cher.f

          SUBROUTINE CHER(UPLO,N,ALPHA,X,INCX,A,LDA)
    *     .. Scalar Arguments ..
          REAL ALPHA
          INTEGER INCX,LDA,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          COMPLEX A(LDA,*),X(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CHER   performs the hermitian rank 1 operation
    *
    *     A := alpha*x*conjg( x' ) + A,
    *
    *  where alpha is a real scalar, x is an n element vector 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  - REAL            .
    *           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.
    *
    *  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 TEMP
          INTEGER I,INFO,IX,J,JX,KX
    *     ..
    *     .. 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 (LDA.LT.MAX(1,N)) THEN
              INFO = 7
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('CHER  ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF ((N.EQ.0) .OR. (ALPHA.EQ.REAL(ZERO))) RETURN
    *
    *     Set the start point in X if the increment is not unity.
    *
          IF (INCX.LE.0) THEN
              KX = 1 - (N-1)*INCX
          ELSE IF (INCX.NE.1) THEN
              KX = 1
          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 upper triangle.
    *
              IF (INCX.EQ.1) THEN
                  DO 20 J = 1,N
                      IF (X(J).NE.ZERO) THEN
                          TEMP = ALPHA*CONJG(X(J))
                          DO 10 I = 1,J - 1
                              A(I,J) = A(I,J) + X(I)*TEMP
       10                 CONTINUE
                          A(J,J) = REAL(A(J,J)) + REAL(X(J)*TEMP)
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
       20         CONTINUE
              ELSE
                  JX = KX
                  DO 40 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*CONJG(X(JX))
                          IX = KX
                          DO 30 I = 1,J - 1
                              A(I,J) = A(I,J) + X(IX)*TEMP
                              IX = IX + INCX
       30                 CONTINUE
                          A(J,J) = REAL(A(J,J)) + REAL(X(JX)*TEMP)
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
                      JX = JX + INCX
       40         CONTINUE
              END IF
          ELSE
    *
    *        Form  A  when A is stored in lower triangle.
    *
              IF (INCX.EQ.1) THEN
                  DO 60 J = 1,N
                      IF (X(J).NE.ZERO) THEN
                          TEMP = ALPHA*CONJG(X(J))
                          A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(J))
                          DO 50 I = J + 1,N
                              A(I,J) = A(I,J) + X(I)*TEMP
       50                 CONTINUE
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
       60         CONTINUE
              ELSE
                  JX = KX
                  DO 80 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*CONJG(X(JX))
                          A(J,J) = REAL(A(J,J)) + REAL(TEMP*X(JX))
                          IX = JX
                          DO 70 I = J + 1,N
                              IX = IX + INCX
                              A(I,J) = A(I,J) + X(IX)*TEMP
       70                 CONTINUE
                      ELSE
                          A(J,J) = REAL(A(J,J))
                      END IF
                      JX = JX + INCX
       80         CONTINUE
              END IF
          END IF
    *
          RETURN
    *
    *     End of CHER  .
    *
          END