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*AIX Version 4.3 Base Operating System and Extensions Technical Reference, 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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