CSPMV   -   perform  the  matrix-vector  operation   y  :=
       alpha*A*x + beta*y,


SYNOPSIS

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

           CHARACTER     UPLO

           INTEGER       INCX, INCY, N

           COMPLEX       ALPHA, BETA

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


PURPOSE

       CSPMV  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 symmetric matrix, sup­
       plied in packed form.


ARGUMENTS

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

       AP     - COMPLEX 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

              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      - COMPLEX 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   - INTEGER
              On entry, INCX specifies the increment for the ele­
              ments 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, dimension at least
              (  1  + ( N - 1 )*abs( INCY ) ).  Before entry, the
              incremented array Y must contain the n element vec­
              tor  y.  On  exit,  Y is overwritten by the updated
              vector y.

       INCY   - INTEGER
              On entry, INCY specifies the increment for the ele­
              ments  of  Y.  INCY must not be zero.  Unchanged on
              exit.


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