Convert a distance matrix into a metric

dmet: an undirected valued graph's edge values, read as a distance matrix, do not always satisfy the triangle inequality (a direct edge can be "longer" than going via a third node). This finds the smallest constant that, added to every distance, makes the whole matrix satisfy it – \(c = \max(0, \max_{i,j,k} d_{ij} - d_{ik} - d_{kj})\) – and returns both the original and the corrected matrix.

Usage

tda_dmet(g, options = list(), dir = tempfile("tda"), ...)

Arguments

g

a tda_graph, undirected and valued.

options

a named list of further TDA options, passed through.

dir

working directory.

...

passed to tda_run.

Value

A list: original and modified, both distance matrices, and constant, the value added to get from one to the other.

See also

Other graph analysis: plot.tda_graph(), tda_g(), tda_g_analyses, tda_graph(), tda_locate_line(), tda_ptree(), tda_ucl()

Examples

e <- data.frame(from = c(1, 2, 3), to = c(2, 3, 1), value = c(1, 2, 5))
g <- tda_graph(e, directed = FALSE)   # 1-3 direct (5) exceeds
                                      # 1-2-3 via node 2 (1+2=3)
tda_dmet(g)
#> $original
#>      [,1] [,2] [,3]
#> [1,]    0    1    5
#> [2,]    1    0    2
#> [3,]    5    2    0
#> 
#> $modified
#>      [,1] [,2] [,3]
#> [1,]    0    3    7
#> [2,]    3    0    4
#> [3,]    7    4    0
#> 
#> $constant
#> [1] 2
#>