NAME

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

SYNOPSIS

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

           DOUBLE       PRECISION ALPHA, BETA

           INTEGER      INCX, INCY, N

           CHARACTER*1  UPLO

           DOUBLE       PRECISION AP( * ), X( * ), Y( * )

PURPOSE

       DSPMV  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  - DOUBLE PRECISION.
              On entry, ALPHA specifies the scalar alpha.  Unchanged on exit.

       AP     - DOUBLE PRECISION 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 must contain the lower 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( 2, 1 ) and a( 3, 1 ) respectively, and so on.  Unchanged  on
              exit.

       X      - DOUBLE PRECISION 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   - DOUBLE PRECISION.
              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      - DOUBLE PRECISION 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.

       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.