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dspmv.f
      SUBROUTINE DSPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
*     .. Scalar Arguments ..
      DOUBLE PRECISION ALPHA,BETA
      INTEGER INCX,INCY,N
      CHARACTER UPLO
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION AP(*),X(*),Y(*)
*     ..
*
*  Purpose
*  =======
*
*  DSPMV  performs the matrix-vector operation
*
*     y := alpha*A*x + beta*y,
*
*  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 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.
*
*  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.
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION ONE,ZERO
      PARAMETER (ONE=1.0D+0,ZERO=0.0D+0)
*     ..
*     .. Local Scalars ..
      DOUBLE PRECISION TEMP1,TEMP2
      INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
*     ..
*     .. External Functions ..
      LOGICAL LSAME
      EXTERNAL LSAME
*     ..
*     .. External Subroutines ..
      EXTERNAL XERBLA
*     ..
*
*     Test the input parameters.
*
      INFO = 0
      IF (.NOT.LSAME(UPLO,'U') .AND. .NOT.LSAME(UPLO,'L')) THEN
          INFO = 1
      ELSE IF (N.LT.0) THEN
          INFO = 2
      ELSE IF (INCX.EQ.0) THEN
          INFO = 6
      ELSE IF (INCY.EQ.0) THEN
          INFO = 9
      END IF
      IF (INFO.NE.0) THEN
          CALL XERBLA('DSPMV ',INFO)
          RETURN
      END IF
*
*     Quick return if possible.
*
      IF ((N.EQ.0) .OR. ((ALPHA.EQ.ZERO).AND. (BETA.EQ.ONE))) RETURN
*
*     Set up the start points in  X  and  Y.
*
      IF (INCX.GT.0) THEN
          KX = 1
      ELSE
          KX = 1 - (N-1)*INCX
      END IF
      IF (INCY.GT.0) THEN
          KY = 1
      ELSE
          KY = 1 - (N-1)*INCY
      END IF
*
*     Start the operations. In this version the elements of the array AP
*     are accessed sequentially with one pass through AP.
*
*     First form  y := beta*y.
*
      IF (BETA.NE.ONE) THEN
          IF (INCY.EQ.1) THEN
              IF (BETA.EQ.ZERO) THEN
                  DO 10 I = 1,N
                      Y(I) = ZERO
   10             CONTINUE
              ELSE
                  DO 20 I = 1,N
                      Y(I) = BETA*Y(I)
   20             CONTINUE
              END IF
          ELSE
              IY = KY
              IF (BETA.EQ.ZERO) THEN
                  DO 30 I = 1,N
                      Y(IY) = ZERO
                      IY = IY + INCY
   30             CONTINUE
              ELSE
                  DO 40 I = 1,N
                      Y(IY) = BETA*Y(IY)
                      IY = IY + INCY
   40             CONTINUE
              END IF
          END IF
      END IF
      IF (ALPHA.EQ.ZERO) RETURN
      KK = 1
      IF (LSAME(UPLO,'U')) THEN
*
*        Form  y  when AP contains the upper triangle.
*
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 60 J = 1,N
                  TEMP1 = ALPHA*X(J)
                  TEMP2 = ZERO
                  K = KK
                  DO 50 I = 1,J - 1
                      Y(I) = Y(I) + TEMP1*AP(K)
                      TEMP2 = TEMP2 + AP(K)*X(I)
                      K = K + 1
   50             CONTINUE
                  Y(J) = Y(J) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
                  KK = KK + J
   60         CONTINUE
          ELSE
              JX = KX
              JY = KY
              DO 80 J = 1,N
                  TEMP1 = ALPHA*X(JX)
                  TEMP2 = ZERO
                  IX = KX
                  IY = KY
                  DO 70 K = KK,KK + J - 2
                      Y(IY) = Y(IY) + TEMP1*AP(K)
                      TEMP2 = TEMP2 + AP(K)*X(IX)
                      IX = IX + INCX
                      IY = IY + INCY
   70             CONTINUE
                  Y(JY) = Y(JY) + TEMP1*AP(KK+J-1) + ALPHA*TEMP2
                  JX = JX + INCX
                  JY = JY + INCY
                  KK = KK + J
   80         CONTINUE
          END IF
      ELSE
*
*        Form  y  when AP contains the lower triangle.
*
          IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
              DO 100 J = 1,N
                  TEMP1 = ALPHA*X(J)
                  TEMP2 = ZERO
                  Y(J) = Y(J) + TEMP1*AP(KK)
                  K = KK + 1
                  DO 90 I = J + 1,N
                      Y(I) = Y(I) + TEMP1*AP(K)
                      TEMP2 = TEMP2 + AP(K)*X(I)
                      K = K + 1
   90             CONTINUE
                  Y(J) = Y(J) + ALPHA*TEMP2
                  KK = KK + (N-J+1)
  100         CONTINUE
          ELSE
              JX = KX
              JY = KY
              DO 120 J = 1,N
                  TEMP1 = ALPHA*X(JX)
                  TEMP2 = ZERO
                  Y(JY) = Y(JY) + TEMP1*AP(KK)
                  IX = JX
                  IY = JY
                  DO 110 K = KK + 1,KK + N - J
                      IX = IX + INCX
                      IY = IY + INCY
                      Y(IY) = Y(IY) + TEMP1*AP(K)
                      TEMP2 = TEMP2 + AP(K)*X(IX)
  110             CONTINUE
                  Y(JY) = Y(JY) + ALPHA*TEMP2
                  JX = JX + INCX
                  JY = JY + INCY
                  KK = KK + (N-J+1)
  120         CONTINUE
          END IF
      END IF
*
      RETURN
*
*     End of DSPMV .
*
      END

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