```
context("f statistics")
test_that("that the f statistics computes the correct paths overlaps.", {
leaves <- c("A", "B", "C", "D")
inner_nodes <- c("AC", "BC", "ABC")
edges <- parent_edges(c(edge("A", "AC"),
edge("B", "BC"),
admixture_edge("C", "AC", "BC"),
edge("AC", "ABC"),
edge("BC", "ABC"),
edge("D", "ABC")))
admix <- admixture_proportions(c(admix_props("C", "AC", "BC", "a")))
graph <- agraph(leaves, inner_nodes, edges, admix)
AB_paths <- all_paths(graph, "A", "B")
CB_paths <- all_paths(graph, "C", "B")
CD_paths <- all_paths(graph, "C", "D")
expect_equal(all_path_overlaps(AB_paths, AB_paths), f2(graph, "A", "B"))
expect_equal(all_path_overlaps(CB_paths, CD_paths), f3(graph, "C", "B", "D"))
expect_equal(all_path_overlaps(AB_paths, CD_paths), f4(graph, "A", "B", "C", "D"))
})
test_that("we get the right symbolic representation of f statistics.", {
leaves <- c("A", "B", "C", "D")
inner_nodes <- c("AC", "BC", "ABC")
edges <- parent_edges(c(edge("A", "AC"),
edge("B", "BC"),
admixture_edge("C", "AC", "BC"),
edge("AC", "ABC"),
edge("BC", "ABC"),
edge("D", "ABC")))
admix <- admixture_proportions(c(admix_props("C", "AC", "BC", "a")))
graph <- agraph(leaves, inner_nodes, edges, admix)
expect_equal(toString(sf2(graph, "A", "B")), "edge_AC_A + edge_ABC_BC + edge_ABC_AC + edge_BC_B")
expect_equal(toString(sf3(graph, "A", "B", "D")), "edge_AC_A + edge_ABC_AC")
expect_equal(toString(sf3(graph, "C", "B", "D")),
"a * a * (edge_ABC_AC + edge_AC_C) + a * (1 - a) * (-edge_ABC_BC) + (1 - a) * (1 - a) * (edge_BC_C)")
expect_equal(toString(sf4(graph, "A", "B", "C", "D")),
"a * (edge_ABC_AC) + (1 - a) * (-edge_ABC_BC)")
expect_equal(toString(sf4(graph, "B", "D", "A", "C")), "(1 - a) * (-edge_ABC_BC)")
expect_equal(toString(sf4(graph, "B", "D", "C", "A")), "(1 - a) * (edge_ABC_BC)")
})
```

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