public void CreateUniformBins_BasicTest()
{
// arbitrary unpleasent numbers
var start = -0.123456789E10;
var end = 0.987654321E10;
var counts = new[] { 13, 17, 113, 1023, 1234567, 1234569 };
foreach (var count in counts)
{
var breaks = HistogramHelpers.CreateUniformBins(start, end, count);
// ensure that CreateUniformBins gives back the exact same start and end
Assert.AreEqual(count + 1, breaks.Count);
Assert.AreEqual(breaks[0], start);
Assert.AreEqual(breaks[count], end);
// ensure the gab between breaks is reasonably consistent
double expectedGap = (end - start) / count;
for (int i = 0; i < count; i++)
{
double gap = breaks[i + 1] - breaks[i];
Assert.AreEqual(expectedGap, gap, 1E-5); // near limits of resoltuion
}
}
}
public static PlotModel CreateIndividualBinColors(double mean = 1, int n = 10000)
{
var model = new PlotModel {
Title = "Individual Bin Colors", Subtitle = "Minimum is Red, Maximum is Green"
};
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Title = "Frequency"
});
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Title = "Observation"
});
Random rnd = new Random(1);
HistogramSeries chs = new HistogramSeries()
{
FillColor = OxyColors.Gray, RenderInLegend = true, Title = "Measurements"
};
var binningOptions = new BinningOptions(BinningOutlierMode.CountOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
var binBreaks = HistogramHelpers.CreateUniformBins(0, 10, 20);
var bins = HistogramHelpers.Collect(SampleUniform(rnd, 0, 10, 1000), binBreaks, binningOptions).OrderBy(b => b.Count).ToArray();
bins.First().Color = OxyColors.Red;
bins.Last().Color = OxyColors.Green;
chs.Items.AddRange(bins);
chs.StrokeThickness = 1;
model.Series.Add(chs);
return(model);
}
public static PlotModel CreateExponentialDistribution(double mean = 1, int n = 10000)
{
var model = new PlotModel {
Title = "Exponential Distribution", Subtitle = "Uniformly distributed bins (" + n + " samples)"
};
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Title = "Frequency"
});
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Title = "x"
});
Random rnd = new Random(1);
HistogramSeries chs = new HistogramSeries();
var binningOptions = new BinningOptions(BinningOutlierMode.CountOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
var binBreaks = HistogramHelpers.CreateUniformBins(0, 5, 15);
chs.Items.AddRange(HistogramHelpers.Collect(SampleExps(rnd, 1.0, n), binBreaks, binningOptions));
chs.StrokeThickness = 1;
model.Series.Add(chs);
return(model);
}
public void CreateUniformBins_SingleBin()
{
var start = double.Epsilon;
var end = 1.0;
var breaks = HistogramHelpers.CreateUniformBins(start, end, 1);
Assert.AreEqual(2, breaks.Count);
Assert.AreEqual(breaks[0], start);
Assert.AreEqual(breaks[1], end);
}
public void CreateUniformBins_InvalidParameters()
{
// explicitly disallow extreme values for start and end
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(double.NaN, 0.0, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(double.NegativeInfinity, 0.0, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(double.PositiveInfinity, 0.0, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(0.0, double.NaN, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(0.0, double.NegativeInfinity, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(0.0, double.PositiveInfinity, 5));
// disallow binCount < 1
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(0.0, 1.0, -100));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(0.0, 1.0, 0));
// disallow start >= end
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(1.0, 0.0, 5));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.CreateUniformBins(1.0, 1.0, 5));
}
public static PlotModel CreateNormalDistribution(double mean = 0, double std = 1, int n = 1000000)
{
var model = new PlotModel {
Title = $"Normal Distribution (μ={mean}, σ={std})", Subtitle = "95% of the distribution (" + n + " samples)"
};
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Left, Title = "Frequency"
});
model.Axes.Add(new LinearAxis {
Position = AxisPosition.Bottom, Title = "x"
});
Random rnd = new Random();
HistogramSeries chs = new HistogramSeries();
var binningOptions = new BinningOptions(BinningOutlierMode.CountOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
var binBreaks = HistogramHelpers.CreateUniformBins(-std * 4, std * 4, 100);
chs.Items.AddRange(HistogramHelpers.Collect(SampleNormal(rnd, mean, std, n), binBreaks, binningOptions));
chs.StrokeThickness = 1;
double LimitHi = mean + 1.96 * std;
double LimitLo = mean - 1.96 * std;
OxyColor ColorHi = OxyColors.DarkRed;
OxyColor ColorLo = OxyColors.DarkRed;
chs.ColorMapping = (item) =>
{
if (item.RangeCenter > LimitHi)
{
return(ColorHi);
}
else if (item.RangeCenter < LimitLo)
{
return(ColorLo);
}
return(chs.ActualFillColor);
};
model.Series.Add(chs);
return(model);
}
public void CreateUniformBins_IntegerBins()
{
int[] primes = new int[] { 1, 2, 3, 5, 7, 11, 13, 17 };
// ensure we produce nice integer results over a reasonable range
int end = primes.Aggregate((a, b) => a * b);
int start = -end;
foreach (var interval in primes)
{
int count = (end - start) / interval;
var breaks = HistogramHelpers.CreateUniformBins(start, end, count);
Assert.AreEqual(count, breaks.Count - 1);
int i = 0;
for (int b = start; b <= end; b += interval, i++)
{
Assert.AreEqual(b, breaks[i]);
}
}
}
public static PlotModel HistogramSeries()
{
// prepare the model
var model = new PlotModel()
{
Title = "Cubic Distribution",
LegendPlacement = LegendPlacement.Outside,
LegendPosition = LegendPosition.TopCenter,
LegendOrientation = LegendOrientation.Horizontal
};
// add two linear axes
model.Axes.Add(new LinearAxis()
{
Title = "Observation", Position = AxisPosition.Bottom
});
model.Axes.Add(new LinearAxis()
{
Title = "Frequency", Position = AxisPosition.Left
});
// generate random samples from a polynomial distribution
double power = 3;
double max = 10.0;
int sampleCount = 1000;
double integral = Math.Pow(max, power + 1) / (power + 1);
var rnd = new Random(0);
List <double> samples = new List <double>();
for (int i = 0; i < sampleCount; i++)
{
samples.Add(Math.Pow(rnd.NextDouble() * (power + 1) * integral, 1.0 / (power + 1)));
}
// plot histogram of samples
var histogramSeries = new HistogramSeries()
{
Title = $"Empirical Distribution",
FillColor = OxyColors.Green,
StrokeColor = OxyColors.Black,
StrokeThickness = 2
};
var bins = HistogramHelpers.CreateUniformBins(0, max, 20);
var binningOptions = new BinningOptions(BinningOutlierMode.RejectOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.IncludeExtremeValues);
var items = HistogramHelpers.Collect(samples, bins, binningOptions);
histogramSeries.Items.AddRange(items);
model.Series.Add(histogramSeries);
// plot ideal line for comparison
var functionSeries = new FunctionSeries(x => Math.Pow(x, power) / integral, 0, max, 1000)
{
Title = "Ideal Distribution",
Color = OxyColors.Red
};
model.Series.Add(functionSeries);
return(model);
}
