zhpr.f

          SUBROUTINE ZHPR(UPLO,N,ALPHA,X,INCX,AP)
    *     .. Scalar Arguments ..
          DOUBLE PRECISION ALPHA
          INTEGER INCX,N
          CHARACTER UPLO
    *     ..
    *     .. Array Arguments ..
          DOUBLE COMPLEX AP(*),X(*)
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  ZHPR    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, 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.
    *
    *  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.
    *
    *  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. On exit, the array
    *           AP is overwritten by the upper triangular part of the
    *           updated matrix.
    *           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. On exit, the array
    *           AP 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.
    *
    *
    *  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 ZERO
          PARAMETER (ZERO= (0.0D+0,0.0D+0))
    *     ..
    *     .. Local Scalars ..
          DOUBLE COMPLEX TEMP
          INTEGER I,INFO,IX,J,JX,K,KK,KX
    *     ..
    *     .. 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 = 5
          END IF
          IF (INFO.NE.0) THEN
              CALL XERBLA('ZHPR  ',INFO)
              RETURN
          END IF
    *
    *     Quick return if possible.
    *
          IF ((N.EQ.0) .OR. (ALPHA.EQ.DBLE(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 the array AP
    *     are accessed sequentially with one pass through AP.
    *
          KK = 1
          IF (LSAME(UPLO,'U')) THEN
    *
    *        Form  A  when upper triangle is stored in AP.
    *
              IF (INCX.EQ.1) THEN
                  DO 20 J = 1,N
                      IF (X(J).NE.ZERO) THEN
                          TEMP = ALPHA*DCONJG(X(J))
                          K = KK
                          DO 10 I = 1,J - 1
                              AP(K) = AP(K) + X(I)*TEMP
                              K = K + 1
       10                 CONTINUE
                          AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(J)*TEMP)
                      ELSE
                          AP(KK+J-1) = DBLE(AP(KK+J-1))
                      END IF
                      KK = KK + J
       20         CONTINUE
              ELSE
                  JX = KX
                  DO 40 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*DCONJG(X(JX))
                          IX = KX
                          DO 30 K = KK,KK + J - 2
                              AP(K) = AP(K) + X(IX)*TEMP
                              IX = IX + INCX
       30                 CONTINUE
                          AP(KK+J-1) = DBLE(AP(KK+J-1)) + DBLE(X(JX)*TEMP)
                      ELSE
                          AP(KK+J-1) = DBLE(AP(KK+J-1))
                      END IF
                      JX = JX + INCX
                      KK = KK + J
       40         CONTINUE
              END IF
          ELSE
    *
    *        Form  A  when lower triangle is stored in AP.
    *
              IF (INCX.EQ.1) THEN
                  DO 60 J = 1,N
                      IF (X(J).NE.ZERO) THEN
                          TEMP = ALPHA*DCONJG(X(J))
                          AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(J))
                          K = KK + 1
                          DO 50 I = J + 1,N
                              AP(K) = AP(K) + X(I)*TEMP
                              K = K + 1
       50                 CONTINUE
                      ELSE
                          AP(KK) = DBLE(AP(KK))
                      END IF
                      KK = KK + N - J + 1
       60         CONTINUE
              ELSE
                  JX = KX
                  DO 80 J = 1,N
                      IF (X(JX).NE.ZERO) THEN
                          TEMP = ALPHA*DCONJG(X(JX))
                          AP(KK) = DBLE(AP(KK)) + DBLE(TEMP*X(JX))
                          IX = JX
                          DO 70 K = KK + 1,KK + N - J
                              IX = IX + INCX
                              AP(K) = AP(K) + X(IX)*TEMP
       70                 CONTINUE
                      ELSE
                          AP(KK) = DBLE(AP(KK))
                      END IF
                      JX = JX + INCX
                      KK = KK + N - J + 1
       80         CONTINUE
              END IF
          END IF
    *
          RETURN
    *
    *     End of ZHPR  .
    *
          END