 11i -> IRIX
·  Linux HOWTOs
·  FreeBSD Tips
·  *niX Forums

man pages->IRIX man pages -> complib/zsprfs (3)
 Title
 Content
 Arch
 Section All Sections 1 - General Commands 2 - System Calls 3 - Subroutines 4 - Special Files 5 - File Formats 6 - Games 7 - Macros and Conventions 8 - Maintenance Commands 9 - Kernel Interface n - New Commands

### Contents

```
ZSPRFS(3F)							    ZSPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZSPRFS(	UPLO, N, NRHS, AP, AFP,	IPIV, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO	)

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IPIV( *	)

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

COMPLEX*16	AFP( * ), AP( *	), B( LDB, * ),	WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     ZSPRFS improves the computed solution to a	system of linear equations
when the coefficient matrix is symmetric indefinite and packed, 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.

AP	     (input) COMPLEX*16	array, dimension (N*(N+1)/2)
The upper or lower	triangle of the	symmetric matrix A, packed
columnwise	in a linear array.  The	j-th column of A is stored in
the array AP as follows:  if UPLO = 'U', AP(i + (j-1)*j/2)	=
A(i,j) for	1<=i<=j; if UPLO = 'L',	AP(i + (j-1)*(2*n-j)/2)	=
A(i,j) for	j<=i<=n.

AFP     (input) COMPLEX*16	array, dimension (N*(N+1)/2)
The factored form of the matrix A.	 AFP contains the block
diagonal matrix D and the multipliers used	to obtain the factor U
or	L from the factorization A = U*D*U**T or A = L*D*L**T as
computed by ZSPTRF, stored	as a packed triangular matrix.

Page 1

ZSPRFS(3F)							    ZSPRFS(3F)

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

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 ZSPTRS.  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.
ZSPRFS(3F)							    ZSPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZSPRFS(	UPLO, N, NRHS, AP, AFP,	IPIV, B, LDB, X, LDX, FERR,
BERR, WORK, RWORK, INFO	)

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IPIV( *	)

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

COMPLEX*16	AFP( * ), AP( *	), B( LDB, * ),	WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     ZSPRFS improves the computed solution to a	system of linear equations
when the coefficient matrix is symmetric indefinite and packed, 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.

AP	     (input) COMPLEX*16	array, dimension (N*(N+1)/2)
The upper or lower	triangle of the	symmetric matrix A, packed
columnwise	in a linear array.  The	j-th column of A is stored in
the array AP as follows:  if UPLO = 'U', AP(i + (j-1)*j/2)	=
A(i,j) for	1<=i<=j; if UPLO = 'L',	AP(i + (j-1)*(2*n-j)/2)	=
A(i,j) for	j<=i<=n.

AFP     (input) COMPLEX*16	array, dimension (N*(N+1)/2)
The factored form of the matrix A.	 AFP contains the block
diagonal matrix D and the multipliers used	to obtain the factor U
or	L from the factorization A = U*D*U**T or A = L*D*L**T as
computed by ZSPTRF, stored	as a packed triangular matrix.

Page 1

ZSPRFS(3F)							    ZSPRFS(3F)

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

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 ZSPTRS.  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```
[ Back ]
Similar pages