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

## CHPMV or ZHPMV Subroutine

### Purpose

Performs matrix-vector operations using a packed Hermitian matrix.

### Library

BLAS Library (**libblas.a**)

### FORTRAN Syntax

**SUBROUTINE CHPMV(***UPLO***, ***N***, ***ALPHA***, ***AP***, ***X***,**
*INCX***, ***BETA***, ***Y***, ***INCY***)**
**COMPLEX** *ALPHA***,***BETA*
**INTEGER** *INCX***,***INCY***,***N*
**CHARACTER*1** *UPLO*
**COMPLEX** *AP***(*), ***X***(*), ***Y***(*)**

**SUBROUTINE ZHPMV**
**COMPLEX*16** *ALPHA***,***BETA*
**INTEGER** *INCX***,***INCY***,***N*
**CHARACTER*1** *UPLO*
**COMPLEX*16** *AP***(*), ***X***(*), ***Y***(*)**

### Description

The **CHPMV** or **ZHPMV** subroutine performs the matrix-vector operation:

`y := alpha * ``A`` * x + beta * y`

where alpha and beta are scalars, x and y are *N* element vectors and *A* is an *N* by *N* Hermitian matrix, supplied in packed form.

### Parameters

*UPLO* |
On entry, *UPLO* specifies whether the upper or lower triangular part of the matrix *A* is supplied in the packed array *AP* as follows:
*UPLO* = 'U' or 'u' |
The upper triangular part of *A* is supplied in *AP*. |
*UPLO* = 'L' or 'l' |
The lower triangular part of *A* is supplied in *AP*. |
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. |

*AP* |
A vector of dimension at least ( ( *N* * (*N*+1) )/2 ); on entry with *UPLO* = 'U' or 'u', the array *AP* must contain the upper triangular part of the Hermitian matrix packed sequentially, column by column, so that *AP*(1) contains *A*(1,1), *AP*(2) and *AP*(3) contain *A*(1,2) and *A*(2,2) respectively, and so on; on entry with *UPLO* = 'L' or 'l', the array *AP* must contain the lower triangular part of the Hermitian matrix packed sequentially, column by column, so that *AP*(1) contains *A*(1,1), *AP*(2) and *AP*(3) contain *A*(2,1) and *A*(3,1) respectively, and so on. The imaginary parts of the diagonal elements need not be set and are assumed to be 0; 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. |

*BETA* |
On entry, *BETA* specifies the scalar beta; when *BETA* is supplied as 0 then *Y* need not be set on input; unchanged on exit. |

*Y* |
A vector of dimension at least (1 + (*N*-1) * abs( *INCY* ) ); on entry, the incremented array *Y* must contain the *N* element vector y; on exit, *Y* is overwritten by the updated vector y. |

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

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