chemv.f

          SUBROUTINE CHEMV(UPLO,N,ALPHA,A,LDA,X,INCX,BETA,Y,INCY)
    *     .. Scalar Arguments ..
          COMPLEX ALPHA,BETA
          INTEGER INCX,INCY,LDA,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),X(*),Y(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHEMV  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.
    *
    *  Arguments
    *  ==========
    *
    *  UPLO   - CHARACTER*1.
    *           On entry, UPLO specifies whether the upper or lower
    *           triangular part of the array A is to be referenced as
    *           follows:
    *
    *              UPLO = 'U' or 'u'   Only the upper triangular part of A
    *                                  is to be referenced.
    *
    *              UPLO = 'L' or 'l'   Only the lower triangular part of A
    *                                  is to be referenced.
    *
    *           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         .
    *           On entry, ALPHA specifies the scalar alpha.
    *           Unchanged on exit.
    *
    *  A      - COMPLEX          array of DIMENSION ( LDA, n ).
    *           Before entry with  UPLO = 'U' or 'u', the leading n by n
    *           upper triangular part of the array A must contain the upper
    *           triangular part of the hermitian matrix and the strictly
    *           lower triangular part of A is not referenced.
    *           Before entry with UPLO = 'L' or 'l', the leading n by n
    *           lower triangular part of the array A must contain the lower
    *           triangular part of the hermitian matrix and the strictly
    *           upper triangular part of A is not referenced.
    *           Note that the imaginary parts of the diagonal elements need
    *           not be set and are assumed to be zero.
    *           Unchanged on exit.
    *
    *  LDA    - INTEGER.
    *           On entry, LDA specifies the first dimension of A as declared
    *           in the calling (sub) program. LDA must be at least
    *           max( 1, n ).
    *           Unchanged on exit.
    *
    *  X      - COMPLEX          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         .
    *           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          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 ..
          COMPLEX ONE
          PARAMETER (ONE= (1.0E+0,0.0E+0))
          COMPLEX ZERO
          PARAMETER (ZERO= (0.0E+0,0.0E+0))
    *     ..
    *     .. Local Scalars ..
          COMPLEX TEMP1,TEMP2
          INTEGER I,INFO,IX,IY,J,JX,JY,KX,KY
    *     ..
    *     .. External Functions ..
          LOGICAL LSAME
          EXTERNAL LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC CONJG,MAX,REAL
    *     ..
    *
    *     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 (LDA.LT.MAX(1,N)) THEN
              INFO = 5
          ELSE IF (INCX.EQ.0) THEN
              INFO = 7
          ELSE IF (INCY.EQ.0) THEN
              INFO = 10
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('CHEMV ',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 A are
    *     accessed sequentially with one pass through the triangular part
    *     of A.
    *
    *     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
          IF (LSAME(UPLO,'U')) THEN
    *
    *        Form  y  when A is stored in upper triangle.
    *
              IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
                  DO 60 J = 1,N
                      TEMP1 = ALPHA*X(J)
                      TEMP2 = ZERO
                      DO 50 I = 1,J - 1
                          Y(I) = Y(I) + TEMP1*A(I,J)
                          TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
       50             CONTINUE
                      Y(J) = Y(J) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
       60         CONTINUE
              ELSE
                  JX = KX
                  JY = KY
                  DO 80 J = 1,N
                      TEMP1 = ALPHA*X(JX)
                      TEMP2 = ZERO
                      IX = KX
                      IY = KY
                      DO 70 I = 1,J - 1
                          Y(IY) = Y(IY) + TEMP1*A(I,J)
                          TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
                          IX = IX + INCX
                          IY = IY + INCY
       70             CONTINUE
                      Y(JY) = Y(JY) + TEMP1*REAL(A(J,J)) + ALPHA*TEMP2
                      JX = JX + INCX
                      JY = JY + INCY
       80         CONTINUE
              END IF
          ELSE
    *
    *        Form  y  when A is stored in 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*REAL(A(J,J))
                      DO 90 I = J + 1,N
                          Y(I) = Y(I) + TEMP1*A(I,J)
                          TEMP2 = TEMP2 + CONJG(A(I,J))*X(I)
       90             CONTINUE
                      Y(J) = Y(J) + ALPHA*TEMP2
      100         CONTINUE
              ELSE
                  JX = KX
                  JY = KY
                  DO 120 J = 1,N
                      TEMP1 = ALPHA*X(JX)
                      TEMP2 = ZERO
                      Y(JY) = Y(JY) + TEMP1*REAL(A(J,J))
                      IX = JX
                      IY = JY
                      DO 110 I = J + 1,N
                          IX = IX + INCX
                          IY = IY + INCY
                          Y(IY) = Y(IY) + TEMP1*A(I,J)
                          TEMP2 = TEMP2 + CONJG(A(I,J))*X(IX)
      110             CONTINUE
                      Y(JY) = Y(JY) + ALPHA*TEMP2
                      JX = JX + INCX
                      JY = JY + INCY
      120         CONTINUE
              END IF
          END IF
    *
          RETURN
    *
    *     End of CHEMV .
    *
          END