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      SUBROUTINE DSPMVF( UPLO, N, ALPHA, AP, X, INCX, BETA, Y, INCY )
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*     .. Scalar Arguments ..
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      DOUBLE PRECISION   ALPHA, BETA
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      INTEGER            INCX, INCY, N
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      CHARACTER*1        UPLO
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*     .. Array Arguments ..
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      DOUBLE PRECISION   AP( * ), X( * ), Y( * )
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*     ..
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*
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*  Purpose
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*  =======
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*
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*  DSPMV  performs the matrix-vector operation
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*
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*     y := alpha*A*x + beta*y,
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*
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*  where alpha and beta are scalars, x and y are n element vectors and
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*  A is an n by n symmetric matrix, supplied in packed form.
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*
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*  Parameters
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*  ==========
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*
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*  UPLO   - CHARACTER*1.
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*           On entry, UPLO specifies whether the upper or lower
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*           triangular part of the matrix A is supplied in the packed
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*           array AP as follows:
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*
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*              UPLO = 'U' or 'u'   The upper triangular part of A is
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*                                  supplied in AP.
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*
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*              UPLO = 'L' or 'l'   The lower triangular part of A is
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*                                  supplied in AP.
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*
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*           Unchanged on exit.
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*
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*  N      - INTEGER.
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*           On entry, N specifies the order of the matrix A.
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*           N must be at least zero.
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*           Unchanged on exit.
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*
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*  ALPHA  - DOUBLE PRECISION.
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*           On entry, ALPHA specifies the scalar alpha.
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*           Unchanged on exit.
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*
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*  AP     - DOUBLE PRECISION array of DIMENSION at least
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*           ( ( n*( n + 1 ) )/2 ).
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*           Before entry with UPLO = 'U' or 'u', the array AP must
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*           contain the upper triangular part of the symmetric matrix
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*           packed sequentially, column by column, so that AP( 1 )
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*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 1, 2 )
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*           and a( 2, 2 ) respectively, and so on.
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*           Before entry with UPLO = 'L' or 'l', the array AP must
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*           contain the lower triangular part of the symmetric matrix
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*           packed sequentially, column by column, so that AP( 1 )
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*           contains a( 1, 1 ), AP( 2 ) and AP( 3 ) contain a( 2, 1 )
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*           and a( 3, 1 ) respectively, and so on.
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*           Unchanged on exit.
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*
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*  X      - DOUBLE PRECISION array of dimension at least
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*           ( 1 + ( n - 1 )*abs( INCX ) ).
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*           Before entry, the incremented array X must contain the n
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*           element vector x.
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*           Unchanged on exit.
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*
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*  INCX   - INTEGER.
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*           On entry, INCX specifies the increment for the elements of
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*           X. INCX must not be zero.
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*           Unchanged on exit.
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*
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*  BETA   - DOUBLE PRECISION.
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*           On entry, BETA specifies the scalar beta. When BETA is
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*           supplied as zero then Y need not be set on input.
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*           Unchanged on exit.
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*
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*  Y      - DOUBLE PRECISION array of dimension at least
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*           ( 1 + ( n - 1 )*abs( INCY ) ).
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*           Before entry, the incremented array Y must contain the n
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*           element vector y. On exit, Y is overwritten by the updated
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*           vector y.
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*
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*  INCY   - INTEGER.
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*           On entry, INCY specifies the increment for the elements of
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*           Y. INCY must not be zero.
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*           Unchanged on exit.
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*
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*
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*  Level 2 Blas routine.
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*
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*  -- Written on 22-October-1986.
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*     Jack Dongarra, Argonne National Lab.
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*     Jeremy Du Croz, Nag Central Office.
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*     Sven Hammarling, Nag Central Office.
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*     Richard Hanson, Sandia National Labs.
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*
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*
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*     .. Parameters ..
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      DOUBLE PRECISION   ONE         , ZERO
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      PARAMETER        ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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*     .. Local Scalars ..
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      DOUBLE PRECISION   TEMP1, TEMP2
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      INTEGER            I, INFO, IX, IY, J, JX, JY, K, KK, KX, KY
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*     .. External Functions ..
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      LOGICAL            LSAME
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      EXTERNAL           LSAME
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*     .. External Subroutines ..
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      EXTERNAL           XERBLA
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*     ..
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*     .. Executable Statements ..
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*
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*     Test the input parameters.
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*
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      INFO = 0
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      IF     ( .NOT.LSAME( UPLO, 'U' ).AND.
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     $         .NOT.LSAME( UPLO, 'L' )      )THEN
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         INFO = 1
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      ELSE IF( N.LT.0 )THEN
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         INFO = 2
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      ELSE IF( INCX.EQ.0 )THEN
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         INFO = 6
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      ELSE IF( INCY.EQ.0 )THEN
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         INFO = 9
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      END IF
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      IF( INFO.NE.0 )THEN
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         CALL XERBLA( 'DSPMV ', INFO )
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         RETURN
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      END IF
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*
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*     Quick return if possible.
