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)