CHEEQUB 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.

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 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 REAL array, dimension (N)


          If INFO = 0, S contains the scale factors for A.

SCOND

          SCOND is REAL


          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 REAL


          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 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.

April 2012

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