---
name: "zherk.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/zherk.f"
---

# zherk.f(3)

## NAME

BLAS/SRC/zherk.f

## SYNOPSIS

### Functions/Subroutines

subroutine **zherk** (uplo, trans, n, k, alpha, a, lda, beta, c, ldc)\
 **ZHERK**

## Function/Subroutine Documentation

### subroutine zherk (character uplo, character trans, integer n, integer k, double precision alpha, complex\*16, dimension(lda,\*) a, integer lda, double precision beta, complex\*16, dimension(ldc,\*) c, integer ldc)

**ZHERK**

**Purpose:**

```
!>
!> ZHERK  performs one of the hermitian rank k operations
!>
!>    C := alpha*A*A**H + beta*C,
!>
!> or
!>
!>    C := alpha*A**H*A + beta*C,
!>
!> where  alpha and beta  are  real scalars,  C is an  n by n  hermitian
!> matrix and  A  is an  n by k  matrix in the  first case and a  k by n
!> matrix in the second case.
!>
```

**Parameters**

*UPLO*

```
!>          UPLO is CHARACTER*1
!>           On  entry,   UPLO  specifies  whether  the  upper  or  lower
!>           triangular  part  of the  array  C  is to be  referenced  as
!>           follows:
!>
!>              UPLO = 'U' or 'u'   Only the  upper triangular part of  C
!>                                  is to be referenced.
!>
!>              UPLO = 'L' or 'l'   Only the  lower triangular part of  C
!>                                  is to be referenced.
!>
```

*TRANS*

```
!>          TRANS is CHARACTER*1
!>           On entry,  TRANS  specifies the operation to be performed as
!>           follows:
!>
!>              TRANS = 'N' or 'n'   C := alpha*A*A**H + beta*C.
!>
!>              TRANS = 'C' or 'c'   C := alpha*A**H*A + beta*C.
!>
```

*N*

```
!>          N is INTEGER
!>           On entry,  N specifies the order of the matrix C.  N must be
!>           at least zero.
!>
```

*K*

```
!>          K is INTEGER
!>           On entry with  TRANS = 'N' or 'n',  K  specifies  the number
!>           of  columns   of  the   matrix   A,   and  on   entry   with
!>           TRANS = 'C' or 'c',  K  specifies  the number of rows of the
!>           matrix A.  K must be at least zero.
!>
```

*ALPHA*

```
!>          ALPHA is DOUBLE PRECISION .
!>           On entry, ALPHA specifies the scalar alpha.
!>
```

*A*

```
!>          A is COMPLEX*16 array, dimension ( LDA, ka ), where ka is
!>           k  when  TRANS = 'N' or 'n',  and is  n  otherwise.
!>           Before entry with  TRANS = 'N' or 'n',  the  leading  n by k
!>           part of the array  A  must contain the matrix  A,  otherwise
!>           the leading  k by n  part of the array  A  must contain  the
!>           matrix A.
!>
```

*LDA*

```
!>          LDA is INTEGER
!>           On entry, LDA specifies the first dimension of A as declared
!>           in  the  calling  (sub)  program.   When  TRANS = 'N' or 'n'
!>           then  LDA must be at least  max( 1, n ), otherwise  LDA must
!>           be at least  max( 1, k ).
!>
```

*BETA*

```
!>          BETA is DOUBLE PRECISION.
!>           On entry, BETA specifies the scalar beta.
!>
```

*C*

```
!>          C is COMPLEX*16 array, dimension ( LDC, N )
!>           Before entry  with  UPLO = 'U' or 'u',  the leading  n by n
!>           upper triangular part of the array C must contain the upper
!>           triangular part  of the  hermitian matrix  and the strictly
!>           lower triangular part of C is not referenced.  On exit, the
!>           upper triangular part of the array  C is overwritten by the
!>           upper triangular part of the updated matrix.
!>           Before entry  with  UPLO = 'L' or 'l',  the leading  n by n
!>           lower triangular part of the array C must contain the lower
!>           triangular part  of the  hermitian matrix  and the strictly
!>           upper triangular part of C is not referenced.  On exit, the
!>           lower triangular part of the array  C is overwritten by the
!>           lower triangular part of the updated matrix.
!>           Note that the imaginary parts of the diagonal elements need
!>           not be set,  they are assumed to be zero,  and on exit they
!>           are set to zero.
!>
```

*LDC*

```
!>          LDC is INTEGER
!>           On entry, LDC specifies the first dimension of C as declared
!>           in  the  calling  (sub)  program.   LDC  must  be  at  least
!>           max( 1, n ).
!>
```

**Author**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Further Details:**

```
!>
!>  Level 3 Blas routine.
!>
!>  -- Written on 8-February-1989.
!>     Jack Dongarra, Argonne National Laboratory.
!>     Iain Duff, AERE Harwell.
!>     Jeremy Du Croz, Numerical Algorithms Group Ltd.
!>     Sven Hammarling, Numerical Algorithms Group Ltd.
!>
!>  -- Modified 8-Nov-93 to set C(J,J) to DBLE( C(J,J) ) when BETA = 1.
!>     Ed Anderson, Cray Research Inc.
!>
```

Definition at line **172** of file **zherk.f**.

## Author

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