SYNOPSIS

SUBROUTINE ZHPMV

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

    

COMPLEX*16 ALPHA, BETA

    

INTEGER INCX, INCY, N

    

CHARACTER*1 UPLO

    

COMPLEX*16 AP( * ), X( * ), Y( * )

PURPOSE

ZHPMV performs the matrix-vector operation

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 - 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.

Unchanged on exit.

N - INTEGER.

On entry, N specifies the order of the matrix A. N must be at least zero. Unchanged on exit.

ALPHA - COMPLEX*16 .

On entry, ALPHA specifies the scalar alpha. Unchanged on exit.

AP - 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. Unchanged on exit.

X - 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. Unchanged on exit.

INCX - INTEGER.

On entry, INCX specifies the increment for the elements of X. INCX must not be zero. Unchanged on exit.

BETA - COMPLEX*16 .

On entry, BETA specifies the scalar beta. When BETA is supplied as zero then Y need not be set on input. Unchanged on exit.

Y - 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 - INTEGER.

On entry, INCY specifies the increment for the elements of Y. INCY must not be zero. Unchanged on exit.

Level 2 Blas routine.

-- 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.