# sspmv.f

          SUBROUTINE SSPMV (UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY)
    C***BEGIN PROLOGUE  SSPMV
    C***PURPOSE  Perform the matrix-vector operation.
    C***LIBRARY   SLATEC (BLAS)
    C***CATEGORY  D1B4
    C***TYPE      SINGLE PRECISION (SSPMV-S, DSPMV-D, CSPMV-C)
    C***KEYWORDS  LEVEL 2 BLAS, LINEAR ALGEBRA
    C***AUTHOR  Dongarra, J. J., (ANL)
    C           Du Croz, J., (NAG)
    C           Hammarling, S., (NAG)
    C           Hanson, R. J., (SNLA)
    C***DESCRIPTION
    C
    C  SSPMV  performs the matrix-vector operation
    C
    C     y := alpha*A*x + beta*y,
    C
    C  where alpha and beta are scalars, x and y are n element vectors and
    C  A is an n by n symmetric matrix, supplied in packed form.
    C
    C  Parameters
    C  ==========
    C
    C  UPLO   - CHARACTER*1.
    C           On entry, UPLO specifies whether the upper or lower
    C           triangular part of the matrix A is supplied in the packed
    C           array AP as follows:
    C
    C              UPLO = 'U' or 'u'   The upper triangular part of A is
    C                                  supplied in AP.
    C
    C              UPLO = 'L' or 'l'   The lower triangular part of A is
    C                                  supplied in AP.
    C
    C           Unchanged on exit.
    C
    C  N      - INTEGER.
    C           On entry, N specifies the order of the matrix A.
    C           N must be at least zero.
    C           Unchanged on exit.
    C
    C  ALPHA  - REAL            .
    C           On entry, ALPHA specifies the scalar alpha.
    C           Unchanged on exit.
    C
    C  AP     - REAL             array of DIMENSION at least
    C           ( ( n*( n + 1))/2).
    C           Before entry with UPLO = 'U' or 'u', the array AP must
    C           contain the upper triangular part of the symmetric matrix
    C           packed sequentially, column by column, so that AP( 1 )
    C           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
    C           and a( 2, 2 ) respectively, and so on.
    C           Before entry with UPLO = 'L' or 'l', the array AP must
    C           contain the lower triangular part of the symmetric matrix
    C           packed sequentially, column by column, so that AP( 1 )
    C           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
    C           and a( 3, 1 ) respectively, and so on.
    C           Unchanged on exit.
    C
    C  X      - REAL             array of dimension at least
    C           ( 1 + ( n - 1 )*abs( INCX ) ).
    C           Before entry, the incremented array X must contain the n
    C           element vector x.
    C           Unchanged on exit.
    C
    C  INCX   - INTEGER.
    C           On entry, INCX specifies the increment for the elements of
    C           X. INCX must not be zero.
    C           Unchanged on exit.
    C
    C  BETA   - REAL            .
    C           On entry, BETA specifies the scalar beta. When BETA is
    C           supplied as zero then Y need not be set on input.
    C           Unchanged on exit.
    C
    C  Y      - REAL             array of dimension at least
    C           ( 1 + ( n - 1 )*abs( INCY ) ).
    C           Before entry, the incremented array Y must contain the n
    C           element vector y. On exit, Y is overwritten by the updated
    C           vector y.
    C
    C  INCY   - INTEGER.
    C           On entry, INCY specifies the increment for the elements of
    C           Y. INCY must not be zero.
    C           Unchanged on exit.
    C
    C***REFERENCES  Dongarra, J. J., Du Croz, J., Hammarling, S., and
    C                 Hanson, R. J.  An extended set of Fortran basic linear
    C                 algebra subprograms.  ACM TOMS, Vol. 14, No. 1,
    C                 pp. 1-17, March 1988.
    C***ROUTINES CALLED  LSAME, XERBLA
    C***REVISION HISTORY  (YYMMDD)
    C   861022  DATE WRITTEN
    C   910605  Modified to meet SLATEC prologue standards.  Only comment
    C           lines were modified.  (BKS)
    C***END PROLOGUE  SSPMV