reduceMatrix: Apply reduction method from Scholtus (2008)
Description
Apply the reduction method in the appendix of Scholtus (2008) to a matrix.
Let $A$ with coefficients in $\{-1,0,1\}$. If, after a possible
permutation of columns it can be written
in the form $A=[B,C]$ where each column in $B$ has at most 1 nonzero
element, then $A$ is totally unimodular if and only if $C$ is totally
unimodular. By transposition, a similar theorem holds for the rows of A. This
function iteratively removes rows and columns with only 1 nonzero element
from $A$ and returns the reduced result.
Usage
reduceMatrix(A)
Arguments
A
An object of class matrix in $\{-1,0,1\}^{m\times n}$.
Value
The reduction of A.
References
Scholtus S (2008). Algorithms for correcting some obvious
inconsistencies and rounding errors in business survey data. Technical
Report 08015, Netherlands.