---
name: "zptrfs.f"
section: "3"
platform: "linux"
package: "lapack-doc"
version: "3.12.1-2"
release: "Arch Linux 2026-11-01"
platforms: ["linux"]
url: "https://new.carta.tech/zptrfs.f"
---

# zptrfs.f(3)

## NAME

SRC/zptrfs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zptrfs** (uplo, n, nrhs, d, e, df, ef, b, ldb, x, ldx, ferr, berr, work, rwork, info)\
 **ZPTRFS**

## Function/Subroutine Documentation

### subroutine zptrfs (character uplo, integer n, integer nrhs, double precision, dimension( \* ) d, complex\*16, dimension( \* ) e, double precision, dimension( \* ) df, complex\*16, dimension( \* ) ef, complex\*16, dimension( ldb, \* ) b, integer ldb, complex\*16, dimension( ldx, \* ) x, integer ldx, double precision, dimension( \* ) ferr, double precision, dimension( \* ) berr, complex\*16, dimension( \* ) work, double precision, dimension( \* ) rwork, integer info)

**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.

Definition at line **181** of file **zptrfs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.