CHEEQUB(3)     LAPACK routine of NEC Numeric Library Collection     CHEEQUB(3)



NAME
       CHEEQUB

SYNOPSIS
       SUBROUTINE CHEEQUB (UPLO, N, A, LDA, S, SCOND, AMAX, WORK, INFO)



PURPOSE
            CHEEQUB computes row and column scalings intended to equilibrate a
            Hermitian 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
           UPLO      (input)
                     UPLO is CHARACTER*1
                     = 'U':  Upper triangles of A and B are stored;
                     = 'L':  Lower triangles of A and B are stored.

           N         (input)
                     N is INTEGER
                     The order of the matrix A.  N >= 0.

           A         (input)
                     A is COMPLEX array, dimension (LDA,N)
                     The N-by-N Hermitian matrix whose scaling
                     factors are to be computed.  Only the diagonal elements of A
                     are referenced.

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

           S         (output)
                     S is REAL array, dimension (N)
                     If INFO = 0, S contains the scale factors for A.

           SCOND     (output)
                     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      (output)
                     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.

           WORK      (output)
                     WORK is COMPLEX array, dimension (3*N)

           INFO      (output)
                     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.



LAPACK routine                  31 October 2017                     CHEEQUB(3)