View source: R/unimodularity.R
is_totally_unimodular | R Documentation |
Check wether a matrix is totally unimodular.
is_totally_unimodular(A)
A |
An object of class |
A matrix for which the determinant of every square submatrix equals -1, 0 or 1 is called totally unimodular. This function tests wether a matrix with coefficients in \{-1,0,1\} is totally unimodular. It tries to reduce the matrix using the reduction method described in Scholtus (2008). Next, a test based on Heller and Tompkins (1956) or Raghavachari is performed.
logical
Heller I and Tompkins CB (1956). An extension of a theorem of Danttzig's In kuhn HW and Tucker AW (eds.), pp. 247-254. Princeton University Press.
Raghavachari M (1976). A constructive method to recognize the total unimodularity of a matrix. _Zeitschrift fur operations research_, *20*, pp. 59-61.
Scholtus S (2008). Algorithms for correcting some obvious inconsistencies and rounding errors in business survey data. Technical Report 08015, Netherlands.
# Totally unimodular matrix, reduces to nothing A <- matrix(c( 1,1,0,0,0, -1,0,0,1,0, 0,0,01,1,0, 0,0,0,-1,1),nrow=5) is_totally_unimodular(A) # Totally unimodular matrix, by Heller-Tompson criterium A <- matrix(c( 1,1,0,0, 0,0,1,1, 1,0,1,0, 0,1,0,1),nrow=4) is_totally_unimodular(A) # Totally unimodular matrix, by Raghavachani recursive criterium A <- matrix(c( 1,1,1, 1,1,0, 1,0,1)) is_totally_unimodular(A)
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