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SSPMV(1)			 BLAS routine			      SSPMV(1)

NAME
       SSPMV - performs 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					    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.

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 fol‐
	      lows:

	      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 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      - REAL		 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   - 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 vector y. On exit, Y is over‐
	      written 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.

FURTHER DETAILS
       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.

BLAS routine			 November 2008			      SSPMV(1)

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