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// Package ewma implements exponentially weighted moving averages.
package ewma
// Copyright (c) 2013 VividCortex, Inc. All rights reserved.
// Please see the LICENSE file for applicable license terms.
const (
// By default, we average over a one-minute period, which means the average
// age of the metrics in the period is 30 seconds.
AVG_METRIC_AGE float64 = 30.0
// The formula for computing the decay factor from the average age comes
// from "Production and Operations Analysis" by Steven Nahmias.
DECAY float64 = 2 / (float64(AVG_METRIC_AGE) + 1)
// For best results, the moving average should not be initialized to the
// samples it sees immediately. The book "Production and Operations
// Analysis" by Steven Nahmias suggests initializing the moving average to
// the mean of the first 10 samples. Until the VariableEwma has seen this
// many samples, it is not "ready" to be queried for the value of the
// moving average. This adds some memory cost.
WARMUP_SAMPLES uint8 = 10
)
// MovingAverage is the interface that computes a moving average over a time-
// series stream of numbers. The average may be over a window or exponentially
// decaying.
type MovingAverage interface {
Add(float64)
Value() float64
Set(float64)
}
// NewMovingAverage constructs a MovingAverage that computes an average with the
// desired characteristics in the moving window or exponential decay. If no
// age is given, it constructs a default exponentially weighted implementation
// that consumes minimal memory. The age is related to the decay factor alpha
// by the formula given for the DECAY constant. It signifies the average age
// of the samples as time goes to infinity.
func NewMovingAverage(age ...float64) MovingAverage {
if len(age) == 0 || age[0] == AVG_METRIC_AGE {
return new(SimpleEWMA)
}
return &VariableEWMA{
decay: 2 / (age[0] + 1),
}
}
// A SimpleEWMA represents the exponentially weighted moving average of a
// series of numbers. It WILL have different behavior than the VariableEWMA
// for multiple reasons. It has no warm-up period and it uses a constant
// decay. These properties let it use less memory. It will also behave
// differently when it's equal to zero, which is assumed to mean
// uninitialized, so if a value is likely to actually become zero over time,
// then any non-zero value will cause a sharp jump instead of a small change.
// However, note that this takes a long time, and the value may just
// decays to a stable value that's close to zero, but which won't be mistaken
// for uninitialized. See http://play.golang.org/p/litxBDr_RC for example.
type SimpleEWMA struct {
// The current value of the average. After adding with Add(), this is
// updated to reflect the average of all values seen thus far.
value float64
}
// Add adds a value to the series and updates the moving average.
func (e *SimpleEWMA) Add(value float64) {
if e.value == 0 { // this is a proxy for "uninitialized"
e.value = value
} else {
e.value = (value * DECAY) + (e.value * (1 - DECAY))
}
}
// Value returns the current value of the moving average.
func (e *SimpleEWMA) Value() float64 {
return e.value
}
// Set sets the EWMA's value.
func (e *SimpleEWMA) Set(value float64) {
e.value = value
}
// VariableEWMA represents the exponentially weighted moving average of a series of
// numbers. Unlike SimpleEWMA, it supports a custom age, and thus uses more memory.
type VariableEWMA struct {
// The multiplier factor by which the previous samples decay.
decay float64
// The current value of the average.
value float64
// The number of samples added to this instance.
count uint8
}
// Add adds a value to the series and updates the moving average.
func (e *VariableEWMA) Add(value float64) {
switch {
case e.count < WARMUP_SAMPLES:
e.count++
e.value += value
case e.count == WARMUP_SAMPLES:
e.count++
e.value = e.value / float64(WARMUP_SAMPLES)
e.value = (value * e.decay) + (e.value * (1 - e.decay))
default:
e.value = (value * e.decay) + (e.value * (1 - e.decay))
}
}
// Value returns the current value of the average, or 0.0 if the series hasn't
// warmed up yet.
func (e *VariableEWMA) Value() float64 {
if e.count <= WARMUP_SAMPLES {
return 0.0
}
return e.value
}
// Set sets the EWMA's value.
func (e *VariableEWMA) Set(value float64) {
e.value = value
if e.count <= WARMUP_SAMPLES {
e.count = WARMUP_SAMPLES + 1
}
}
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