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 matrixvector operationwhere 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 22October1986. Jack Dongarra, Argonne National Lab. Jeremy Du Croz, Nag Central Office. Sven Hammarling, Nag Central Office. Richard Hanson, Sandia National Labs.