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

```
CPTRFS(3F)							    CPTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CPTRFS(	UPLO, N, NRHS, D, E, DF, EF, B,	LDB, X,	LDX, FERR,
BERR, WORK, RWORK, INFO	)

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

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

COMPLEX	B( LDB,	* ), E(	* ), EF( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
Specifies whether the superdiagonal or the	subdiagonal of the
tridiagonal matrix	A is stored and	the form of the	factorization:
= 'U':  E is the superdiagonal of A, and A	= U**H*D*U;
= 'L':  E is the subdiagonal of A,	and A =	L*D*L**H.  (The	two
forms are equivalent if A is real.)

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 matrix	B.  NRHS >= 0.

D	     (input) REAL array, dimension (N)
The n real	diagonal elements of the tridiagonal matrix A.

E	     (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of	the tridiagonal	matrix A (see
UPLO).

DF	     (input) REAL array, dimension (N)
The n diagonal elements of	the diagonal matrix D from the
factorization computed by CPTTRF.

Page 1

CPTRFS(3F)							    CPTRFS(3F)

EF	     (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of	the unit bidiagonal factor U
or	L from the factorization computed by CPTTRF (see UPLO).

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/output) COMPLEX array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by CPTTRS.  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 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).

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 (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.
CPTRFS(3F)							    CPTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	CPTRFS(	UPLO, N, NRHS, D, E, DF, EF, B,	LDB, X,	LDX, FERR,
BERR, WORK, RWORK, INFO	)

CHARACTER	UPLO

INTEGER	INFO, LDB, LDX,	N, NRHS

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

COMPLEX	B( LDB,	* ), E(	* ), EF( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     UPLO    (input) CHARACTER*1
Specifies whether the superdiagonal or the	subdiagonal of the
tridiagonal matrix	A is stored and	the form of the	factorization:
= 'U':  E is the superdiagonal of A, and A	= U**H*D*U;
= 'L':  E is the subdiagonal of A,	and A =	L*D*L**H.  (The	two
forms are equivalent if A is real.)

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 matrix	B.  NRHS >= 0.

D	     (input) REAL array, dimension (N)
The n real	diagonal elements of the tridiagonal matrix A.

E	     (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of	the tridiagonal	matrix A (see
UPLO).

DF	     (input) REAL array, dimension (N)
The n diagonal elements of	the diagonal matrix D from the
factorization computed by CPTTRF.

Page 1

CPTRFS(3F)							    CPTRFS(3F)

EF	     (input) COMPLEX array, dimension (N-1)
The (n-1) off-diagonal elements of	the unit bidiagonal factor U
or	L from the factorization computed by CPTTRF (see UPLO).

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/output) COMPLEX array, dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by CPTTRS.  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 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).

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 (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```
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