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

```
SPTRFS(3F)							    SPTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDB, LDX,	N, NRHS

REAL		B( LDB,	* ), BERR( * ),	D( * ),	DF( * ), E( * ), EF( *
), FERR( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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 diagonal elements of	the tridiagonal	matrix A.

E	     (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

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

EF	     (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit	bidiagonal factor L
from the factorization computed by	SPTTRF.

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

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

Page 1

SPTRFS(3F)							    SPTRFS(3F)

X	     (input/output) REAL array,	dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by SPTTRS.  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) REAL array, dimension (2*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.
SPTRFS(3F)							    SPTRFS(3F)

```

### NAME[Toc][Back]

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

### SYNOPSIS[Toc][Back]

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

INTEGER	INFO, LDB, LDX,	N, NRHS

REAL		B( LDB,	* ), BERR( * ),	D( * ),	DF( * ), E( * ), EF( *
), FERR( * ), WORK( * ), X( LDX, * )
```

### PURPOSE[Toc][Back]

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

```

### ARGUMENTS[Toc][Back]

```     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 diagonal elements of	the tridiagonal	matrix A.

E	     (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the tridiagonal matrix A.

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

EF	     (input) REAL array, dimension (N-1)
The (n-1) subdiagonal elements of the unit	bidiagonal factor L
from the factorization computed by	SPTTRF.

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

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

Page 1

SPTRFS(3F)							    SPTRFS(3F)

X	     (input/output) REAL array,	dimension (LDX,NRHS)
On	entry, the solution matrix X, as computed by SPTTRS.  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) REAL array, dimension (2*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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