·  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/cpprfs (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

```
CPPRFS(3F)							    CPPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

REAL		BERR( *	), FERR( * ), RWORK( * )

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

### PURPOSE[Toc][Back]

```     CPPRFS improves the computed solution to a	system of linear equations
when the coefficient matrix is Hermitian positive definite	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 array, dimension (N*(N+1)/2)
The upper or lower	triangle of the	Hermitian 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)*(2n-j)/2) =
A(i,j) for	j<=i<=n.

AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or	L from the Cholesky factorization A =
U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, packed
columnwise	in a linear array in the same format as	A (see AP).

B	     (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix	B.

Page 1

CPPRFS(3F)							    CPPRFS(3F)

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

X	     (input/output) COMPLEX array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by CPPTRS.  On exit,
the improved 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) COMPLEX array,	dimension (2*N)

RWORK   (workspace) REAL 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.
CPPRFS(3F)							    CPPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

REAL		BERR( *	), FERR( * ), RWORK( * )

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

### PURPOSE[Toc][Back]

```     CPPRFS improves the computed solution to a	system of linear equations
when the coefficient matrix is Hermitian positive definite	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 array, dimension (N*(N+1)/2)
The upper or lower	triangle of the	Hermitian 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)*(2n-j)/2) =
A(i,j) for	j<=i<=n.

AFP     (input) COMPLEX array, dimension (N*(N+1)/2)
The triangular factor U or	L from the Cholesky factorization A =
U**H*U or A = L*L**H, as computed by SPPTRF/CPPTRF, packed
columnwise	in a linear array in the same format as	A (see AP).

B	     (input) COMPLEX array, dimension (LDB,NRHS)
The right hand side matrix	B.

Page 1

CPPRFS(3F)							    CPPRFS(3F)

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

X	     (input/output) COMPLEX array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by CPPTRS.  On exit,
the improved 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) COMPLEX array,	dimension (2*N)

RWORK   (workspace) REAL 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