# zptrfs.f man page

zptrfs.f —

## Synopsis

### Functions/Subroutines

subroutinezptrfs(UPLO, N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, RWORK, INFO)ZPTRFS

## Function/Subroutine Documentation

### subroutine zptrfs (characterUPLO, integerN, integerNRHS, double precision, dimension( * )D, complex*16, dimension( * )E, double precision, dimension( * )DF, complex*16, dimension( * )EF, complex*16, dimension( ldb, * )B, integerLDB, complex*16, dimension( ldx, * )X, integerLDX, double precision, dimension( * )FERR, double precision, dimension( * )BERR, complex*16, dimension( * )WORK, double precision, dimension( * )RWORK, integerINFO)

**ZPTRFS**

**Purpose:**

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

**Parameters:**

*UPLO*

```
UPLO is CHARACTER*1
Specifies whether the superdiagonal or the subdiagonal of the
tridiagonal matrix A is stored and the form of the
factorization:
= 'U': E is the superdiagonal of A, and A = U**H*D*U;
= 'L': E is the subdiagonal of A, and A = L*D*L**H.
(The two forms are equivalent if A is real.)
```

*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 real diagonal elements of the tridiagonal matrix A.
```

*E*

```
E is COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the tridiagonal matrix A
(see UPLO).
```

*DF*

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

*EF*

```
EF is COMPLEX*16 array, dimension (N-1)
The (n-1) off-diagonal elements of the unit bidiagonal
factor U or L from the factorization computed by ZPTTRF
(see UPLO).
```

*B*

```
B is COMPLEX*16 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 COMPLEX*16 array, dimension (LDX,NRHS)
On entry, the solution matrix X, as computed by ZPTTRS.
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 COMPLEX*16 array, dimension (N)`

*RWORK*

`RWORK is DOUBLE PRECISION array, dimension (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 183 of file zptrfs.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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