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

NAME
       SRC/zheequb.f

SYNOPSIS
   Functions/Subroutines
       subroutine zheequb (uplo, n, a, lda, s, scond, amax, work, info)
           ZHEEQUB

Function/Subroutine Documentation
   subroutine zheequb (character uplo, integer n, complex*16, dimension( lda,
       * ) a, integer lda, double precision, dimension( * ) s, double
       precision scond, double precision amax, complex*16, dimension( * )
       work, integer info)
       ZHEEQUB

       Purpose:


            ZHEEQUB computes row and column scalings intended to equilibrate a
            Hermitian matrix A (with respect to the Euclidean norm) and reduce
            its condition number. The scale factors S are computed by the BIN
            algorithm (see references) so that the scaled matrix B with elements
            B(i,j) = S(i)*A(i,j)*S(j) has a condition number within a factor N of
            the smallest possible condition number over all possible diagonal
            scalings.

       Parameters
           UPLO

                     UPLO is CHARACTER*1
                     = 'U':  Upper triangle of A is stored;
                     = 'L':  Lower triangle of A is stored.

           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 matrix whose scaling factors are to be
                     computed.

           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
                     Largest absolute value of any matrix element. If AMAX is
                     very close to overflow or very close to underflow, the
                     matrix should be scaled.

           WORK

                     WORK is COMPLEX*16 array, dimension (2*N)

           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.

       References:
           Livne, O.E. and Golub, G.H., 'Scaling by Binormalization',
            Numerical Algorithms, vol. 35, no. 1, pp. 97-120, January 2004.
            DOI 10.1023/B:NUMA.0000016606.32820.69
            Tech report version:
           http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.3.1679

       Definition at line 131 of file zheequb.f.

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

LAPACK                          Version 3.12.0                SRC/zheequb.f(3)