Matrix Entries Inspection

This tool is useful for basic matrix inspection:

• Test if the input matrix is integer.
• Test if the input matrix is ternary, i.e, it has only entries in \( \{-1,0,+1\} \).
• Test if the input matrix is binary, i.e, it has only entries in \( \{0,+1\} \).

Recognizing Binary and Ternary Matrices

The command

cmr-k-ary IN-MAT [OPTION...]

determines whether the matrix given in file IN-MAT is integer (resp. binary or ternary).

Options:

• -i FORMAT Format of file IN-MAT, among dense for dense-matrix and sparse for sparse-matrix; default: dense.
• -b Test whether the matrix is binary, i.e., has entries in \( \{0,+1\} \).
• -t Test whether the matrix is ternary, i.e., has entries in \( \{-1,0,+1\} \).
• -I Test whether the matrix is integer.
• -e EPSILON Allows rounding of numbers up to tolerance EPSILON; default: \( 10^{-9} \).

If IN-MAT is - then the matrix is read from stdin.

Finding Large Binary or Ternary Submatrices

The command

cmr-k-ary IN-MAT -R OUT-SUB [OPTION...]

finds a large binary (resp. ternary) submatrix of the matrix given in file IN-MAT.

Options:

• -i FORMAT Format of file IN-MAT, among dense for dense-matrix and sparse for sparse-matrix; default: dense.
• -b Find a large binary submatrix, i.e., one with only entries in \( \{0,+1\} \).
• -t Find a large ternary submatrix, i.e., one with only entries in \( \{-1,0,+1\} \).
• -e EPSILON Allows rounding of numbers up to tolerance EPSILON; default: \( 10^{-9} \).

If IN-MAT is - then the matrix is read from stdin. If OUT-SUB is - then the submatrix is written to stdout.

Algorithm

The implemented algorithm successively removes a row or a column with the maximum number of forbidden entries.