public static DensityHistogram Build([NotNull] this IDensityHistogramBuilder builder, IReadOnlyList <double> values,
IReadOnlyList <double> weights, int binCount)
{
Assertion.NotNull(nameof(builder), builder);
return(builder.Build(new Sample(values, weights), binCount));
}
public ModalityData DetectModes(Sample sample, [CanBeNull] IDensityHistogramBuilder densityHistogramBuilder, bool diagnostics = false)
{
Assertion.NotNull(nameof(sample), sample);
if (sample.Values.Max() - sample.Values.Min() < 1e-9)
{
throw new ArgumentException($"{nameof(sample)} should contain at least two different elements", nameof(sample));
}
densityHistogramBuilder ??= QuantileRespectfulDensityHistogramBuilder.Instance;
int binCount = (int)Math.Round(1 / precision);
var histogram = densityHistogramBuilder.Build(sample, binCount);
var bins = histogram.Bins;
double binArea = 1.0 / bins.Count;
var binHeights = bins.Select(bin => bin.Height).ToList();
var diagnosticsBins = diagnostics
? histogram.Bins.Select(b => new LowlandModalityDiagnosticsData.DiagnosticsBin(b)).ToArray()
: Array.Empty <LowlandModalityDiagnosticsData.DiagnosticsBin>();
var peaks = new List <int>();
for (int i = 1; i < binCount - 1; i++)
{
if (binHeights[i] > binHeights[i - 1] && binHeights[i] >= binHeights[i + 1])
{
peaks.Add(i);
if (diagnostics)
{
diagnosticsBins[i].IsPeak = true;
}
}
}
RangedMode GlobalMode(double location) => new RangedMode(location, histogram.GlobalLower, histogram.GlobalUpper, sample);
RangedMode LocalMode(double location, double left, double right)
{
var modeValues = new List <double>();
var modeWeights = sample.IsWeighted ? new List <double>() : null;
for (int i = 0; i < sample.SortedValues.Count; i++)
{
double value = sample.SortedValues[i];
if (left <= value && value <= right)
{
modeValues.Add(value);
modeWeights?.Add(sample.SortedWeights[i]);
}
}
var modeSample = modeWeights == null ? new Sample(modeValues) : new Sample(modeValues, modeWeights);
return(new RangedMode(location, left, right, modeSample));
}
ModalityData Result(IReadOnlyList <RangedMode> modes) => diagnostics
? new LowlandModalityDiagnosticsData(modes, histogram, diagnosticsBins)
: new ModalityData(modes, histogram);
switch (peaks.Count)
{
case 0:
return(Result(new[] { GlobalMode(bins[binHeights.WhichMax()].Middle) }));
case 1:
return(Result(new[] { GlobalMode(bins[peaks.First()].Middle) }));
default:
{
var modeLocations = new List <double>();
var cutPoints = new List <double>();
bool TrySplit(int peak0, int peak1, int peak2)
{
int left = peak1, right = peak2;
double height = Math.Min(binHeights[peak1], binHeights[peak2]);
while (left < right && binHeights[left] > height)
{
left++;
}
while (left < right && binHeights[right] > height)
{
right--;
}
if (diagnostics)
{
for (int i = left; i <= right; i++)
{
diagnosticsBins[i].WaterLevel = height;
}
}
double width = bins[right].Upper - bins[left].Lower;
double totalArea = width * height;
int totalBinCount = right - left + 1;
double totalBinArea = totalBinCount * binArea;
double binProportion = totalBinArea / totalArea;
if (binProportion < sensitivity)
{
modeLocations.Add(bins[peak0].Middle);
cutPoints.Add(bins[binHeights.WhichMin(peak1, peak2 - peak1)].Middle);
if (diagnostics)
{
diagnosticsBins[peak0].IsMode = true;
for (int i = left; i <= right; i++)
{
diagnosticsBins[i].IsLowland = true;
}
}
return(true);
}
return(false);
}
var previousPeaks = new List <int> {
peaks[0]
};
for (int i = 1; i < peaks.Count; i++)
{
int currentPeak = peaks[i];
while (previousPeaks.Any() && binHeights[previousPeaks.Last()] < binHeights[currentPeak])
{
if (TrySplit(previousPeaks.First(), previousPeaks.Last(), currentPeak))
{
previousPeaks.Clear();
}
else
{
previousPeaks.RemoveAt(previousPeaks.Count - 1);
}
}
if (previousPeaks.Any() && binHeights[previousPeaks.Last()] > binHeights[currentPeak])
{
if (TrySplit(previousPeaks.First(), previousPeaks.Last(), currentPeak))
{
previousPeaks.Clear();
}
}
previousPeaks.Add(currentPeak);
}
modeLocations.Add(bins[previousPeaks.First()].Middle);
if (diagnostics)
{
diagnosticsBins[previousPeaks.First()].IsMode = true;
}
var modes = new List <RangedMode>();
switch (modeLocations.Count)
{
case 0:
modes.Add(GlobalMode(bins[binHeights.WhichMax()].Middle));
break;
case 1:
modes.Add(GlobalMode(modeLocations.First()));
break;
default:
{
modes.Add(LocalMode(modeLocations.First(), histogram.GlobalLower, cutPoints.First()));
for (int i = 1; i < modeLocations.Count - 1; i++)
{
modes.Add(LocalMode(modeLocations[i], cutPoints[i - 1], cutPoints[i]));
}
modes.Add(LocalMode(modeLocations.Last(), cutPoints.Last(), histogram.GlobalUpper));
}
break;
}
return(Result(modes));
}
}
}
