Module: Corkscrews::Statistics

Defined in:
lib/corkscrews/statistics.rb

Class Method Summary collapse

Class Method Details

.bootstrap_mean_ci(values, iterations: 1_000, random: Random.new(12_345)) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 35

def bootstrap_mean_ci(values, iterations: 1_000, random: Random.new(12_345))
  return [0.0, 0.0] if values.empty?
  return [values.first.to_f, values.first.to_f] if values.length == 1

  # Paper basis: Kalibera & Jones, "Quantifying Performance Changes
  # with Effect Size Confidence Intervals" (arXiv:2007.10899),
  # motivates reporting uncertainty for performance effect sizes.
  # Paper URL: https://arxiv.org/abs/2007.10899
  means = Array.new(iterations) do
    sample = Array.new(values.length) { values.fetch(random.rand(values.length)) }
    mean(sample)
  end
  percentile_ci(means)
end

.kendall_tau(left, right) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 86

def kendall_tau(left, right)
  return 0.0 unless left.length == right.length
  return 1.0 if left.length < 2

  concordant = 0
  discordant = 0
  (0...(left.length - 1)).each do |i|
    ((i + 1)...left.length).each do |j|
      left_delta = left[i] <=> left[j]
      right_delta = right[i] <=> right[j]
      next if left_delta.zero? || right_delta.zero?

      if left_delta == right_delta
        concordant += 1
      else
        discordant += 1
      end
    end
  end

  total = concordant + discordant
  return 0.0 if total.zero?

  (concordant - discordant).to_f / total
end

.mean(values) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 7

def mean(values)
  return 0.0 if values.empty?

  values.sum.to_f / values.length
end

.median(values) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 25

def median(values)
  return 0.0 if values.empty?

  sorted = values.sort
  middle = sorted.length / 2
  return sorted.fetch(middle).to_f if sorted.length.odd?

  (sorted.fetch(middle - 1) + sorted.fetch(middle)).to_f / 2.0
end

.monotonic_regression(points) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 50

def monotonic_regression(points)
  ordered = points.sort_by { |point| point[:speedup_pct] }
  blocks = []

  # Paper basis: Coz SOSP'15 Section 2 plots increasing virtual
  # speedup on the x-axis; this pool-adjacent-violators pass enforces
  # the physical monotonicity expected from that curve.
  # Paper URL: https://arxiv.org/abs/1608.03676
  ordered.each do |point|
    blocks << {
      start: point[:speedup_pct],
      finish: point[:speedup_pct],
      weight: 1.0,
      value: point[:improvement_pct].to_f
    }

    while blocks.length >= 2 && blocks[-2][:value] > blocks[-1][:value]
      right = blocks.pop
      left = blocks.pop
      weight = left[:weight] + right[:weight]
      blocks << {
        start: left[:start],
        finish: right[:finish],
        weight: weight,
        value: ((left[:value] * left[:weight]) + (right[:value] * right[:weight])) / weight
      }
    end
  end

  blocks.flat_map do |block|
    ordered
      .select { |point| point[:speedup_pct] >= block[:start] && point[:speedup_pct] <= block[:finish] }
      .map { |point| point.merge(improvement_pct: block[:value]) }
  end
end

.percentile(values, pct) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 13

def percentile(values, pct)
  return 0.0 if values.empty?

  sorted = values.sort
  index = (pct * (sorted.length - 1)).round
  sorted.fetch(index)
end

.percentile_ci(values, lower: 0.025, upper: 0.975) ⇒ Object 



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# File 'lib/corkscrews/statistics.rb', line 21

def percentile_ci(values, lower: 0.025, upper: 0.975)
  [percentile(values, lower), percentile(values, upper)]
end