A biproportion is an adjustment of a nonnegative matrix 
to prescribed row and column totals
while preserving its multiplicative structure. The adjusted matrix
has the form
 |
where 
and 
are positive diagonal
matrices. The diagonal entries are chosen so that the row and column sums of
equal the prescribed totals.
The RAS method computes a biproportion by alternately rescaling all rows and all columns. Under the usual feasibility conditions on the support and the prescribed
totals, the iteration converges to the unique adjusted matrix 
, even though the individual diagonal
factors need not be unique.
