/// <summary>
/// Shuffles the data randonly and then estimates the value at the given quantile.
///
/// It chooses as its seed the mean of the first three items after shuffling.
/// </summary>
/// <param name="data">The data to analyze.
/// Best results for randomly ordered, Gaussian distributed data.
/// Poorest results for sorted data or data drawn from an unusual distribution.</param>
/// <param name="quantileNumerator">Quantile numerator.
/// For the third quartile, use three, for example.</param>
/// <param name="quantileDenominator">Quantile denominator.
/// For the third quartile, use four, for example.
/// </param>
/// <returns>The quantile value.
/// For example, if quantileNumerator / quantileDenominator is one half, the median value is returned.
/// </returns>
public static int ShuffledEstimate(IEnumerable <int> data, double quantileNumerator = 50, double quantileDenominator = 100, Func <int, int> stepAdjuster = null)
{
var dataArray = data.ToArray();
if (dataArray.Length == 0)
{
return(0);
}
else if (dataArray.Length < 100)
{
Array.Sort(dataArray);
return(dataArray[(int)Math.Round((dataArray.Length - 1) * quantileNumerator / quantileDenominator, 0)]);
}
else
{
var shuffledData = dataArray.Shuffle();
Array.Sort(shuffledData, 0, 21);
var seed = shuffledData[(int)(20 * quantileNumerator / quantileDenominator)];
var probe = new FrugalQuantile(seed, quantileNumerator, quantileDenominator)
{
StepAdjuster = stepAdjuster ?? FrugalQuantile.LinearStepAdjuster
};
var estimate = probe.AddRange(shuffledData);
// Console.WriteLine($"seed = {seed}, estimate = {estimate}");
return(estimate);
}
}
/// <summary>
/// Estimates the value at the given quantile for a collection of data.
/// </summary>
/// <param name="data">The data to analyze.
/// Best results for randomly ordered, Gaussian distributed data.
/// Poorest results for sorted data or data drawn from an unusual distribution.</param>
/// <param name="quantileNumerator">Quantile numerator.
/// For the third quartile, use three, for example.</param>
/// <param name="quantileDenominator">Quantile denominator.
/// For the third quartile, use four, for example.
/// </param>
/// <param name="seed">Seed value to use as initial value of the estimate.</param>
/// <returns>The quantile value.
/// For example, if quantileNumerator / quantileDenominator is one half, the median value is returned.
/// </returns>
public static int Estimate(IEnumerable <int> data, double quantileNumerator = 50, double quantileDenominator = 100, int seed = 0)
{
var probe = new FrugalQuantile(seed, quantileNumerator, quantileDenominator)
{
StepAdjuster = LinearStepAdjuster
};
return(probe.AddRange(data));
}
public DimensionTransform(IEnumerable <int> values)
{
Median = FrugalQuantile.ShuffledEstimate(
values.Select(x =>
{
// Since FrugalQuantile is going to iterate over the data once anyways,
// might as well piggyback to compute Minimum and Maximum.
Minimum = Min(Minimum, x);
Maximum = Max(Maximum, x);
return(x);
})
);
MinimumBitsRequired = BitsPerDimension = (Maximum + 1).SmallestPowerOfTwo();
}