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

```
DTPRFS(3F)							    DTPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DTPRFS(	UPLO, TRANS, DIAG, N, NRHS, AP,	B, LDB,	X, LDX,	FERR,
BERR, WORK, IWORK, INFO	)

CHARACTER	DIAG, TRANS, UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IWORK( * )

DOUBLE		PRECISION AP( *	), B( LDB, * ),	BERR( *	), FERR( * ),
WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     DTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular	packed
coefficient matrix.

The solution matrix X must	be computed by DTPTRS or some other means
before entering this routine.  DTPRFS 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.

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

Page 1

DTPRFS(3F)							    DTPRFS(3F)

AP	     (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower	triangular 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.  If
DIAG = 'U', the diagonal elements of A are	not referenced and are
assumed to	be 1.

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) DOUBLE PRECISION array, dimension (LDX,NRHS)
The 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
DTPRFS(3F)							    DTPRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	DTPRFS(	UPLO, TRANS, DIAG, N, NRHS, AP,	B, LDB,	X, LDX,	FERR,
BERR, WORK, IWORK, INFO	)

CHARACTER	DIAG, TRANS, UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IWORK( * )

DOUBLE		PRECISION AP( *	), B( LDB, * ),	BERR( *	), FERR( * ),
WORK( *	), X( LDX, * )
```

### PURPOSE[Toc][Back]

```     DTPRFS provides error bounds and backward error estimates for the
solution to a system of linear equations with a triangular	packed
coefficient matrix.

The solution matrix X must	be computed by DTPTRS or some other means
before entering this routine.  DTPRFS 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.

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

Page 1

DTPRFS(3F)							    DTPRFS(3F)

AP	     (input) DOUBLE PRECISION array, dimension (N*(N+1)/2)
The upper or lower	triangular 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.  If
DIAG = 'U', the diagonal elements of A are	not referenced and are
assumed to	be 1.

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) DOUBLE PRECISION array, dimension (LDX,NRHS)
The 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

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