# sptrfs.f (3) - Linux Manuals

sptrfs.f -

## SYNOPSIS

### Functions/Subroutines

subroutine sptrfs (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