# sptrfs.f man page

sptrfs.f —

## Synopsis

### Functions/Subroutines

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

## Function/Subroutine Documentation

### subroutine sptrfs (integerN, integerNRHS, real, dimension( * )D, real, dimension( * )E, real, dimension( * )DF, real, dimension( * )EF, real, dimension( ldb, * )B, integerLDB, real, dimension( ldx, * )X, integerLDX, real, dimension( * )FERR, real, dimension( * )BERR, real, dimension( * )WORK, integerINFO)

**SPTRFS**

**Purpose:**

```
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.
```

**Parameters:**

*N*

```
N is INTEGER
The order of the matrix A. N >= 0.
```

*NRHS*

```
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
```

*D*

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

*E*

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

*DF*

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

*EF*

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

*B*

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

*LDB*

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

*X*

```
X is REAL array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by SPTTRS.
On exit, the improved solution matrix X.
```

*LDX*

```
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
```

*FERR*

```
FERR is 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*

```
BERR is 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*

`WORK is REAL array, dimension (2*N)`

*INFO*

```
INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
```

**Internal Parameters:**

`ITMAX is the maximum number of steps of iterative refinement.`

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

Definition at line 163 of file sptrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sptrfs(3) is an alias of sptrfs.f(3).