CPOEQUB 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.


 This routine differs from CPOEQU by restricting the scaling factors


 to a power of the radix.  Barring over- and underflow, scaling by


 these factors introduces no additional rounding errors.  However, the


 scaled diagonal entries are no longer approximately 1 but lie


 between sqrt(radix) and 1/sqrt(radix).

N

          N is INTEGER


          The order of the matrix A.  N >= 0.

A

          A is COMPLEX 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

          LDA is INTEGER


          The leading dimension of the array A.  LDA >= max(1,N).

S

          S is REAL array, dimension (N)


          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is 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

          AMAX is 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

          INFO is 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.

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December 2016