public void CacheHitRatioCase(int n, double cacheSizePercentage, double alpha, double expectedHitRate, int maxTrials)
{
var zipf = new ZipfDistribution(n, alpha, 10, 0.0001);
var capacity = (int)(n * cacheSizePercentage / 100);
var cache = new PseudoLRUCache <string>(capacity);
var allItems = new PseudoLRUCache <string> .CacheItem[n + 1];
var rankHistogram = new int[n + 1];
for (var trial = 0; trial < maxTrials; trial++)
{
var rank = zipf.NextRandomRank();
if (allItems[rank] == null)
{
allItems[rank] = cache.Add(rank.ToString());
}
else
{
allItems[rank].GetOrCreate(() => rank.ToString());
}
rankHistogram[rank]++;
}
Console.WriteLine($"The Hit Ratio is {cache.HitRatio}; hoped for {expectedHitRate}");
var histogram = "Rank Histogram for first 100 items\n";
var cumePct = 0.0;
for (var rank = 1; rank <= 100; rank++)
{
var pct = 100.0 * rankHistogram[rank] / (double)maxTrials;
cumePct += pct;
histogram += $"{rank} chosen {rankHistogram[rank]} times ({pct}%, {cumePct}% cume)\n";
}
Console.WriteLine(histogram);
Assert.GreaterOrEqual(cache.HitRatio, expectedHitRate, $"Cache Hit Ratio is lower than expected: {cache.HitRatio} < {expectedHitRate}");
}
public void ZipfInterpolatedInverseRanksMatch()
{
var n = 10000;
var k = 100;
var alpha = 1.0;
var epsilon = 0.0002; // Uses Interpolation
var zipf = new ZipfDistribution(n, alpha, k, epsilon);
var lowestRankWithDifference = new int[1000];
var success = true;
var detailedLog = "";
var countWithDifferenceMoreThanTwo = 0;
var prevDifference = 0;
for (var rank = 1; rank <= n; rank++)
{
var cdf = zipf.CDF(rank);
var actualRank = zipf.Rank(cdf);
var trueDifference = rank - actualRank;
var difference = Abs(trueDifference);
if (lowestRankWithDifference[difference] == 0)
{
lowestRankWithDifference[difference] = rank;
}
success = success && difference <= 2;
if (difference > 0 && zipf.InterpolationCDFRanks.Contains(rank))
{
Console.WriteLine($"Difference = {difference} for interpolation point at rank = {rank}");
}
if (trueDifference != prevDifference)
{
detailedLog += $"{rank}. {trueDifference}\n";
}
if (difference > 2)
{
countWithDifferenceMoreThanTwo++;
}
prevDifference = trueDifference;
}
Console.WriteLine(zipf.ToString());
Console.WriteLine($"Count with Difference > 2: {countWithDifferenceMoreThanTwo}");
for (var i = 1; i < lowestRankWithDifference.Length; i++)
{
if (lowestRankWithDifference[i] > 0)
{
Console.WriteLine($"Difference = {i}, Rank = {lowestRankWithDifference[i]}");
}
}
Console.WriteLine(detailedLog);
Assert.IsTrue(success, $"Interpolation failed for rank {lowestRankWithDifference[3]}.");
}
public void ZipfUninterpolatedInverseRanksMatchWhenAlphaIsOne()
{
var n = 1000;
var alpha = 1.0;
var epsilon = 0; // Uses No interpolation
var zipf = new ZipfDistribution(n, alpha, 5, epsilon);
for (var rank = 1; rank <= n; rank++)
{
var cdf = zipf.CDF(rank);
var actualRank = zipf.Rank(cdf);
Assert.IsTrue(Abs(rank - actualRank) <= 1, $"Interpolation failed for rank {rank}. CDF = {cdf}. Inverse Rank {actualRank}");
}
}
public void ZipfPDFValuesDecrease()
{
var n = 1000;
var alpha = .01;
var zipf = new ZipfDistribution(n, alpha, 5, 0.01);
var prevPdf = zipf.PDF(1);
Assert.IsTrue(prevPdf < 1 && prevPdf > 0, $"PDF(1) is out of range: {prevPdf}");
for (var rank = 2; rank <= n; rank++)
{
var pdf = zipf.PDF(rank);
Assert.Less(pdf, prevPdf, $"PDF({rank}) is not less than PDF({rank-1}): {pdf}");
prevPdf = pdf;
}
}
public void ZipfApproximateCDFIsCloseToCDF()
{
var n = 10000;
var alpha = 0.95;
var epsilon = 0.01;
var zipf = new ZipfDistribution(n, alpha, 10, epsilon, ZipfDistribution.InterpolationMethod.Hyperbolic);
Console.WriteLine(zipf.ToString());
for (var rank = 1; rank <= n; rank++)
{
var expectedCdf = zipf.CDF(rank);
var actualCdf = zipf.ApproximateCDF(rank);
Assert.IsFalse(RelativeErrorExceedsTolerance(expectedCdf, actualCdf, epsilon), $"Approximate CDF has unacceptable error for rank {rank} with {zipf.InterpolationSize} control points: Expected {expectedCdf} vs actual {actualCdf}");
}
}
public void ZipfInterpolationSizeIncreasesWithAccuracy()
{
var n = 10000;
var alpha = 0.95;
var epsilons = new[] { 0.05, 0.04, 0.03, 0.02, 0.01, 0.005, 0.001, 0.0005, 0.0001, 0.00005 };
var previousCount = 1;
foreach (var epsilon in epsilons)
{
var zipf = new ZipfDistribution(n, alpha, 10, epsilon, ZipfDistribution.InterpolationMethod.Hyperbolic);
Console.WriteLine(zipf.ToString());
var currentCount = zipf.InterpolationSize;
Assert.GreaterOrEqual(currentCount, previousCount, $"Number of interpolation points decreased unexpectedly for epsilon = {epsilon}");
previousCount = currentCount;
}
}
public void ZipfCDFValuesIncreaseToOne()
{
var n = 1000;
var alpha = 0.9;
var zipf = new ZipfDistribution(n, alpha, 5, 0.01);
var prevCdf = zipf.CDF(1);
Assert.IsTrue(prevCdf < 1 && prevCdf > 0, $"CDF(1) is out of range: {prevCdf}");
for (var rank = 2; rank <= n; rank++)
{
var cdf = zipf.CDF(rank);
Assert.Greater(cdf, prevCdf, $"CDF({rank}) is not greater than CDF({rank - 1}): {cdf}");
prevCdf = cdf;
}
var actualCdf = zipf.CDF(n);
Assert.AreEqual(1.0, actualCdf, $"CDF(N) should equal one, but is instead {actualCdf}");
}