public Task <double> GetVarianceForCombinationAsync(IPs latWeights, IPs lonWeights, ICellRequest cell, double baseNodeVariance)
{
Tuple <IPs, IPs, ICellRequest, double> capturedValues = Tuple.Create(latWeights, lonWeights, cell, baseNodeVariance);
return(Task.Factory.StartNew(obj =>
{
Tuple <IPs, IPs, ICellRequest, double> arg = (Tuple <IPs, IPs, ICellRequest, double>)obj;
var cell2 = arg.Item3;
var name = cell2.VariableName;
double[] targetLats, targetLons;
if (cell2.LatMax == cell2.LatMin && cell2.LonMax == cell2.LonMin)
{
targetLats = new double[] { cell2.LatMax };
targetLons = new double[] { cell2.LonMax };
}
else
{
double latStep = (cell2.LatMax - cell2.LatMin) / (cellDevisionCount - 1);
double lonStep = (cell2.LonMax - cell2.LonMin) / (cellDevisionCount - 1);
targetLats = Enumerable.Range(0, cellDevisionCount).Select(j => cell2.LatMin + j * latStep).ToArray();
targetLons = Enumerable.Range(0, cellDevisionCount).Select(j => cell2.LonMin + j * lonStep).ToArray();
}
//coerce each target location to the closest data grid node. As closest data grid node is representative for its region. (indirect coercing of distance function by moving target locations)
targetLats = Align(latAxis, targetLats);
targetLons = Align(lonAxis, targetLons);
var fieldDescription = dict.GetOrAdd(name, new Lazy <IGaussianFieldDescription>(() =>
{
var v = variogramsFactory.Create(name);
if (v == null)
{
ts.TraceEvent(TraceEventType.Warning, 1, string.Format("Could not find spatial variogram for the \"{0}\" variable. Skipping uncertainty propagation analysis", name));
}
else
{
ts.TraceEvent(TraceEventType.Information, 2, string.Format("Loaded spatial variogram for \"{0}\" variable", name));
}
return v;
}, System.Threading.LazyThreadSafetyMode.ExecutionAndPublication)).Value;
if (fieldDescription == null)
{
return double.MaxValue;
}
var variogram = fieldDescription.Variogram;
var spatPrecomputedSill = variogram.Sill;
var spatPrecomputedNugget = variogram.Nugget;
var coercedBaseVariance = double.IsNaN(arg.Item4) ? (spatPrecomputedNugget) : arg.Item4;
var spatDistance = new Func <double, double, double, double, double>((lat1, lon1, lat2, lon2) => fieldDescription.Dist(lat1, lon1, lat2, lon2));
var spatCovariogram = new Func <double, double>(distance => (spatPrecomputedSill - variogram.GetGamma(distance)));
SpatialVarianceProperties svp = new SpatialVarianceProperties(spatPrecomputedSill - spatPrecomputedNugget + coercedBaseVariance, spatDistance, spatCovariogram);
return GetSpatialVariance(arg.Item1, arg.Item2, latAxis, lonAxis, targetLats, targetLons, svp); //basic scale_factor/add_offset data transform are assumed to be applied during variograms fitting
}, capturedValues));
}
private static double GetSpatialVariance(IPs latWeights, IPs lonWeights, double[] latNodes, double[] lonNodes, double[] targetLats, double[] targetLons, SpatialVarianceProperties varianceProps)
{
//Var(x) = Cov(0) + sum(sum(v_i*v_j*Cov(X_i,X_j)) - 2.0 * sum(v_i*Cov(X_i,X))) for semivariograms
double spatCov0 = varianceProps.Cov0;
var spatCovariogram = varianceProps.Covariance;
var dist = varianceProps.Distance;
double acc = spatCov0; //Cov(0)
var weights1 = latWeights.Weights;
var indices1 = latWeights.Indices;
var weights2 = lonWeights.Weights;
var indices2 = lonWeights.Indices;
var N1 = weights1.Length;
var N2 = weights2.Length;
int N_T = N1 * N2;
var M1 = targetLats.Length;
var M2 = targetLons.Length;
double sum2 = 0.0;
Tuple <double, double, double>[] stratched = new Tuple <double, double, double> [N_T];
for (int i = 0; i < N1; i++)
{
for (int j = 0; j < N2; j++)
{
stratched[N2 * i + j] = Tuple.Create(weights1[i] * weights2[j], latNodes[indices1[i]], lonNodes[indices2[j]]);
}
}
for (int i = 0; i < N_T; i++)
{
var element_i = stratched[i];
double weight_i = element_i.Item1;
double lat_i = element_i.Item2;
double lon_i = element_i.Item3;
acc += weight_i * weight_i * spatCov0;
for (int j = i + 1; j < N_T; j++)
{
var element_j = stratched[j];
// sum(sum(lambda.[i]*lambda.[j]*Cov(X_i,X_j))
acc += 2.0 * weight_i * element_j.Item1 * spatCovariogram(dist(lat_i, lon_i, element_j.Item2, element_j.Item3));
}
double cov_x_xi = 0.0;
for (int k = 0; k < M1; k++) //average cov(x,x_i) as in block kriging for region requsts
{
for (int l = 0; l < M2; l++)
{
cov_x_xi += spatCovariogram(dist(targetLats[k], targetLons[l], lat_i, lon_i));
}
}
//v_i*Cov(X_i,X)))
sum2 += weight_i * cov_x_xi / (M1 * M2);
}
return(0.5 * acc - sum2); //as working with full variograms instead of semivariograms
}
