Fit binary relations to a valued graph

TDA's rfit: finds the relations with the requested properties closest to the graph, via linear programming.

Usage

tda_rfit(
  d,
  properties = c("symmetric", "transitive"),
  max_solutions = 10,
  variant = c("standard", "experimental"),
  ...
)

Arguments

d

symmetric matrix (proximities).

properties

character subset of "reflexive", "symmetric", "antisymmetric", "transitive", "complete".

max_solutions

cap on the number of equally good relations TDA keeps (max=, 10). When more exist the fit is refused with an error naming this argument; a linear-order request (antisymmetric, transitive, complete) on a symmetric input has 17 optimal relations for 4 nodes and 491 for 6. What comes back is correct but not always complete: against every relation on 4 nodes enumerated in R (test-gap-wrappers.R, and 30 directed cases in the session-52 notes) rfit's value is always the optimum and every relation it lists is optimal with the properties, but in about one case in five with ties it lists a subset of the tied optima (2 of 4, 4 of 5) – a limit of the CACM 449 enumeration it uses.

variant

"standard" runs rfit; "experimental" runs the rfit1 sibling (same syntax, alternative implementation).

...

passed to tda_run.

Value

relations, one fitted relation matrix per solution, and output.

Examples

d <- rbind(c(0, 2, 1), c(2, 0, 2), c(1, 2, 0))
r <- tda_rfit(d)
r$relations[[1]]
#>      [,1] [,2] [,3]
#> [1,]    1    1    1
#> [2,]    1    1    1
#> [3,]    1    1    1