rank: Rank and Independence

Description

calculate the rank of any subset of a matroid, or determine whether any subset is independent

Usage

rank( x, subs )
is_independent( x, subs )

Value

rank(x,subs) returns an integer vector with the same length as the list subs. The i'th value is the rank of the i'th set in subs. If a set is not a subset of the ground set of x, the value is NA, and a warning message is printed.

is_independent(x,subs) returns a logical vector with the same length as the list subs. The i'th value is the independence of i'th set in x. It is equal to TRUE iff the rank of the subset is equal to the cardinality of the subset.

For both functions the names are copied from input to output.

Arguments

x: a matroid object, as returned from the constructor matroid()
subs: a list of integer vectors, representing subsets of the ground set of x. subs can also be an integer vector, which is put into a list of length 1.

References

Matroid - Wikipedia. https://en.wikipedia.org/w/index.php?title=Matroid&oldid=1086234057

Examples

Run this code

# make a matroid with rank 3
mat = matroid( classics.genlist[['RT']] )


# the ground set itself should have rank 3
rank( mat, getground(mat) )
##  [1] 3


# single points should have rank 1  (there are no loops)
rank( mat, as.list(getground(mat)) )
##  [1] 1 1 1 1 1 1

# all hyperplanes should have rank 2
rank( mat, gethyperplane(mat) )
##  [1] 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2


# a point not in the ground set should have rank NA
# and the emtpy set should have rank 0
rank( mat, list(100L,integer(0)) )
##  1 of 1 subsets are not a subset of ground.
##  [1] NA 0