# chpmv.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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chpmv.f

## SYNOPSIS

### Functions/Subroutines

subroutine chpmv (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
CHPMV

## Function/Subroutine Documentation

### subroutine chpmv (character UPLO, integer N, complex ALPHA, complex, dimension(*) AP, complex, dimension(*) X, integer INCX, complex BETA, complex, dimension(*) Y, integer INCY)

CHPMV

Purpose:

``` CHPMV  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
On entry, ALPHA specifies the scalar alpha.
```

AP

```          AP is COMPLEX array, 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 array, 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
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 array, 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:

December 2016

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 151 of file chpmv.f.

## Author

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