ZSPMV(3)                   MathKeisan LAPACK routine                  ZSPMV(3)



NAME
       ZSPMV - the matrix-vector operation   y := alpha*A*x + beta*y,

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

           CHARACTER     UPLO

           INTEGER       INCX, INCY, N

           COMPLEX*16    ALPHA, BETA

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

PURPOSE
       ZSPMV  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 symmetric matrix, supplied in packed form.


ARGUMENTS
       UPLO     (input) 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        (input) INTEGER
                On entry, N specifies the order of the matrix A.  N must be at
                least zero.  Unchanged on exit.

       ALPHA    (input) COMPLEX*16
                On  entry,  ALPHA  specifies  the  scalar alpha.  Unchanged on
                exit.

       AP       (input) COMPLEX*16 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
                symmetric 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 symmetric matrix  packed  sequen-
                tially,  column by column, so that AP( 1 ) contains a( 1, 1 ),
                AP( 2 ) and AP( 3 ) contain a( 2, 1 ) and a( 3,  1  )  respec-
                tively, and so on.  Unchanged on exit.

       X        (input) COMPLEX*16 array, 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     (input) INTEGER
                On  entry, INCX specifies the increment for the elements of X.
                INCX must not be zero.  Unchanged on exit.

       BETA     (input) COMPLEX*16
                On entry, BETA specifies the scalar beta. When  BETA  is  sup-
                plied  as  zero then Y need not be set on input.  Unchanged on
                exit.

       Y        (input/output) COMPLEX*16 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     (input) INTEGER
                On entry, INCY specifies the increment for the elements of  Y.
                INCY must not be zero.  Unchanged on exit.



 LAPACK auxiliary routine (versionNo3v.e1m)ber 2006                        ZSPMV(3)