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*AIX Version 4.3 Base Operating System and Extensions Technical Reference, Volume 2*

## CHER or ZHER Subroutine

### Purpose

Performs the Hermitian rank 1 operation.

### Library

BLAS Library (**libblas.a**)

### FORTRAN Syntax

**SUBROUTINE** **CHER(***UPLO***,*** N***,*** ALPHA***,**
*X***,*** INCX***,*** A***,*** LDA***)**
**REAL** *ALPHA*
**INTEGER** *INCX***,***LDA***,***N*
**CHARACTER*1 ***UPLO*
**COMPLEX** *A***(***LDA***,*),** *X***(*)**

**SUBROUTINE** **ZHER(***UPLO***,*** N***,*** ALPHA***,**
*X***,*** INCX***,*** A***,*** LDA***)**
**DOUBLE PRECISION** *ALPHA*
**INTEGER** *INCX***,***LDA***,***N*
**CHARACTER*1** *UPLO*
**COMPLEX*16** *A***(***LDA***,*),*** X***(*)**

### Description

The **CHER** or **ZHER** subroutine performs the Hermitian rank 1 operation:

`A`` := alpha * x * conjg( x' ) + ``A`

where alpha is a real scalar, x is an *N* element vector and *A* is an *N* by *N* Hermitian matrix.

### Parameters

*UPLO* |
On entry, *UPLO* specifies whether the upper or lower triangular part of the array *A* is to be referenced as follows:
*UPLO* = 'U' or 'u' |
Only the upper triangular part of *A *is to be referenced. |
*UPLO *= 'L' or 'l' |
Only the lower triangular part of *A* is to be referenced. |
Unchanged on exit. |

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

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

*X* |
A vector of dimension at least (1 + (*N*-1) * abs(*INCX*) ); on entry, the incremented array *X *must contain the *N* element vector x; unchanged on exit. |

*INCX* |
On entry, *INCX* specifies the increment for the elements of *X*; *INCX* must not be 0; unchanged on exit. |

*A* |
An array of dimension ( *LDA*, *N* ); on entry with *UPLO* = 'U' or 'u', the leading *N* by *N* upper triangular part of the array *A* must contain the upper triangular part of the Hermitian matrix and the strictly lower triangular part of *A* is not referenced. On exit, the upper triangular part of the array *A* 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 *A *must contain the lower triangular part of the Hermitian matrix and the strictly upper triangular part of *A* is not referenced. On exit, the lower triangular part of the array *A* 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. |

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

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