zhpmv.f

          SUBROUTINE ZHPMV(UPLO,N,ALPHA,AP,X,INCX,BETA,Y,INCY)
    *     .. Scalar Arguments ..
          DOUBLE COMPLEX ALPHA,BETA
          INTEGER INCX,INCY,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          DOUBLE COMPLEX AP(*),X(*),Y(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZHPMV  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 hermitian 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  - COMPLEX*16      .
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  AP     - COMPLEX*16       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 hermitian 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 hermitian 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.
    *           Note that the imaginary parts of the diagonal elements need
    *           not be set and are assumed to be zero.
    *           Unchanged on exit.
    *
    *  X      - COMPLEX*16       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   - COMPLEX*16      .
    *           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      - COMPLEX*16       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.
    *
    *
    *     .. Parameters ..
          DOUBLE COMPLEX ONE
          PARAMETER (ONE= (1.0D+0,0.0D+0))
          DOUBLE COMPLEX ZERO
          PARAMETER (ZERO= (0.0D+0,0.0D+0))
    *     ..
    *     .. Local Scalars ..
          DOUBLE COMPLEX TEMP1,TEMP2
          INTEGER I,INFO,IX,IY,J,JX,JY,K,KK,KX,KY
    *     ..
    *     .. External Functions ..
          LOGICAL LSAME
          EXTERNAL LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC DBLE,DCONJG
    *     ..
    *
    *     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('ZHPMV ',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 + DCONJG(AP(K))*X(I)
                          K = K + 1
       50             CONTINUE
                      Y(J) = Y(J) + TEMP1*DBLE(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 + DCONJG(AP(K))*X(IX)
                          IX = IX + INCX
                          IY = IY + INCY
       70             CONTINUE
                      Y(JY) = Y(JY) + TEMP1*DBLE(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*DBLE(AP(KK))
                      K = KK + 1
                      DO 90 I = J + 1,N
                          Y(I) = Y(I) + TEMP1*AP(K)
                          TEMP2 = TEMP2 + DCONJG(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*DBLE(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 + DCONJG(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 ZHPMV .
    *
          END