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 void Collect_InvalidParameters()
{
// valid test data
var testSamples = new double[] { 1, 2, 3 };
var testBreaks = new double[] { 1, 2, 3 };
// choice of test options
var testOptions = new BinningOptions(BinningOutlierMode.RejectOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
// disallow null parameters
Assert.Throws(typeof(ArgumentNullException), () => HistogramHelpers.Collect(null, testBreaks, testOptions));
Assert.Throws(typeof(ArgumentNullException), () => HistogramHelpers.Collect(testSamples, null, testOptions));
Assert.Throws(typeof(ArgumentNullException), () => HistogramHelpers.Collect(testSamples, testBreaks, null));
// disallow fewer than 2 distinct bin breaks
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { }, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { 1.0 }, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { 1.0, 1.0 }, testOptions));
// disallow NaN and infinite samples
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(new double[] { 1.0, double.NaN, 2.0 }, testBreaks, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(new double[] { 1.0, double.PositiveInfinity, 2.0 }, testBreaks, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(new double[] { 1.0, double.NegativeInfinity, 2.0 }, testBreaks, testOptions));
// disallow NaN and infinite bin breaks
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { 1.0, double.NaN, 2.0 }, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { 1.0, double.PositiveInfinity, 2.0 }, testOptions));
Assert.Throws(typeof(ArgumentException), () => HistogramHelpers.Collect(testSamples, new double[] { 1.0, double.NegativeInfinity, 2.0 }, testOptions));
// BinningOutlierMode.RejectOutliers disallows outliers
Assert.Throws(typeof(ArgumentOutOfRangeException), () => HistogramHelpers.Collect(new double[] { 0.0 }, testBreaks, testOptions));
Assert.Throws(typeof(ArgumentOutOfRangeException), () => HistogramHelpers.Collect(new double[] { 3.0 }, testBreaks, testOptions));
}
public static PlotModel CreateExponentialDistributionCustomBins(double mean = 1, int n = 50000)
{
var model = new PlotModel {
Title = "Exponential Distribution", Subtitle = "Custom 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();
HistogramSeries chs = new HistogramSeries();
var binningOptions = new BinningOptions(BinningOutlierMode.CountOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
chs.Items.AddRange(HistogramHelpers.Collect(SampleExps(rnd, 1.0, n), new double[] { 0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.75, 1.0, 2.0, 3.0, 4.0, 5.0 }, binningOptions));
chs.StrokeThickness = 1;
chs.FillColor = OxyColors.Purple;
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 Collect_OutOfOrderBinBreaks()
{
// binBreaks should be ordered by Collect
var sample = new double[] { 2, 3, 9, 8, 7 };
var outOfOrderBreaks = new double[] { 0.0, 10.0, 5.0, 15.0 };
var expectedCounts = new int[] { 2, 3, 0 };
var expectedAreas = new double[] { 0.4, 0.6, 0.0 };
foreach (var binningMode in new[] { BinningOutlierMode.CountOutliers, BinningOutlierMode.IgnoreOutliers })
{
var binningOptions = new BinningOptions(binningMode, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
TestCollect(sample, outOfOrderBreaks, expectedCounts, expectedAreas, binningOptions);
}
}
public void Collect_OutlierSamples()
{
// when Collect is unable to bin any items, it should return areas of 0 rather than NaN
var outlierSamples = new double[] { -1.0, 2.0, 3.0 };
var breaks = new double[] { 0.0, 1.0, 2.0 };
var expectedCounts = new int[] { 0, 0 };
var expectedAreas = new double[] { 0.0, 0.0 };
foreach (var binningMode in new[] { BinningOutlierMode.CountOutliers, BinningOutlierMode.IgnoreOutliers })
{
var binningOptions = new BinningOptions(BinningOutlierMode.IgnoreOutliers, BinningIntervalType.InclusiveLowerBound, BinningExtremeValueMode.ExcludeExtremeValues);
TestCollect(outlierSamples, breaks, expectedCounts, expectedAreas, binningOptions);
}
}
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);
}
/// <summary>
/// Performs a basic test on <see cref="HistogramHelpers.Collect(System.Collections.Generic.IEnumerable{double}, System.Collections.Generic.IReadOnlyList{double}, BinningOptions)"/>.
/// </summary>
/// <param name="samples">The samples to collect.</param>
/// <param name="breaks">The bin breaks that define the bins.</param>
/// <param name="expectedCounts">The expected counts.</param>
/// <param name="expectedAreas">The expected counts.</param>
/// <param name="binningOptions">The binning options to use.</param>
private static void TestCollect(double[] samples, double[] breaks, int[] expectedCounts, double[] expectedAreas, BinningOptions binningOptions)
{
Assume.That(breaks.Length - 1 == expectedCounts.Length);
Assume.That(breaks.Length - 1 == expectedAreas.Length);
var items = HistogramHelpers.Collect(samples, breaks, binningOptions).ToArray();
// check number of items
Assert.AreEqual(expectedAreas.Length, items.Length);
// check areas and counts
for (int i = 0; i < expectedAreas.Length; i++)
{
Assert.AreEqual(expectedAreas[i], items[i].Area, expectedAreas[i] * 1E-15);
Assert.AreEqual(expectedCounts[i], items[i].Count);
}
// check item ranges
var orderedBreaks = breaks.Distinct().OrderBy(b => b).ToArray();
for (int i = 0; i < items.Length; i++)
{
Assert.AreEqual(orderedBreaks[i], items[i].RangeStart);
Assert.AreEqual(orderedBreaks[i + 1], items[i].RangeEnd);
}
}
/// <summary>
/// Performs a basic test on <see cref="HistogramHelpers.Collect(System.Collections.Generic.IEnumerable{double}, System.Collections.Generic.IReadOnlyList{double}, BinningOptions)"/>.
/// </summary>
/// <param name="samples">The samples to collect.</param>
/// <param name="breaks">The bin breaks that define the bins.</param>
/// <param name="expectedCounts">The expected counts.</param>
/// <param name="binningOptions">The binning options to use.</param>
private static void TestCollect(double[] samples, double[] breaks, int[] expectedCounts, BinningOptions binningOptions)
{
// compute areas from counts
int expectedCount = binningOptions.OutlierMode == BinningOutlierMode.CountOutliers ? samples.Length : expectedCounts.Sum();
Assume.That(expectedCount > 0);
var expectedAreas = expectedCounts.Select(c => (double)c / expectedCount).ToArray();
TestCollect(samples, breaks, expectedCounts, expectedAreas, binningOptions);
}
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);
}
