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# Technical Reference: Base Operating System and Extensions, Volume 2

## CHER2K or ZHER2K Subroutine

### Purpose

Performs Hermitian rank 2k operations.

### Library

BLAS Library (libblas.a)

### FORTRAN Syntax

`SUBROUTINE CHER2K(UPLO, TRANS, N, K, ALPHA,`

A, LDA, B, LDB, C, LDC)

CHARACTER*1 UPLO, TRANS

INTEGER N, K, LDA, LDB, LDC

REAL BETA

COMPLEX ALPHA

COMPLEX A(LDA,*), B(LDB,*), C(LDC,*)

SUBROUTINE ZHER2K(UPLO, TRANS, N, K, ALPHA,
A, LDA, B, LDB, C, LDC)
CHARACTER*1 UPLO,TRANS
INTEGER N,K,LDA,LDB,LDC
DOUBLE PRECISION BETA
COMPLEX*16 ALPHA
COMPLEX*16 A(LDA,*), B(LDB,*), C(LDC,*)

### Description

The CHER2K or ZHER2K subroutine performs one of the Hermitian rank 2k operations:

`C`` := alpha *`` A`` * conjg(``B``') + conjg(alpha) *`` B`` * conjg(``A``') + beta *`` C`

OR

`C`` := alpha * conjg(``A``') *`` B`` + conjg(alpha) * conjg(``B``') *`` A`` + beta *`` C`

where alpha and beta are scalars with beta real, C is an N by N Hermitian matrix, and A and B are N by K matrices in the first case and K by N matrices in the second case.

### Parameters

UPLO |
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.
Unchanged on exit. |

TRANS |
On entry, TRANS specifies the operation to be performed as follows:
- TRANS = 'N' or 'n'
- C := alpha * A * conjg( B' ) + conjg( alpha ) * B * conjg( A' ) + beta * C
- TRANS = 'C' or 'c'
- C := alpha * conjg( A' ) * B + conjg( alpha ) * conjg( B' ) * A + beta * C
Unchanged on exit. |

N |
On entry, N specifies the order of the matrix C; N must be at least 0; unchanged on exit. |

K |
On entry with TRANS = 'N' or 'n', K specifies the number of columns of the matrices A and B, and on entry with TRANS = 'C' or 'c', K specifies the number of rows of the matrices A and B; K must be at least 0; unchanged on exit. |

ALPHA |
On entry, ALPHA specifies the scalar alpha; unchanged on exit. |

A |
An array of dimension ( LDA, KA ), where KA is K when TRANS = 'N' or 'n', and is N otherwise; on 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; unchanged on exit. |

LDA |
On entry, LDA specifies the first dimension of A as declared in the calling (sub) program. When TRANS = 'N' or 'n', LDA must be at least max( 1, N ); otherwise LDA must be at least max( 1, K ); unchanged on exit. |

B |
An array of dimension ( LDB, KB ), where KB is K when TRANS = 'N' or 'n', and is N otherwise; on entry with TRANS = 'N' or 'n', the leading N by K part of the array B must contain the matrix B, otherwise the leading K by N part of the array B must contain the matrix B; unchanged on exit. |

LDB |
On entry, LDB specifies the first dimension of B as declared in the calling (sub) program. When TRANS = 'N' or 'n', LDB must be at least max( 1, N ); otherwise LDB must be at least max( 1, K ); unchanged on exit. |

BETA |
On entry, BETA specifies the scalar beta; unchanged on exit. |

C |
An array of dimension ( LDC, N ); on 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 reference; on exit, the upper triangular part of the array C is overwritten by the upper triangular part of the updated matrix; on 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. The imaginary parts of the diagonal elements need not be set, they are assumed to be 0, and on exit they are set to 0. |

LDC |
On entry, LDC specifies the first dimension of C as declared in the calling (sub) program; LDC must be at least max( 1, N ); unchanged on exit. |

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