### MC29 Sparse unsymmetric matrix: calculate scaling factors

This subroutine calculates scaling factors for a sparse matrix
$A={\left\{{a}_{ij}\right\}}_{m\times n}$. They
may be used, for instance, to scale the matrix prior to solving a corresponding set of
linear equations, and are chosen so that the scaled matrix has its entries
near to unity in the sense that the sum of the squares of the logarithms
of the entries is minimized. The natural logarithms of the scaling factors
${r}_{i}$,
$i=1,2,...,m$ for the
rows and ${c}_{j}$,
$j=1,2,...,n$ for
the columns are returned so that the scaled matrix has entries

$${b}_{ij}={a}_{ij}exp\left({r}_{i}+{c}_{j}\right).$$