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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.
```