# dptrfs.f man page

dptrfs.f

## Synopsis

### Functions/Subroutines

subroutine dptrfs (N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO)
DPTRFS

## Function/Subroutine Documentation

### subroutine dptrfs (integer N, integer NRHS, double precision, dimension( * ) D, double precision, dimension( * ) E, double precision, dimension( * ) DF, double precision, dimension( * ) EF, double precision, dimension( ldb, * ) B, integer LDB, double precision, dimension( ldx, * ) X, integer LDX, double precision, dimension( * ) FERR, double precision, dimension( * ) BERR, double precision, dimension( * ) WORK, integer INFO)

DPTRFS

Purpose:

``` DPTRFS 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 DOUBLE PRECISION array, dimension (N)
The n diagonal elements of the tridiagonal matrix A.```

E

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

DF

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

EF

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

B

```          B is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by DPTTRS.
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 DOUBLE PRECISION 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 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

`          WORK is DOUBLE PRECISION 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

NAG Ltd.

Date:

December 2016

Definition at line 165 of file dptrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dptrfs(3) is an alias of dptrfs.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK