public void GreatCircleDistanceTest()
{
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 90.0, 90.0, 23.4, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 0.0, 0.0, 90.0, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 0.0, 0.0, -90.0, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 180.0, 0.0, 90.0, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 180.0, 0.0, -90.0, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 360.0, 0.0, 90.0, 1.0), 1e-14);
Assert.AreEqual(System.Math.PI * 0.5, SphereMath.GetDistance(0.0, 360.0, 0.0, -90.0, 1.0), 1e-14);
}
public async Task <double[]> EvaluateCellsBatchAsync(LinearCombinationContext computationalContext, IEnumerable <ICellRequest> cells)
{
var variogramProvider = await variogramProviderFactory.ConstructAsync();
var combinationsIterator = computationalContext.Combinations.GetEnumerator();
traceSource.TraceEvent(TraceEventType.Start, 1, "Filtering out cells that are not requested");
var filtered = cells.Select(cell =>
{
Tuple <ICellRequest, RealValueNodes, IEnumerable <LinearWeight> > currentElement;
ICellRequest contextCell;
do
{
var nextExists = combinationsIterator.MoveNext();
if (!nextExists)
{
throw new InvalidOperationException("Received linear combination does not containg information about requested cell. Context is not synchronize with requested cells sequenece.");
}
currentElement = combinationsIterator.Current;
contextCell = currentElement.Item1;
} while (!contextCell.Equals(cell));
return(currentElement);
}).ToArray();
traceSource.TraceEvent(TraceEventType.Stop, 1, "Filtered out cells that are not requested");
traceSource.TraceEvent(TraceEventType.Start, 2, "Evaluating uncertatinty for sequence of cells using precomputed linear combinations");
var resultsTasks = filtered.AsParallel().AsOrdered().Select(async tuple =>
{
if (tuple.Item2.Lats.Length == 0)
{
return(Double.NaN); //there are no nodes. Out of data request? can't produce uncertainty
}
var variogram = await variogramProvider.GetSpatialVariogramAsync(tuple.Item2);
var cell = tuple.Item1;
var weights = tuple.Item3.ToArray();
var nodes = tuple.Item2;
Debug.Assert(Math.Abs(weights.Sum(w => w.Weight) - 1.0) < 1e-10);
double sill = variogram.Sill;
double cellLat = (cell.LatMax + cell.LatMin) * 0.5;
double cellLon = (cell.LonMax + cell.LonMin) * 0.5;
//var = cov(0)+ sum sum (w[i]*w[j]*cov(i,j))-2.0*sum(w[i]*cov(x,i))
double cov_at_0 = sill;
double acc = cov_at_0; //cov(0)
for (int i = 0; i < weights.Length; i++)
{
double w = weights[i].Weight;
int idx1 = weights[i].DataIndex;
double lat1 = nodes.Lats[idx1];
double lon1 = nodes.Lons[idx1];
for (int j = 0; j < i; j++)
{
int idx2 = weights[j].DataIndex;
double lat2 = nodes.Lats[idx2];
double lon2 = nodes.Lons[idx2];
double dist = SphereMath.GetDistance(lat1, lon1, lat2, lon2);
double cov = sill - variogram.GetGamma(dist);
acc += 2.0 * w * weights[j].Weight * cov;
}
acc += w * w * cov_at_0; //diagonal elements
double dist2 = SphereMath.GetDistance(lat1, lon1, cellLat, cellLon);
double cov2 = sill - variogram.GetGamma(dist2);
acc -= 2.0 * w * cov2;
}
return(acc * 0.5); //as dealing with full variogram instead of semivariogram
}).ToArray();
var results = await Task.WhenAll(resultsTasks);
traceSource.TraceEvent(TraceEventType.Stop, 2, "Evaluated uncertatinty for sequence of cells using precomputed linear combinations");
return(results);
}
protected override async Task <double[]> EvaluateCellsBatchAsync(IRequestContext context, ComputationalContext computationalContext, IEnumerable <GeoCellTuple> cells)
{
await SaveObservationsAndDalanayDiagsForCells(context, computationalContext, cells);
VariogramModule.IVariogramFitter variogramFitter = new LMDotNetVariogramFitter.Fitter();
Dictionary <ITimeSegment, VariogramModule.IVariogram> variograms = new Dictionary <ITimeSegment, VariogramModule.IVariogram>();
Dictionary <ITimeSegment, IObservationsInformation> observations = (Dictionary <ITimeSegment, IObservationsInformation>)computationalContext["observations"];
LimitedConcurrencyLevelTaskScheduler lclts = new LimitedConcurrencyLevelTaskScheduler(Environment.ProcessorCount);
TaskFactory taskFactory = new TaskFactory(lclts);
var variogramTasks = observations.Select(pair => taskFactory.StartNew(() =>
{
ITimeSegment ts = pair.Key;
TraceVerbose(string.Format("Fitting variogram for {0} ({1} observations)", ts, pair.Value.Observations.Length));
Stopwatch sw1 = Stopwatch.StartNew();
var lats = pair.Value.Observations.Select(o => o.Latitude).ToArray();
var lons = pair.Value.Observations.Select(o => o.Longitude).ToArray();
var vals = pair.Value.Observations.Select(o => o.Value).ToArray();
var pointSet = new EmpVariogramBuilder.PointSet(lats, lons, vals);
var dist = FuncConvert.ToFSharpFunc(new Converter <Tuple <double, double>, FSharpFunc <Tuple <double, double>, double> >(t1 =>
