---
name: "zherfs.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/zherfs.f"
---

# zherfs.f(3)

## NAME

SRC/zherfs.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zherfs** (uplo, n, nrhs, a, lda, af, ldaf, ipiv, b, ldb, x, ldx, ferr, berr, work, rwork, info)\
 **ZHERFS**

## Function/Subroutine Documentation

### subroutine zherfs (character uplo, integer n, integer nrhs, complex\*16, dimension( lda, \* ) a, integer lda, complex\*16, dimension( ldaf, \* ) af, integer ldaf, integer, dimension( \* ) ipiv, 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)

**ZHERFS**

**Purpose:**

```
!>
!> ZHERFS improves the computed solution to a system of linear
!> equations when the coefficient matrix is Hermitian indefinite, and
!> provides error bounds and backward error estimates for the solution.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>          = 'U':  Upper triangle of A is stored;
!>          = 'L':  Lower triangle of A is stored.
!>
```

*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 matrices B and X.  NRHS >= 0.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension (LDA,N)
!>          The Hermitian matrix A.  If UPLO = 'U', the leading N-by-N
!>          upper triangular part of A contains the upper triangular part
!>          of the matrix A, and the strictly lower triangular part of A
!>          is not referenced.  If UPLO = 'L', the leading N-by-N lower
!>          triangular part of A contains the lower triangular part of
!>          the matrix A, and the strictly upper triangular part of A is
!>          not referenced.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>          The leading dimension of the array A.  LDA >= max(1,N).
!>
```

*AF*

```
!>          AF is COMPLEX*16 array, dimension (LDAF,N)
!>          The factored form of the matrix A.  AF contains the block
!>          diagonal matrix D and the multipliers used to obtain the
!>          factor U or L from the factorization A = U*D*U**H or
!>          A = L*D*L**H as computed by ZHETRF.
!>
```

*LDAF*

```
!>          LDAF is INTEGER
!>          The leading dimension of the array AF.  LDAF >= max(1,N).
!>
```

*IPIV*

```
!>          IPIV is INTEGER array, dimension (N)
!>          Details of the interchanges and the block structure of D
!>          as determined by ZHETRF.
!>
```

*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 ZHETRS.
!>          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 estimated 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).  The estimate is as reliable as
!>          the estimate for RCOND, and is almost always a slight
!>          overestimate of the true error.
!>
```

*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 (2*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 **190** of file **zherfs.f**.

## Author

Generated automatically by Doxygen for LAPACK from the source code.