func PseudoMetric(m markov.MarkovChain, lambda float64, TPSolver func(markov.MarkovChain, *coupling.Node, [][]float64, float64, int, int)) [][]float64 {
// initialize all the sets and the coupling
n := len(m.Transitions)
tocompute := sets.InitToCompute(len(m.Transitions))
visited := sets.MakeMatrix(n)
exact := sets.MakeMatrix(n)
c := coupling.New()
d := InitD(n)
for !sets.EmptySet(tocompute) {
var node *coupling.Node
s, t := extractrandomfromset(tocompute)
s, t = utils.GetMinMax(s, t)
tocompute[s][t], tocompute[t][s] = false, false
log.Printf("Run with node: (%v,%v)", s, t)
if m.Labels[s] != m.Labels[t] {
// s and t have the same label, so we set its distance to 0, and its exact and visited to true
log.Printf("State %v and %v had different labels", s, t)
d[s][t] = 1
exact[s][t] = true
visited[s][t] = true
continue
} else if s == t {
// s and t are the same state, so we set its distance to 1, and its exact and visited to true
log.Printf("State %v %v) was the same state", s, t)
d[s][t] = 0
exact[s][t] = true
visited[s][t] = true
continue
}
// since the pair of states is not the same and share a label, we have to further process it
// try to find the correpsonding node in the coupling
node = coupling.FindNode(s, t, &c)
if node == nil {
// if FindNode returned a nil pointer, the node does not exist, and we have to make it
node = matching.FindFeasibleMatching(m, s, t, &c)
setpair.Setpair(m, node, exact, visited, d, &c)
} else if node.Adj == nil {
// if FindNode did return a node reference, but its adjacency matrix(matching) is nil, we have to create it
node = matching.FindFeasibleMatching(m, s, t, &c)
setpair.Setpair(m, node, exact, visited, d, &c)
}
disc.Disc(lambda, node, exact, d, &c)
updateUntilOptimalSolutionsFound(lambda, m, node, exact, visited, d, c, TPSolver, []*coupling.Node{})
removeExactEdges(node, exact)
// remove everything that has been computed to exact, such that we will not try to solve it again
tocompute = *sets.DifferensReal(&tocompute, &exact)
}
return d
}
func updateUntilOptimalSolutionsFound(lambda float64, m markov.MarkovChain, node *coupling.Node, exact [][]bool, visited [][]bool, d [][]float64, c coupling.Coupling, TPSolver func(markov.MarkovChain, *coupling.Node, [][]float64, float64, int, int), solvedNodes []*coupling.Node) {
log.Printf("find optimal for: (%v,%v)", node.S, node.T)
min, i, j := uvmethod.Run(node, d)
// if min is negative, we can further improve it, so we update it using the TPSolver and iterated until we cannot improve it further
for min < 0 && !utils.ApproxEqual(min, 0) {
previ, prevj := i, j
TPSolver(m, node, d, min, i, j)
setpair.Setpair(m, node, exact, visited, d, &c)
disc.Disc(lambda, node, exact, d, &c)
min, i, j = uvmethod.Run(node, d)
if previ == i && prevj == j && min < 0 {
break
}
}
// append solved nodes such that we do not end up recurively calling nodes that have already been found to be optimal
solvedNodes = append(solvedNodes, node)
for _, row := range node.Adj {
for _, edge := range row {
if edge.To.Adj == nil {
// if the node do not have an adjacency matrix or is exact, we do not have to proccess it
continue
}
if coupling.IsNodeInSlice(edge.To, solvedNodes) {
// if the node has already been proccesses, we do not have to do it again
continue
}
updateUntilOptimalSolutionsFound(lambda, m, edge.To, exact, visited, d, c, TPSolver, solvedNodes)
}
}
exact[node.S][node.T] = true
exact[node.S][node.T] = true
return
}