private static double computeExpectedSim(
final int nbCat,
final double[] X,
final double[] Y,
final int nbRings,
final List<Double> rings,
final Map<Double, Integer> ringsPn) {
double similarityExpected = 0;
for (int j = 0; j < nbCat; j++) {
similarityExpected += X[j] * Y[j];
}
double dist = 0;
for (int p = 0; p < nbRings; p++) {
double dist1 = dist;
dist = rings.get(p);
double Mdi = FastMath.pow(2, dist / -2);
double Ei = 0;
for (int a = 0; a < nbCat; a++) {
double Ya = Y[a];
for (int b = 0; b < nbCat; b++) {
double Xb = X[b];
int kro_delta = a == b ? 1 : 0;
Ei +=
(1 - kro_delta)
* Ya
* Xb
* (p(dist, a, b, X, Y, ringsPn) - p(dist1, a, b, X, Y, ringsPn));
}
}
similarityExpected += Mdi * Ei;
}
return similarityExpected;
}
private static int buildRings(
final IScope scope,
final IAgentFilter filter,
final Double distance,
final List<Double> rings,
final Map<Double, Integer> ringsPn,
final IAddressableContainer<Integer, IAgent, Integer, IAgent> agents) {
IList<ILocation> locs = GamaListFactory.create(Types.POINT);
for (IAgent ag : agents.iterable(scope)) {
locs.add(ag.getLocation());
}
ILocation centralLoc = (ILocation) Stats.getMean(scope, locs);
IAgent centralAg = scope.getTopology().getAgentClosestTo(scope, centralLoc, filter);
List<IAgent> neighbors =
distance == 0 || filter == null
? new ArrayList<IAgent>()
: new ArrayList<IAgent>(
scope.getTopology().getNeighborsOf(scope, centralAg, distance, filter));
for (IAgent ag : neighbors) {
double dist = centralLoc.euclidianDistanceTo(ag.getLocation());
if (dist == 0) {
continue;
}
if (!rings.contains(dist)) {
rings.add(dist);
ringsPn.put(dist, 1);
} else {
ringsPn.put(dist, 1 + ringsPn.get(dist));
}
}
Collections.sort(rings);
for (int i = 1; i < rings.size(); i++) {
double dist = rings.get(i);
double dist1 = rings.get(i - 1);
ringsPn.put(dist, ringsPn.get(dist) + ringsPn.get(dist1));
}
return rings.size();
}
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 = {"kappa"},
content_type = IType.FLOAT,
category = {IOperatorCategory.MAP_COMPARAISON},
concept = {})
@doc(
value =
"kappa indicator for 2 map comparisons: kappa(list_vals1,list_vals2,categories, weights). Reference: Cohen, J. A coefficient of agreement for nominal scales. Educ. Psychol. Meas. 1960, 20. ",
examples = {
@example(
value =
"kappa([cat1,cat1,cat2,cat3,cat2],[cat2,cat1,cat2,cat1,cat2],[cat1,cat2,cat3], [1.0, 2.0, 3.0, 1.0, 5.0])",
isExecutable = false)
})
public static double kappa(
final IScope scope,
final IList<Object> vals1,
final IList<Object> vals2,
final List<Object> categories,
final IList<Object> weights) {
if (vals1 == null || vals2 == null) {
return 1;
}
int nb = vals1.size();
if (nb != vals2.size()) {
return 0;
}
int nbCat = categories.size();
double[] X = new double[nbCat];
double[] Y = new double[nbCat];
double[][] contigency = new double[nbCat][nbCat];
for (int j = 0; j < nbCat; j++) {
X[j] = 0;
Y[j] = 0;
for (int k = 0; k < nbCat; k++) {
contigency[j][k] = 0;
}
}
Map<Object, Integer> categoriesId = new TOrderedHashMap<Object, Integer>();
for (int i = 0; i < nbCat; i++) {
categoriesId.put(categories.get(i), i);
}
double total = 0;
for (int i = 0; i < nb; i++) {
double weight = weights == null ? 1.0 : Cast.asFloat(scope, weights.get(i));
total += weight;
Object val1 = vals1.get(i);
Object val2 = vals2.get(i);
int indexVal1 = categoriesId.get(val1);
int indexVal2 = categoriesId.get(val2);
X[indexVal1] += weight;
Y[indexVal2] += weight;
contigency[indexVal1][indexVal2] += weight;
}
for (int j = 0; j < nbCat; j++) {
X[j] /= total;
Y[j] /= total;
for (int k = 0; k < nbCat; k++) {
contigency[j][k] /= total;
}
}
double po = 0;
double pe = 0;
for (int i = 0; i < nbCat; i++) {
po += contigency[i][i];
pe += X[i] * Y[i];
}
if (pe == 1) {
return 1;
}
return (po - pe) / (1 - pe);
}
@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);
}
@operator(
value = {"fuzzy_kappa"},
content_type = IType.FLOAT,
category = {IOperatorCategory.MAP_COMPARAISON},
concept = {})
@doc(
value =
"fuzzy kappa indicator for 2 map comparisons: fuzzy_kappa(agents_list,list_vals1,list_vals2, output_similarity_per_agents,categories,fuzzy_categories_matrix, fuzzy_distance, weights). Reference: Visser, H., and T. de Nijs, 2006. The map comparison kit, Environmental Modelling & Software, 21",
examples = {
@example(
value =