FuncConvert.ToFSharpFunc(new Converter <Tuple <double, double>, double>(t2 => SphereMath.GetDistance(t1.Item1, t1.Item2, t2.Item1, t2.Item2)))));
var empVar = EmpVariogramBuilder.EmpiricalVariogramBuilder.BuildEmpiricalVariogram(pointSet, dist);
var fitted_variogram = variogramFitter.Fit(empVar);
VariogramModule.IVariogram effectiveVariogram = null;
sw1.Stop();
if (FSharpOption <VariogramModule.IDescribedVariogram> .get_IsSome(fitted_variogram))
{
effectiveVariogram = fitted_variogram.Value;
TraceVerbose(string.Format("Variogram fited for {0} ({1} observations) in {2}", ts, pair.Value.Observations.Length, sw1.Elapsed));
}
else
{
TraceWarning(string.Format("Variogram fitting failed for {0} ({1} observations) in {2}. Using fallback variogram", ts, pair.Value.Observations.Length, sw1.Elapsed));
effectiveVariogram = variogramFitter.GetFallback(empVar);
}
lock ("saving_variograms")
{
variograms.Add(ts, effectiveVariogram);
}
}));
TraceVerbose(string.Format("Starting calculations of linear weights for all cells"));
Stopwatch sw2 = Stopwatch.StartNew();
var weigths = CalcLinearWeights(computationalContext, cells);
sw2.Stop();
TraceVerbose(string.Format("calculations of linear weights for all cells ended in {0}", sw2.Elapsed));
TraceVerbose(string.Format("Waiting for all variograms to be computed"));
await Task.WhenAll(variogramTasks);
TraceVerbose(string.Format("All variograms are computed. Calculating variances and values"));
Stopwatch sw3 = Stopwatch.StartNew();
var resultValues = cells.Zip(weigths, (cell, weightTuple) =>
{
ITimeSegment ts = cell.Time;
var weight = weightTuple.Item2;
VariogramModule.IVariogram variogram = variograms[ts];
var observation = observations[ts].Observations;
Debug.Assert(Math.Abs(weight.Sum(w => w.Weight) - 1.0) < 1e-10);
double sill = variogram.Sill;
double cellLat = (cell.LatMax + cell.LatMin) * 0.5;
double cellLon = (cell.LonMax + cell.LonMin) * 0.5;
//var = cov(0)+ sum sum (w[i]*w[j]*cov(i,j))-2.0*sum(w[i]*cov(x,i))
double cov_at_0 = sill;
double acc = cov_at_0; //cov(0)
for (int i = 0; i < weight.Length; i++)
{
double w = weight[i].Weight;
int idx1 = weight[i].DataIndex;
double lat1 = observation[idx1].Latitude;
double lon1 = observation[idx1].Longitude;
for (int j = 0; j < i; j++)
{
int idx2 = weight[j].DataIndex;
double lat2 = observation[idx2].Latitude;
double lon2 = observation[idx2].Longitude;
double dist = SphereMath.GetDistance(lat1, lon1, lat2, lon2);
double cov = sill - variogram.GetGamma(dist);
acc += 2.0 * w * weight[j].Weight * cov;
}
acc += w * w * cov_at_0; //diagonal elements
double dist2 = SphereMath.GetDistance(lat1, lon1, cellLat, cellLon);
double cov2 = sill - variogram.GetGamma(dist2);
acc -= 2.0 * w * cov2;
}
return(Tuple.Create(cell, Math.Sqrt(acc), weight.Sum(w => observation[w.DataIndex].Value * w.Weight)));
}).ToArray();
sw3.Stop();
TraceVerbose(string.Format("All sigmas calulated in {0}", sw3.Elapsed));
computationalContext.Add("results", resultValues);
return(resultValues.Select(r => r.Item2).ToArray());
}
public Task <VariogramModule.IVariogram> GetSpatialVariogramAsync(LinearCombination.RealValueNodes nodes)
{
var task = taskFactory.StartNew(new Func <object, VariogramModule.IVariogram>(obj =>
{
Stopwatch sw = Stopwatch.StartNew();
LinearCombination.RealValueNodes localNodes = (LinearCombination.RealValueNodes)obj;
var variogramFitter = new LMDotNetVariogramFitter.Fitter() as VariogramModule.IVariogramFitter;
traceSource.TraceEvent(TraceEventType.Start, 1, "Starting build of emperical variogram");
var pointSet = new EmpVariogramBuilder.PointSet(localNodes.Lats, localNodes.Lons, localNodes.Values);
var dist = FuncConvert.ToFSharpFunc(new Converter <Tuple <double, double>, FSharpFunc <Tuple <double, double>, double> >(t1 =>
FuncConvert.ToFSharpFunc(new Converter <Tuple <double, double>, double>(t2 => SphereMath.GetDistance(t1.Item1, t1.Item2, t2.Item1, t2.Item2)))));
var empVar = EmpVariogramBuilder.EmpiricalVariogramBuilder.BuildEmpiricalVariogram(pointSet, dist);
sw.Stop();
traceSource.TraceEvent(TraceEventType.Stop, 1, string.Format("Emperical variogram is build in {0}", sw.Elapsed));
sw = Stopwatch.StartNew();
traceSource.TraceEvent(TraceEventType.Start, 2, "Starting variogram fitting");
var variogramRes = variogramFitter.Fit(empVar);
sw.Stop();
traceSource.TraceEvent(TraceEventType.Stop, 2, string.Format("Emperical variogram is build in {0}", sw.Elapsed));
if (FSharpOption <VariogramModule.IDescribedVariogram> .get_IsNone(variogramRes))
{
traceSource.TraceEvent(TraceEventType.Error, 3, "Fariogram fitting failed. Falling back to coarse variogram approximation");
return(variogramFitter.GetFallback(empVar));
}
else
{
return(variogramRes.Value);
}
}), nodes);
return(task);
}