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

```
ZGTRFS(3F)							    ZGTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZGTRFS(	TRANS, N, NRHS,	DL, D, DU, DLF,	DF, DUF, DU2, IPIV, B,
LDB, X,	LDX, FERR, BERR, WORK, RWORK, INFO )

CHARACTER	TRANS

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IPIV( *	)

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

COMPLEX*16	B( LDB,	* ), D(	* ), DF( * ), DL( * ), DLF( * ), DU( *
), DU2(	* ), DUF( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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)

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.

DL	     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D	     (input) COMPLEX*16	array, dimension (N)
The diagonal elements of A.

DU	     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) multipliers that	define the matrix L from the LU
factorization of A	as computed by ZGTTRF.

Page 1

ZGTRFS(3F)							    ZGTRFS(3F)

DF	     (input) COMPLEX*16	array, dimension (N)
The n diagonal elements of	the upper triangular matrix U from the
LU	factorization of A.

DUF     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) elements	of the first superdiagonal of U.

DU2     (input) COMPLEX*16	array, dimension (N-2)
The (n-2) elements	of the second superdiagonal of U.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices;	for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either i
or	i+1; IPIV(i) = i indicates a row interchange was not required.

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 ZGTTRS.  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

Page 2

ZGTRFS(3F)							    ZGTRFS(3F)

```

### PARAMETERS[Toc][Back]

```     ITMAX is the maximum number of steps of iterative refinement.
ZGTRFS(3F)							    ZGTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

```     SUBROUTINE	ZGTRFS(	TRANS, N, NRHS,	DL, D, DU, DLF,	DF, DUF, DU2, IPIV, B,
LDB, X,	LDX, FERR, BERR, WORK, RWORK, INFO )

CHARACTER	TRANS

INTEGER	INFO, LDB, LDX,	N, NRHS

INTEGER	IPIV( *	)

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

COMPLEX*16	B( LDB,	* ), D(	* ), DF( * ), DL( * ), DLF( * ), DU( *
), DU2(	* ), DUF( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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)

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.

DL	     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) subdiagonal elements of A.

D	     (input) COMPLEX*16	array, dimension (N)
The diagonal elements of A.

DU	     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) superdiagonal elements of A.

DLF     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) multipliers that	define the matrix L from the LU
factorization of A	as computed by ZGTTRF.

Page 1

ZGTRFS(3F)							    ZGTRFS(3F)

DF	     (input) COMPLEX*16	array, dimension (N)
The n diagonal elements of	the upper triangular matrix U from the
LU	factorization of A.

DUF     (input) COMPLEX*16	array, dimension (N-1)
The (n-1) elements	of the first superdiagonal of U.

DU2     (input) COMPLEX*16	array, dimension (N-2)
The (n-2) elements	of the second superdiagonal of U.

IPIV    (input) INTEGER array, dimension (N)
The pivot indices;	for 1 <= i <= n, row i of the matrix was
interchanged with row IPIV(i).  IPIV(i) will always be either i
or	i+1; IPIV(i) = i indicates a row interchange was not required.

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 ZGTTRS.  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

Page 2

ZGTRFS(3F)							    ZGTRFS(3F)

```

### 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 3333```
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