          SUBROUTINE CPPEQU( UPLO, N, AP, S, SCOND, AMAX, INFO )
    *
    *  -- LAPACK routine (version 3.1) --
    *     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
    *     November 2006
    *
    *     .. Scalar Arguments ..
          CHARACTER          UPLO
          INTEGER            INFO, N
          REAL               AMAX, SCOND
    *     ..
    *     .. Array Arguments ..
          REAL               S( * )
          COMPLEX            AP( * )
    *     ..
    *
    *  Purpose
    *  =======
    *
    *  CPPEQU computes row and column scalings intended to equilibrate a
    *  Hermitian positive definite matrix A in packed storage and reduce
    *  its condition number (with respect to the two-norm).  S contains the
    *  scale factors, S(i)=1/sqrt(A(i,i)), chosen so that the scaled matrix
    *  B with elements B(i,j)=S(i)*A(i,j)*S(j) has ones on the diagonal.
    *  This choice of S puts the condition number of B within a factor N of
    *  the smallest possible condition number over all possible diagonal
    *  scalings.
    *
    *  Arguments
    *  =========
    *
    *  UPLO    (input) CHARACTER*1
    *          = 'U':  Upper triangle of A is stored;
    *          = 'L':  Lower triangle of A is stored.
    *
    *  N       (input) INTEGER
    *          The order of the matrix A.  N >= 0.
    *
    *  AP      (input) COMPLEX array, dimension (N*(N+1)/2)
    *          The upper or lower triangle of the Hermitian matrix A, packed
    *          columnwise in a linear array.  The j-th column of A is stored
    *          in the array AP as follows:
    *          if UPLO = 'U', AP(i + (j-1)*j/2) = A(i,j) for 1<=i<=j;
    *          if UPLO = 'L', AP(i + (j-1)*(2n-j)/2) = A(i,j) for j<=i<=n.
    *
    *  S       (output) REAL array, dimension (N)
    *          If INFO = 0, S contains the scale factors for A.
    *
    *  SCOND   (output) REAL
    *          If INFO = 0, S contains the ratio of the smallest S(i) to
    *          the largest S(i).  If SCOND >= 0.1 and AMAX is neither too
    *          large nor too small, it is not worth scaling by S.
    *
    *  AMAX    (output) REAL
    *          Absolute value of largest matrix element.  If AMAX is very
    *          close to overflow or very close to underflow, the matrix
    *          should be scaled.
    *
    *  INFO    (output) INTEGER
    *          = 0:  successful exit
    *          < 0:  if INFO = -i, the i-th argument had an illegal value
    *          > 0:  if INFO = i, the i-th diagonal element is nonpositive.
    *
    *  =====================================================================
    *
    *     .. Parameters ..
          REAL               ONE, ZERO
          PARAMETER          ( ONE = 1.0E+0, ZERO = 0.0E+0 )
    *     ..
    *     .. Local Scalars ..
          LOGICAL            UPPER
          INTEGER            I, JJ
          REAL               SMIN
    *     ..
    *     .. External Functions ..
          LOGICAL            LSAME
          EXTERNAL           LSAME
    *     ..
    *     .. External Subroutines ..
          EXTERNAL           XERBLA
    *     ..
    *     .. Intrinsic Functions ..
          INTRINSIC          MAX, MIN, REAL, SQRT
    *     ..
    *     .. Executable Statements ..
    *
    *     Test the input parameters.
    *
          INFO = 0
          UPPER = LSAME( UPLO, 'U' )
          IF( .NOT.UPPER .AND. .NOT.LSAME( UPLO, 'L' ) ) THEN
             INFO = -1
          ELSE IF( N.LT.0 ) THEN
             INFO = -2
          END IF
          IF( INFO.NE.0 ) THEN
             CALL XERBLA( 'CPPEQU', -INFO )
             RETURN
          END IF
    *
    *     Quick return if possible
    *
          IF( N.EQ.0 ) THEN
             SCOND = ONE
             AMAX = ZERO
             RETURN
          END IF
    *
    *     Initialize SMIN and AMAX.
    *
          S( 1 ) = REAL( AP( 1 ) )
          SMIN = S( 1 )
          AMAX = S( 1 )
    *
          IF( UPPER ) THEN
    *
    *        UPLO = 'U':  Upper triangle of A is stored.
    *        Find the minimum and maximum diagonal elements.
    *
             JJ = 1
             DO 10 I = 2, N
                JJ = JJ + I
                S( I ) = REAL( AP( JJ ) )
                SMIN = MIN( SMIN, S( I ) )
                AMAX = MAX( AMAX, S( I ) )
       10    CONTINUE
    *
          ELSE
    *
    *        UPLO = 'L':  Lower triangle of A is stored.
    *        Find the minimum and maximum diagonal elements.
    *
             JJ = 1
             DO 20 I = 2, N
                JJ = JJ + N - I + 2
                S( I ) = REAL( AP( JJ ) )
                SMIN = MIN( SMIN, S( I ) )
                AMAX = MAX( AMAX, S( I ) )
       20    CONTINUE
          END IF
    *
          IF( SMIN.LE.ZERO ) THEN
    *
    *        Find the first non-positive diagonal element and return.
    *
             DO 30 I = 1, N
                IF( S( I ).LE.ZERO ) THEN
                   INFO = I
                   RETURN
                END IF
       30    CONTINUE
          ELSE
    *
    *        Set the scale factors to the reciprocals
    *        of the diagonal elements.
    *
             DO 40 I = 1, N
                S( I ) = ONE / SQRT( S( I ) )
       40    CONTINUE
    *
    *        Compute SCOND = min(S(I)) / max(S(I))
    *
             SCOND = SQRT( SMIN ) / SQRT( AMAX )
          END IF
          RETURN
    *
    *     End of CPPEQU
    *
          END