```      SUBROUTINE ZPOEQU( N, A, LDA, S, SCOND, AMAX, INFO )
*
*  -- LAPACK routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
INTEGER            INFO, LDA, N
DOUBLE PRECISION   AMAX, SCOND
*     ..
*     .. Array Arguments ..
DOUBLE PRECISION   S( * )
COMPLEX*16         A( LDA, * )
*     ..
*
*  Purpose
*  =======
*
*  ZPOEQU computes row and column scalings intended to equilibrate a
*  Hermitian positive definite matrix A 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
*  =========
*
*  N       (input) INTEGER
*          The order of the matrix A.  N >= 0.
*
*  A       (input) COMPLEX*16 array, dimension (LDA,N)
*          The N-by-N Hermitian positive definite matrix whose scaling
*          factors are to be computed.  Only the diagonal elements of A
*          are referenced.
*
*  LDA     (input) INTEGER
*          The leading dimension of the array A.  LDA >= max(1,N).
*
*  S       (output) DOUBLE PRECISION array, dimension (N)
*          If INFO = 0, S contains the scale factors for A.
*
*  SCOND   (output) DOUBLE PRECISION
*          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) DOUBLE PRECISION
*          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 ..
DOUBLE PRECISION   ZERO, ONE
PARAMETER          ( ZERO = 0.0D+0, ONE = 1.0D+0 )
*     ..
*     .. Local Scalars ..
INTEGER            I
DOUBLE PRECISION   SMIN
*     ..
*     .. External Subroutines ..
EXTERNAL           XERBLA
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          DBLE, MAX, MIN, SQRT
*     ..
*     .. Executable Statements ..
*
*     Test the input parameters.
*
INFO = 0
IF( N.LT.0 ) THEN
INFO = -1
ELSE IF( LDA.LT.MAX( 1, N ) ) THEN
INFO = -3
END IF
IF( INFO.NE.0 ) THEN
CALL XERBLA( 'ZPOEQU', -INFO )
RETURN
END IF
*
*     Quick return if possible
*
IF( N.EQ.0 ) THEN
SCOND = ONE
AMAX = ZERO
RETURN
END IF
*
*     Find the minimum and maximum diagonal elements.
*
S( 1 ) = DBLE( A( 1, 1 ) )
SMIN = S( 1 )
AMAX = S( 1 )
DO 10 I = 2, N
S( I ) = DBLE( A( I, I ) )
SMIN = MIN( SMIN, S( I ) )
AMAX = MAX( AMAX, S( I ) )
10 CONTINUE
*
IF( SMIN.LE.ZERO ) THEN
*
*        Find the first non-positive diagonal element and return.
*
DO 20 I = 1, N
IF( S( I ).LE.ZERO ) THEN
INFO = I
RETURN
END IF
20    CONTINUE
ELSE
*
*        Set the scale factors to the reciprocals
*        of the diagonal elements.
*
DO 30 I = 1, N
S( I ) = ONE / SQRT( S( I ) )
30    CONTINUE
*
*        Compute SCOND = min(S(I)) / max(S(I))
*
SCOND = SQRT( SMIN ) / SQRT( AMAX )
END IF
RETURN
*
*     End of ZPOEQU
*
END

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