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


SYNOPSIS

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

           REAL         ALPHA, BETA

           INTEGER      INCX, INCY, N

           CHARACTER*1  UPLO

           REAL         AP( * ), X( * ), Y( * )


PURPOSE

       SSPMV  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.


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

       AP     - REAL             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  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

              metric  matrix  packed sequentially, column by col­
              umn, 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      - REAL             array of dimension at least
              ( 1 + ( n - 1 )*abs( INCX ) ).  Before  entry,  the
              incremented array X must contain the n element vec­
              tor 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   - REAL            .
              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      - REAL             array of 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.

              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.


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