github.com/m3db/m3@v1.5.0/src/query/functions/aggregation/function.go

// Copyright (c) 2018 Uber Technologies, Inc.
//
// Permission is hereby granted, free of charge, to any person obtaining a copy
// of this software and associated documentation files (the "Software"), to deal
// in the Software without restriction, including without limitation the rights
// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
// copies of the Software, and to permit persons to whom the Software is
// furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included in
// all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
// THE SOFTWARE.

package aggregation

import (
	"math"
)

const (
	// SumType adds all non nan elements in a list of series.
	SumType = "sum"
	// MinType takes the minimum all non nan elements in a list of series.
	MinType = "min"
	// MaxType takes the maximum all non nan elements in a list of series.
	MaxType = "max"
	// AverageType averages all non nan elements in a list of series.
	AverageType = "avg"
	// StandardDeviationType takes the population standard deviation of all non
	// nan elements in a list of series.
	StandardDeviationType = "stddev"
	// StandardVarianceType takes the population standard variance of all non
	// nan elements in a list of series.
	StandardVarianceType = "var"
	// CountType counts all non nan elements in a list of series.
	CountType = "count"
)

func absentFn(values []float64, bucket []int) float64 {
	for _, idx := range bucket {
		v := values[idx]
		if !math.IsNaN(v) {
			return math.NaN()
		}
	}

	return 1
}

func sumAndCount(values []float64, bucket []int) (float64, float64) {
	sum := 0.0
	count := 0.0
	for _, idx := range bucket {
		v := values[idx]
		if !math.IsNaN(v) {
			sum += v
			count++
		}
	}

	// If all elements are NaN, sum should be NaN.
	if count == 0 {
		sum = math.NaN()
	}

	return sum, count
}

func sumFn(values []float64, bucket []int) float64 {
	sum, _ := sumAndCount(values, bucket)
	return sum
}

func minFn(values []float64, bucket []int) float64 {
	min := math.NaN()
	for _, idx := range bucket {
		v := values[idx]
		if !math.IsNaN(v) {
			if math.IsNaN(min) || min > v {
				min = v
			}
		}
	}

	return min
}

func maxFn(values []float64, bucket []int) float64 {
	max := math.NaN()
	for _, idx := range bucket {
		v := values[idx]
		if !math.IsNaN(v) {
			if math.IsNaN(max) || max < v {
				max = v
			}
		}
	}

	return max
}

func averageFn(values []float64, bucket []int) float64 {
	sum, count := sumAndCount(values, bucket)

	// Cannot take average of no values
	if count == 0 {
		return math.NaN()
	}

	return sum / count
}

func stddevFn(values []float64, bucket []int) float64 {
	return math.Sqrt(varianceFn(values, bucket))
}

func varianceFn(values []float64, bucket []int) float64 {
	if len(values) == 0 || len(bucket) == 0 {
		return math.NaN()
	}

	// Using Welford's online algorithm for calculating variance
	// https://en.wikipedia.org/wiki/Algorithms_for_calculating_variance#Welford's_online_algorithm
	//
	// This algorithm is used in Prometheus and also should provide better numerical precision than
	// the straight-forward implementation of the variance formula. The algorithm iterates through the values
	// and at the each step recalculates mean and variance of the values seen so far.

	var (
		count                = 0
		partialMean          = 0.0
		partialVarTimesCount = 0.0 // for better precision, calculate `variance * count` and divide at the end
	)

	for _, idx := range bucket {
		v := values[idx]
		if !math.IsNaN(v) {
			count++

			delta1 := v - partialMean
			partialMean += delta1 / float64(count)
			delta2 := v - partialMean

			partialVarTimesCount += delta1 * delta2
		}
	}

	if count < 1 {
		return math.NaN()
	}

	return partialVarTimesCount / float64(count)
}

func countFn(values []float64, bucket []int) float64 {
	_, count := sumAndCount(values, bucket)
	return count
}