reduceMatrix: Apply reduction method from Scholtus (2008)

In lintools: Manipulation of Linear Systems of (in)Equalities

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.

See Also

is_totally_unimodular

lintools documentation built on Jan. 17, 2023, 1:06 a.m.