!>
!> DSYEQUB computes row and column scalings intended to equilibrate a
!> symmetric 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.
!> 

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 DOUBLE PRECISION array, dimension (LDA,N)
!>          The N-by-N symmetric 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 DOUBLE PRECISION 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.
!> 

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

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