private static void computeXaXsTransitions(
final IScope scope,
final IAgentFilter filter,
final GamaMatrix<Double> fuzzytransitions,
final Double distance,
final IContainer<Integer, IAgent> agents,
final int nbCat,
final Map<List<Integer>, Map<Double, Double>> XaPerTransition,
final Map<List<Integer>, Map<Double, Double>> XsPerTransition,
final Set<Double> Xvals) {
IList<ILocation> locs = GamaListFactory.create(Types.POINT);
for (IAgent ag : agents.iterable(scope)) {
locs.add(ag.getLocation());
}
ILocation centralLoc = (ILocation) Stats.getMean(scope, locs);
if (filter != null) {
IAgent centralAg = scope.getTopology().getAgentClosestTo(scope, centralLoc, filter);
List<IAgent> neighbors =
distance == 0
? new ArrayList<IAgent>()
: new ArrayList<IAgent>(
scope.getTopology().getNeighborsOf(scope, centralAg, distance, filter));
double sizeNorm = FastMath.sqrt(centralAg.getEnvelope().getArea());
Map<IAgent, Double> distancesCoeff = new TOrderedHashMap<IAgent, Double>();
distancesCoeff.put(centralAg, 1.0);
for (IAgent ag : neighbors) {
double euclidDist = centralAg.getLocation().euclidianDistanceTo(ag.getLocation());
double dist = 1 / (1.0 + euclidDist / sizeNorm);
distancesCoeff.put(ag, dist);
}
for (int i = 0; i < nbCat; i++) {
for (int j = 0; j < nbCat; j++) {
for (int k = 0; k < nbCat; k++) {
List<Integer> ca = new ArrayList();
ca.add(i);
ca.add(j);
ca.add(k);
double xa = 0;
double xs = 0;
for (IAgent ag : distancesCoeff.keySet()) {
double dist = distancesCoeff.get(ag);
double xatmp = fuzzyTransition(scope, fuzzytransitions, nbCat, i, k, i, j) * dist;
double xstmp = fuzzyTransition(scope, fuzzytransitions, nbCat, i, j, i, k) * dist;
if (xatmp > xa) {
xa = xatmp;
}
if (xstmp > xs) {
xs = xstmp;
}
}
if (xa > 0) {
Map<Double, Double> mapxa = XaPerTransition.get(ca);
if (mapxa == null) {
mapxa = new TOrderedHashMap<Double, Double>();
mapxa.put(xa, 1.0);
XaPerTransition.put(ca, mapxa);
} else {
if (mapxa.containsKey(xa)) {
mapxa.put(xa, mapxa.get(xa) + 1.0);
} else {
mapxa.put(xa, 1.0);
}
}
Xvals.add(xa);
}
if (xs > 0) {
Map<Double, Double> mapxs = XsPerTransition.get(ca);
if (mapxs == null) {
mapxs = new TOrderedHashMap<Double, Double>();
mapxs.put(xs, 1.0);
XsPerTransition.put(ca, mapxs);
} else {
if (mapxs.containsKey(xa)) {
mapxs.put(xs, mapxs.get(xs) + 1.0);
} else {
mapxs.put(xs, 1.0);
}
}
Xvals.add(xs);
}
}
}
}
}
}
@operator(
value = {"fuzzy_kappa_sim"},
content_type = IType.FLOAT,
category = {IOperatorCategory.MAP_COMPARAISON},
concept = {IConcept.MAP})
@doc(
value =
"fuzzy kappa simulation indicator for 2 map comparisons: fuzzy_kappa_sim(agents_list,list_vals1,list_vals2, output_similarity_per_agents,fuzzy_transitions_matrix, fuzzy_distance, weights). Reference: Jasper van Vliet, Alex Hagen-Zanker, Jelle Hurkens, Hedwig van Delden, A fuzzy set approach to assess the predictive accuracy of land use simulations, Ecological Modelling, 24 July 2013, Pages 32-42, ISSN 0304-3800, ",
examples = {
@example(
value =
