.TH ZHPMV 1 "November 2006" "BLAS routine" "BLAS routine"
.SH NAME
ZHPMV - the matrix-vector operation y := alpha*A*x + beta*y,
.SH SYNOPSIS
.TP 53
SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
.TP 53
.ti +4
DOUBLE
COMPLEX ALPHA,BETA
.TP 53
.ti +4
INTEGER
INCX,INCY,N
.TP 53
.ti +4
CHARACTER
UPLO
.TP 53
.ti +4
DOUBLE
COMPLEX AP(*),X(*),Y(*)
.SH 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.
.SH ARGUMENTS
.TP 7
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 = \(aqU\(aq or \(aqu\(aq The upper triangular part of A is
supplied in AP.
UPLO = \(aqL\(aq or \(aql\(aq The lower triangular part of A is
supplied in AP.
Unchanged on exit.
.TP 7
N - INTEGER.
On entry, N specifies the order of the matrix A.
N must be at least zero.
Unchanged on exit.
.TP 7
ALPHA - COMPLEX*16 .
On entry, ALPHA specifies the scalar alpha.
Unchanged on exit.
.TP 7
AP - COMPLEX*16 array of DIMENSION at least
( ( n*( n + 1 ) )/2 ).
Before entry with UPLO = \(aqU\(aq or \(aqu\(aq, 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 = \(aqL\(aq or \(aql\(aq, 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.
.TP 7
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.
.TP 7
INCX - INTEGER.
On entry, INCX specifies the increment for the elements of
X. INCX must not be zero.
Unchanged on exit.
.TP 7
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.
.TP 7
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.
.TP 7
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.