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

```
CTRRFS(3F)							    CTRRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CTRRFS(	UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )

CHARACTER	DIAG, TRANS, UPLO

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

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

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

### PURPOSE[Toc][Back]

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

The solution matrix X must	be computed by CTRTRS or some other means
before entering this routine.  CTRRFS 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)

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.

A	     (input) COMPLEX array, dimension (LDA,N)
The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper
triangular	part of	the array A contains the upper triangular

Page 1

CTRRFS(3F)							    CTRRFS(3F)

matrix, and the strictly lower triangular part of A is not
referenced.  If UPLO = 'L', the leading N-by-N lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not	referenced.  If	DIAG =
'U', the diagonal elements	of A are also not referenced and are
assumed to	be 1.

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

B	     (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
The 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
CTRRFS(3F)							    CTRRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CTRRFS(	UPLO, TRANS, DIAG, N, NRHS, A, LDA, B, LDB, X, LDX,
FERR, BERR, WORK, RWORK, INFO )

CHARACTER	DIAG, TRANS, UPLO

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

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

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

### PURPOSE[Toc][Back]

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

The solution matrix X must	be computed by CTRTRS or some other means
before entering this routine.  CTRRFS 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)

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.

A	     (input) COMPLEX array, dimension (LDA,N)
The triangular matrix A.  If UPLO = 'U', the leading N-by-N upper
triangular	part of	the array A contains the upper triangular

Page 1

CTRRFS(3F)							    CTRRFS(3F)

matrix, and the strictly lower triangular part of A is not
referenced.  If UPLO = 'L', the leading N-by-N lower triangular
part of the array A contains the lower triangular matrix, and the
strictly upper triangular part of A is not	referenced.  If	DIAG =
'U', the diagonal elements	of A are also not referenced and are
assumed to	be 1.

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

B	     (input) COMPLEX 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) COMPLEX array, dimension (LDX,NRHS)
The 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

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