"fuzzy_kappa_sim([ag1, ag2, ag3, ag4, ag5], [cat1,cat1,cat2,cat3,cat2],[cat2,cat1,cat2,cat1,cat2], similarity_per_agents,[cat1,cat2,cat3],[[1,0,0,0,0,0,0,0,0],[0,1,0,0,0,0,0,0,0],[0,0,1,0,0,0,0,0,0],[0,0,0,1,0,0,0,0,0],[0,0,0,0,1,0,0,0,0],[0,0,0,0,0,1,0,0,0],[0,0,0,0,0,0,1,0,0],[0,0,0,0,0,0,0,1,0],[0,0,0,0,0,0,0,0,1]], 2,[1.0,3.0,2.0,2.0,4.0])",
isExecutable = false)
})
public static double fuzzyKappaSimulation(
final IScope scope,
final IAddressableContainer<Integer, IAgent, Integer, IAgent> agents,
final IList<Object> valsInit,
final IList<Object> valsObs,
final IList<Object> valsSim,
final IList<Double> similarities,
final List<Object> categories,
final GamaMatrix<Double> fuzzytransitions,
final Double distance,
final IList<Object> weights) {
if (agents == null) {
return 1;
}
int nb = agents.length(scope);
if (nb < 1) {
return 1;
}
similarities.clear();
int nbCat = categories.size();
double[] nbObs = new double[nbCat];
double[] nbSim = new double[nbCat];
double[] nbInit = new double[nbCat];
double[][] nbInitObs = new double[nbCat][nbCat];
double[][] nbInitSim = new double[nbCat][nbCat];
Map<Object, Integer> categoriesId = new TOrderedHashMap<Object, Integer>();
Map<List<Integer>, Map<Double, Double>> XaPerTransition =
new TOrderedHashMap<List<Integer>, Map<Double, Double>>();
Map<List<Integer>, Map<Double, Double>> XsPerTransition =
new TOrderedHashMap<List<Integer>, Map<Double, Double>>();
Set<Double> Xvals = new HashSet<Double>();
for (int i = 0; i < nbCat; i++) {
categoriesId.put(categories.get(i), i);
}
for (int i = 0; i < nbCat; i++) {
nbInit[i] = 0;
nbObs[i] = 0;
nbSim[i] = 0;
for (int j = 0; j < nbCat; j++) {
nbInitObs[i][j] = 0;
nbInitSim[i][j] = 0;
}
}
IAgentFilter filter = In.list(scope, agents);
double total = 0;
for (int i = 0; i < nb; i++) {
double weight = weights == null ? 1.0 : Cast.asFloat(scope, weights.get(i));
total += weight;
int idCatInit = categoriesId.get(valsInit.get(i));
int idCatObs = categoriesId.get(valsObs.get(i));
int idCatSim = categoriesId.get(valsSim.get(i));
nbInit[idCatInit] += weight;
nbSim[idCatSim] += weight;
nbObs[idCatObs] += weight;
nbInitObs[idCatInit][idCatObs] += weight;
nbInitSim[idCatInit][idCatSim] += weight;
}
double po =
computePo(
scope,
filter,
categoriesId,
fuzzytransitions,
distance,
valsInit,
valsObs,
valsSim,
agents,
nbCat,
nb,
similarities,
weights);
double pe = 0;
computeXaXsTransitions(
scope,
filter,
fuzzytransitions,
distance,
agents,
nbCat,
XaPerTransition,
XsPerTransition,
Xvals);
for (int i = 0; i < nbCat; i++) {
for (int j = 0; j < nbCat; j++) {
for (int k = 0; k < nbCat; k++) {
List<Integer> ca = new ArrayList<Integer>();
ca.add(i);
ca.add(j);
ca.add(k);
Map<Double, Double> pmuXa = XaPerTransition.get(ca);
Map<Double, Double> pmuXs = XsPerTransition.get(ca);
double emu = 0;
for (Double xval : Xvals) {
double XaVal = pmuXa == null || !pmuXa.containsKey(xval) ? 0 : pmuXa.get(xval);
double XsVal = pmuXs == null || !pmuXs.containsKey(xval) ? 0 : pmuXs.get(xval);
double proba = xval * XaVal * XsVal;
emu += proba;
}
double poas = nbInit[i] == 0 ? 0 : nbInitObs[i][j] / nbInit[i] * nbInitSim[i][k] / total;
pe += emu * poas;
}
}
}
if (pe == 1) {
return 1;
}
return (po - pe) / (1 - pe);
}