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 filloutAdj(row, col []int, lenrow, lencol int, w [][]*coupling.Edge, c *coupling.Coupling) {
for i := 0; i < lenrow; i++ {
for j := 0; j < lencol; j++ {
var node *coupling.Node
s, t := utils.GetMinMax(row[i], col[j])
node = coupling.FindNode(s, t, c)
if node == nil {
node = &coupling.Node{S: s, T: t, Succ: []*coupling.Node{}}
c.Nodes = append(c.Nodes, node)
}
w[i][j] = &coupling.Edge{To: node}
}
}
}
func FindFeasibleMatching(m markov.MarkovChain, u int, v int, c *coupling.Coupling) *coupling.Node {
n := len(m.Transitions[u])
u, v = utils.GetMinMax(u, v)
// tries to find the node (u,v) in c, if not make a new one and add to c
node := coupling.FindNode(u, v, c)
if node == nil {
node = &coupling.Node{S: u, T: v, Succ: []*coupling.Node{}}
c.Nodes = append(c.Nodes, node)
}
log.Printf("copy the transitions from the states %v and %v", u, v)
uTransitions := make([]float64, n, n)
vTransitions := make([]float64, n, n)
// copies the transitions of u and v such that we do not makes changes in the markov chain
copy(uTransitions, m.Transitions[u])
copy(vTransitions, m.Transitions[v])
// finds the length of the rows and columns in the matching for u and v
lenrow, lencol := matchingDimensions(uTransitions, vTransitions, n)
log.Printf("row and column length are: %v and %v", lenrow, lencol)
rowindex := make([]int, lenrow, lenrow)
colindex := make([]int, lencol, lencol)
// finds the row and column indexs for the u and v matching
setMatchingIndexes(uTransitions, vTransitions, n, rowindex, colindex)
log.Printf("row index: %s", rowindex)
log.Printf("column index: %s", colindex)
matching := make([][]*coupling.Edge, lenrow, lenrow)
for i := range matching {
matching[i] = make([]*coupling.Edge, lencol, lencol)
}
// fills out the matching with node pointers, using nodes already in the coupling c if they exist
filloutAdj(rowindex, colindex, lenrow, lencol, matching, c)
// completes the matching by inserting probabilities and setting appropriate cells to basic
i, j := 0, 0
for i < lenrow && j < lencol {
if utils.ApproxEqual(uTransitions[rowindex[i]], vTransitions[colindex[j]]) {
matching[i][j].Prob = uTransitions[rowindex[i]]
// check if we are in the lower right corner, such that we do not get an out of bounds error
if !(i+1 == lenrow && j+1 == lencol) {
matching[i][j+1].Basic = true
node.BasicCount++
}
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
i++
j++
} else if uTransitions[rowindex[i]] < vTransitions[colindex[j]] {
matching[i][j].Prob = uTransitions[rowindex[i]]
vTransitions[colindex[j]] = vTransitions[colindex[j]] - uTransitions[rowindex[i]]
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
i++
} else {
matching[i][j].Prob = vTransitions[colindex[j]]
uTransitions[rowindex[i]] = uTransitions[rowindex[i]] - vTransitions[colindex[j]]
matching[i][j].Basic = true
matching[i][j].To.Succ = append(matching[i][j].To.Succ, node)
node.BasicCount++
j++
}
}
log.Println("Logging matching:")
for i := 0; i < lenrow; i++ {
for j := 0; j < lencol; j++ {
log.Printf(" - At: u %d, %d prob: %f, basic: %t",
matching[i][j].To.S,
matching[i][j].To.T,
matching[i][j].Prob,
matching[i][j].Basic)
}
}
node.Adj = matching
return node
}