# ?hpmv

Computes a matrix-vector product using a Hermitian packed matrix.

## Syntax

FORTRAN 77:

call chpmv(uplo, n, alpha, ap, x, incx, beta, y, incy )

call zhpmv(uplo, n, alpha, ap, x, incx, beta, y, incy )

Fortran 95:

call hpmv(a, x, y [,uplo][,alpha] [,beta])

## Description

The ?hpmv routines perform a matrix-vector operation defined as
`y := alpha*A*x + beta*y,`

where:

alpha and beta are scalars,

x and y are n-element vectors,

A is an n-by-n Hermitian matrix, supplied in packed form.

## Input Parameters

uplo

  CHARACTER*1. Specifies whether the upper or lower triangular part of the matrix A is supplied in the packed array ap.

  If `uplo = 'U'` or 'u', then the upper triangular part of the matrix A is supplied in the packed array ap .

  If `uplo = 'L'` or 'l', then the low triangular part of the matrix A is supplied in the packed array ap .

n

  INTEGER. Specifies the order of the matrix A. The value of n must be at least zero.

alpha

  COMPLEX for chpmv

  DOUBLE COMPLEX for zhpmv

  Specifies the scalar alpha.

ap

  COMPLEX for chpmv

  DOUBLE COMPLEX for zhpmv

  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.

  The imaginary parts of the diagonal elements need not be set and are assumed to be zero.

x

  COMPLEX for chpmv

  DOUBLE PRECISION COMPLEX for zhpmv

  Array, DIMENSION at least `(1 +(n - 1)*abs(incx))`. Before entry, the incremented array x must contain the n-element vector x.

incx

  INTEGER. Specifies the increment for the elements of x.

  The value of incx must not be zero.

beta

  COMPLEX for chpmv

  DOUBLE COMPLEX for zhpmv

  Specifies the scalar beta.

  When beta is equal to zero then y need not be set on input.

y

  COMPLEX for chpmv

  DOUBLE COMPLEX for zhpmv

  Array, DIMENSION at least `(1 + (n - 1)*abs(incy))`. Before entry, the incremented array y must contain the n-element vector y.

incy

  INTEGER. Specifies the increment for the elements of y.

  The value of incy must not be zero.

## Output Parameters

y

  Overwritten by the updated vector y.

## Fortran 95 Interface Notes

Routines in Fortran 95 interface have fewer arguments in the calling sequence than their FORTRAN 77 counterparts. For general conventions applied to skip redundant or reconstructible arguments, see Fortran 95 Interface Conventions.

Specific details for the routine hpmv interface are the following:

a

  Holds the array a of size (n*(n+1)/2).

x

  Holds the vector of length (n).

y

  Holds the vector of length (n).

uplo

  Must be 'U' or 'L'. The default value is 'U'.

alpha

  The default value is 1.

beta

  The default value is 1.

Parent topic: BLAS Level 2 Routines