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*
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      IF( ( N.EQ.0 ).OR.( ( ALPHA.EQ.ZERO ).AND.( BETA.EQ.ONE ) ) )
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     $   RETURN
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*
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*     Set up the start points in  X  and  Y.
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*
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      IF( INCX.GT.0 )THEN
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         KX = 1
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      ELSE
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         KX = 1 - ( N - 1 )*INCX
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      END IF
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      IF( INCY.GT.0 )THEN
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         KY = 1
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      ELSE
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         KY = 1 - ( N - 1 )*INCY
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      END IF
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*
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*     Start the operations. In this version the elements of the array AP
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*     are accessed sequentially with one pass through AP.
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*
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*     First form  y := beta*y.
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*
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      IF( BETA.NE.ONE )THEN
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         IF( INCY.EQ.1 )THEN
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            IF( BETA.EQ.ZERO )THEN
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               DO 10, I = 1, N
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                  Y( I ) = ZERO
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   10          CONTINUE
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            ELSE
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               DO 20, I = 1, N
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                  Y( I ) = BETA*Y( I )
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   20          CONTINUE
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            END IF
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         ELSE
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            IY = KY
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            IF( BETA.EQ.ZERO )THEN
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               DO 30, I = 1, N
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                  Y( IY ) = ZERO
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                  IY      = IY   + INCY
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   30          CONTINUE
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            ELSE
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               DO 40, I = 1, N
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                  Y( IY ) = BETA*Y( IY )
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                  IY      = IY           + INCY
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   40          CONTINUE
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            END IF
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         END IF
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      END IF
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      IF( ALPHA.EQ.ZERO )
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     $   RETURN
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      KK = 1
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      IF( LSAME( UPLO, 'U' ) )THEN
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*
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*        Form  y  when AP contains the upper triangle.
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*
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         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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            DO 60, J = 1, N
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               TEMP1 = ALPHA*X( J )
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               TEMP2 = ZERO
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               K     = KK
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               DO 50, I = 1, J - 1
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                  Y( I ) = Y( I ) + TEMP1*AP( K )
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                  TEMP2  = TEMP2  + AP( K )*X( I )
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                  K      = K      + 1
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   50          CONTINUE
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               Y( J ) = Y( J ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2
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               KK     = KK     + J
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   60       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 80, J = 1, N
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               TEMP1 = ALPHA*X( JX )
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               TEMP2 = ZERO
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               IX    = KX
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               IY    = KY
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               DO 70, K = KK, KK + J - 2
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                  Y( IY ) = Y( IY ) + TEMP1*AP( K )
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                  TEMP2   = TEMP2   + AP( K )*X( IX )
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                  IX      = IX      + INCX
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                  IY      = IY      + INCY
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   70          CONTINUE
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               Y( JY ) = Y( JY ) + TEMP1*AP( KK + J - 1 ) + ALPHA*TEMP2
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               JX      = JX      + INCX
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               JY      = JY      + INCY
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               KK      = KK      + J
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   80       CONTINUE
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         END IF
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      ELSE
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*
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*        Form  y  when AP contains the lower triangle.
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*
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         IF( ( INCX.EQ.1 ).AND.( INCY.EQ.1 ) )THEN
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            DO 100, J = 1, N
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               TEMP1  = ALPHA*X( J )
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               TEMP2  = ZERO
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               Y( J ) = Y( J )       + TEMP1*AP( KK )
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               K      = KK           + 1
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               DO 90, I = J + 1, N
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                  Y( I ) = Y( I ) + TEMP1*AP( K )
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                  TEMP2  = TEMP2  + AP( K )*X( I )
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                  K      = K      + 1
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   90          CONTINUE
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               Y( J ) = Y( J ) + ALPHA*TEMP2
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               KK     = KK     + ( N - J + 1 )
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  100       CONTINUE
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         ELSE
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            JX = KX
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            JY = KY
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            DO 120, J = 1, N
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               TEMP1   = ALPHA*X( JX )
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               TEMP2   = ZERO
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               Y( JY ) = Y( JY )       + TEMP1*AP( KK )
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               IX      = JX
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               IY      = JY
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               DO 110, K = KK + 1, KK + N - J
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                  IX      = IX      + INCX
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                  IY      = IY      + INCY
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                  Y( IY ) = Y( IY ) + TEMP1*AP( K )
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                  TEMP2   = TEMP2   + AP( K )*X( IX )
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  110          CONTINUE
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               Y( JY ) = Y( JY ) + ALPHA*TEMP2
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               JX      = JX      + INCX
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               JY      = JY      + INCY
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               KK      = KK      + ( N - J + 1 )
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  120       CONTINUE
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         END IF
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      END IF
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*
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      RETURN
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*
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*     End of DSPMV .
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*
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      END