CHPMV(3)        BLAS routine of NEC Numeric Library Collection        CHPMV(3)



NAME
       CHPMV - perform the matrix-vector operation   y := alpha*A*x + beta*y

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

           COMPLEX      ALPHA, BETA

           INTEGER      INCX, INCY, N

           CHARACTER*1  UPLO

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

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   - 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 fol-
              lows:

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

       AP     - COMPLEX          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  imagi-
              nary  parts  of  the  diagonal  elements need not be set and are
              assumed to be zero.  Unchanged on exit.

       X      - COMPLEX          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         .
              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          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 over-
              written 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.



BLAS routine                    16 October 1992                       CHPMV(3)