cher2.f

          SUBROUTINE CHER2(UPLO,N,ALPHA,X,INCX,Y,INCY,A,LDA)
    *     .. Scalar Arguments ..
          COMPLEX ALPHA
          INTEGER INCX,INCY,LDA,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),X(*),Y(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHER2  performs the hermitian rank 2 operation
    *
    *     A := alpha*x*conjg( y' ) + conjg( alpha )*y*conjg( x' ) + A,
    *
    *  where alpha is a scalar, 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.
    *
    *  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.
    *
    *  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.
    *           Unchanged on exit.
    *
    *  INCY   - INTEGER.
    *           On entry, INCY specifies the increment for the elements of
    *           Y. INCY must not be zero.
    *           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. On exit, the
    *           upper triangular part of the array A is overwritten by the
    *           upper triangular part of the updated matrix.
    *           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. On exit, the
    *           lower triangular part of the array A is overwritten by the
    *           lower triangular part of the updated matrix.
    *           Note that the imaginary parts of the diagonal elements need
    *           not be set, they are assumed to be zero, and on exit they
    *           are set to zero.
    *
    *  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.
    *
    *
    *  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 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 (INCX.EQ.0) THEN
              INFO = 5
          ELSE IF (INCY.EQ.0) THEN
              INFO = 7
          ELSE IF (LDA.LT.MAX(1,N)) THEN
              INFO = 9
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('CHER2 ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF ((N.EQ.0) .OR. (ALPHA.EQ.ZERO)) RETURN
    *
    *     Set up the start points in X and Y if the increments are not both
    *     unity.
    *
          IF ((INCX.NE.1) .OR. (INCY.NE.1)) THEN
              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
              JX = KX
              JY = KY
          END IF
    *
    *     Start the operations. In this version the elements of A are
    *     accessed sequentially with one pass through the triangular part
    *     of A.
    *
          IF (LSAME(UPLO,'U')) THEN
    *
    *        Form  A  when A is stored in the upper triangle.
    *
              IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
                  DO 20 J = 1,N
                      IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                          TEMP1 = ALPHA*CONJG(Y(J))
                          TEMP2 = CONJG(ALPHA*X(J))
                          DO 10 I = 1,J - 1
                              A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
       10                 CONTINUE
                          A(J,J) = REAL(A(J,J)) +
         +                         REAL(X(J)*TEMP1+Y(J)*TEMP2)
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
       20         CONTINUE
              ELSE
                  DO 40 J = 1,N
                      IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                          TEMP1 = ALPHA*CONJG(Y(JY))
                          TEMP2 = CONJG(ALPHA*X(JX))
                          IX = KX
                          IY = KY
                          DO 30 I = 1,J - 1
                              A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
                              IX = IX + INCX
                              IY = IY + INCY
       30                 CONTINUE
                          A(J,J) = REAL(A(J,J)) +
         +                         REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
                      JX = JX + INCX
                      JY = JY + INCY
       40         CONTINUE
              END IF
          ELSE
    *
    *        Form  A  when A is stored in the lower triangle.
    *
              IF ((INCX.EQ.1) .AND. (INCY.EQ.1)) THEN
                  DO 60 J = 1,N
                      IF ((X(J).NE.ZERO) .OR. (Y(J).NE.ZERO)) THEN
                          TEMP1 = ALPHA*CONJG(Y(J))
                          TEMP2 = CONJG(ALPHA*X(J))
                          A(J,J) = REAL(A(J,J)) +
         +                         REAL(X(J)*TEMP1+Y(J)*TEMP2)
                          DO 50 I = J + 1,N
                              A(I,J) = A(I,J) + X(I)*TEMP1 + Y(I)*TEMP2
       50                 CONTINUE
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
       60         CONTINUE
              ELSE
                  DO 80 J = 1,N
                      IF ((X(JX).NE.ZERO) .OR. (Y(JY).NE.ZERO)) THEN
                          TEMP1 = ALPHA*CONJG(Y(JY))
                          TEMP2 = CONJG(ALPHA*X(JX))
                          A(J,J) = REAL(A(J,J)) +
         +                         REAL(X(JX)*TEMP1+Y(JY)*TEMP2)
                          IX = JX
                          IY = JY
                          DO 70 I = J + 1,N
                              IX = IX + INCX
                              IY = IY + INCY
                              A(I,J) = A(I,J) + X(IX)*TEMP1 + Y(IY)*TEMP2
       70                 CONTINUE
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
                      JX = JX + INCX
                      JY = JY + INCY
       80         CONTINUE
              END IF
          END IF
    *
          RETURN
    *
    *     End of CHER2 .
    *
          END