# zhpmv.f man page

zhpmv.f —

## Synopsis

### Functions/Subroutines

subroutinezhpmv(UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)ZHPMV

## Function/Subroutine Documentation

### subroutine zhpmv (characterUPLO, integerN, complex*16ALPHA, complex*16, dimension(*)AP, complex*16, dimension(*)X, integerINCX, complex*16BETA, complex*16, dimension(*)Y, integerINCY)

**ZHPMV Purpose:**

```
ZHPMV 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*

```
UPLO is CHARACTER*1
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.
```

*N*

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

*ALPHA*

```
ALPHA is COMPLEX*16
On entry, ALPHA specifies the scalar alpha.
```

*AP*

```
AP is COMPLEX*16 array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before 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.
Before 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.
Note that the imaginary parts of the diagonal elements need
not be set and are assumed to be zero.
```

*X*

```
X is COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCX ) ).
Before entry, the incremented array X must contain the n
element vector x.
```

*INCX*

```
INCX is INTEGER
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
```

*BETA*

```
BETA is COMPLEX*16
On entry, BETA specifies the scalar beta. When BETA is
supplied as zero then Y need not be set on input.
```

*Y*

```
Y is COMPLEX*16 array of dimension at least
( 1 + ( n - 1 )*abs( INCY ) ).
Before entry, the incremented array Y must contain the n
element vector y. On exit, Y is overwritten by the updated
vector y.
```

*INCY*

```
INCY is INTEGER
On entry, INCY specifies the increment for the elements of
Y. INCY must not be zero.
```

**Author:**

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

**Date:**

November 2011

**Further Details:**

```
Level 2 Blas routine.
The vector and matrix arguments are not referenced when N = 0, or M = 0
-- Written on 22-October-1986.
Jack Dongarra, Argonne National Lab.
Jeremy Du Croz, Nag Central Office.
Sven Hammarling, Nag Central Office.
Richard Hanson, Sandia National Labs.
```

Definition at line 150 of file zhpmv.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zhpmv(3) is an alias of zhpmv.f(3).