SRC/zpoequb.f(3)           Library Functions Manual           SRC/zpoequb.f(3)

NAME
       SRC/zpoequb.f

SYNOPSIS
   Functions/Subroutines
       subroutine zpoequb (n, a, lda, s, scond, amax, info)
           ZPOEQUB

Function/Subroutine Documentation
   subroutine zpoequb (integer n, complex*16, dimension( lda, * ) a, integer
       lda, double precision, dimension( * ) s, double precision scond, double
       precision amax, integer info)
       ZPOEQUB

       Purpose:


            ZPOEQUB 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 ZPOEQU 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).

       Parameters
           N

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

           A

                     A is 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

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

           S

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

           SCOND

                     SCOND is 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

                     AMAX is 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

                     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.

       Author
           Univ. of Tennessee

           Univ. of California Berkeley

           Univ. of Colorado Denver

           NAG Ltd.

       Definition at line 118 of file zpoequb.f.

Author
       Generated automatically by Doxygen for LAPACK from the source code.

LAPACK                          Version 3.12.0                SRC/zpoequb.f(3)