"fuzzy_kappa([ag1, ag2, ag3, ag4, ag5],[cat1,cat1,cat2,cat3,cat2],[cat2,cat1,cat2,cat1,cat2], similarity_per_agents,[cat1,cat2,cat3],[[1,0,0],[0,1,0],[0,0,1]], 2, [1.0,3.0,2.0,2.0,4.0])",
isExecutable = false)
})
public static double fuzzyKappa(
final IScope scope,
final IAddressableContainer<Integer, IAgent, Integer, IAgent> agents,
final IList<Object> vals1,
final IList<Object> vals2,
final IList<Double> similarities,
final List<Object> categories,
final GamaMatrix<Double> fuzzycategories,
final Double distance,
final IList<Object> weights) {
if (agents == null) {
return 1;
}
int nb = agents.length(scope);
if (nb < 1) {
return 1;
}
int nbCat = categories.size();
similarities.clear();
boolean[] sim = new boolean[nb];
double[][] crispVector1 = new double[nb][nbCat];
double[][] crispVector2 = new double[nb][nbCat];
double[][] fuzzyVector1 = new double[nb][nbCat];
double[][] fuzzyVector2 = new double[nb][nbCat];
double[] X = new double[nbCat];
double[] Y = new double[nbCat];
Map<Object, Integer> categoriesId = new TOrderedHashMap<Object, Integer>();
for (int i = 0; i < nbCat; i++) {
categoriesId.put(categories.get(i), i);
}
IAgentFilter filter = In.list(scope, agents);
computeXYCrispVector(
scope,
categoriesId,
categories,
vals1,
vals2,
fuzzycategories,
nbCat,
nb,
crispVector1,
crispVector2,
X,
Y,
sim,
weights);
double meanSimilarity =
computeSimilarity(
scope,
filter,
distance,
vals1,
vals2,
agents,
nbCat,
nb,
crispVector1,
crispVector2,
sim,
fuzzyVector1,
fuzzyVector2,
similarities,
weights);
List<Double> rings = new ArrayList<Double>();
Map<Double, Integer> ringsPn = new TOrderedHashMap<Double, Integer>();
int nbRings = buildRings(scope, filter, distance, rings, ringsPn, agents);
double similarityExpected = computeExpectedSim(nbCat, X, Y, nbRings, rings, ringsPn);
if (similarityExpected == 1) {
return 1;
}
return (meanSimilarity - similarityExpected) / (1 - similarityExpected);
}
@operator(
value = {"kappa_sim"},
content_type = IType.FLOAT,
category = {IOperatorCategory.MAP_COMPARAISON},
concept = {})
@doc(
value =
"kappa simulation indicator for 2 map comparisons: kappa(list_valsInits,list_valsObs,list_valsSim, categories, weights). Reference: van Vliet, J., Bregt, A.K. & Hagen-Zanker, A. (2011). Revisiting Kappa to account for change in the accuracy assessment of land-use change models, Ecological Modelling 222(8)",
examples = {
@example(
value =
"kappa([cat1,cat1,cat2,cat2,cat2],[cat2,cat1,cat2,cat1,cat3],[cat2,cat1,cat2,cat3,cat3], [cat1,cat2,cat3],[1.0, 2.0, 3.0, 1.0, 5.0])",
isExecutable = false)
})
public static double kappaSimulation(
final IScope scope,
final IList<Object> valsInit,
final IList<Object> valsObs,
final IList<Object> valsSim,
final List<Object> categories,
final IList<Object> weights) {
if (valsInit == null || valsObs == null || valsSim == null) {
return 1;
}
int nb = valsInit.size();
if (nb != valsObs.size() || nb != valsSim.size()) {
return 0;
}
int nbCat = categories.size();
double[] O = new double[nbCat];
double[][] contigency = new double[nbCat][nbCat];
double[][] contigencyOA = new double[nbCat][nbCat];
double[][] contigencyOS = new double[nbCat][nbCat];
for (int j = 0; j < nbCat; j++) {
O[j] = 0;
for (int k = 0; k < nbCat; k++) {
contigency[j][k] = 0;
contigencyOA[j][k] = 0;
contigencyOS[j][k] = 0;
}
}
Map<Object, Integer> categoriesId = new TOrderedHashMap<Object, Integer>();
for (int i = 0; i < nbCat; i++) {
categoriesId.put(categories.get(i), i);
}
double total = 0;
for (int i = 0; i < nb; i++) {
double weight = weights == null ? 1.0 : Cast.asFloat(scope, weights.get(i));
total += weight;
Object val1 = valsObs.get(i);
Object val2 = valsSim.get(i);
Object valO = valsInit.get(i);
int indexVal1 = categoriesId.get(val1);
int indexVal2 = categoriesId.get(val2);
int indexValO = categoriesId.get(valO);
O[indexValO] += weight;
contigency[indexVal1][indexVal2] += weight;
contigencyOA[indexValO][indexVal1] += weight;
contigencyOS[indexValO][indexVal2] += weight;
}
for (int j = 0; j < nbCat; j++) {
for (int k = 0; k < nbCat; k++) {
contigency[j][k] /= total;
if (O[j] > 0) {
contigencyOA[j][k] /= O[j];
contigencyOS[j][k] /= O[j];
}
}
O[j] /= total;
}
double po = 0;
double pe = 0;
for (int j = 0; j < nbCat; j++) {
po += contigency[j][j];
double sum = 0;
for (int i = 0; i < nbCat; i++) {
sum += contigencyOA[j][i] * contigencyOS[j][i];
}
pe += O[j] * sum;
}
if (pe == 1) {
return 1;
}
return (po - pe) / (1 - pe);
}
