DSYEQUB computes row and column scalings intended to equilibrate a


 symmetric 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.

UPLO

          UPLO is CHARACTER*1


          Specifies whether the details of the factorization are stored


          as an upper or lower triangular matrix.


          = 'U':  Upper triangular, form is A = U*D*U**T;


          = 'L':  Lower triangular, form is A = L*D*L**T.

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.  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.

WORK

          WORK is DOUBLE PRECISION array, dimension (3*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.

November 2011

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://ruready.utah.edu/archive/papers/bin.pdf