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diff --git a/dependencies/pkg/mod/github.com/!vivid!cortex/ewma@v1.2.0/README.md b/dependencies/pkg/mod/github.com/!vivid!cortex/ewma@v1.2.0/README.md new file mode 100644 index 0000000..87b4a3c --- /dev/null +++ b/dependencies/pkg/mod/github.com/!vivid!cortex/ewma@v1.2.0/README.md @@ -0,0 +1,145 @@ +# EWMA + +[](https://godoc.org/github.com/VividCortex/ewma) + +[](https://codecov.io/gh/VividCortex/ewma) + +This repo provides Exponentially Weighted Moving Average algorithms, or EWMAs for short, [based on our +Quantifying Abnormal Behavior talk](https://vividcortex.com/blog/2013/07/23/a-fast-go-library-for-exponential-moving-averages/). + +### Exponentially Weighted Moving Average + +An exponentially weighted moving average is a way to continuously compute a type of +average for a series of numbers, as the numbers arrive. After a value in the series is +added to the average, its weight in the average decreases exponentially over time. This +biases the average towards more recent data. EWMAs are useful for several reasons, chiefly +their inexpensive computational and memory cost, as well as the fact that they represent +the recent central tendency of the series of values. + +The EWMA algorithm requires a decay factor, alpha. The larger the alpha, the more the average +is biased towards recent history. The alpha must be between 0 and 1, and is typically +a fairly small number, such as 0.04. We will discuss the choice of alpha later. + +The algorithm works thus, in pseudocode: + +1. Multiply the next number in the series by alpha. +2. Multiply the current value of the average by 1 minus alpha. +3. Add the result of steps 1 and 2, and store it as the new current value of the average. +4. Repeat for each number in the series. + +There are special-case behaviors for how to initialize the current value, and these vary +between implementations. One approach is to start with the first value in the series; +another is to average the first 10 or so values in the series using an arithmetic average, +and then begin the incremental updating of the average. Each method has pros and cons. + +It may help to look at it pictorially. Suppose the series has five numbers, and we choose +alpha to be 0.50 for simplicity. Here's the series, with numbers in the neighborhood of 300. + + + +Now let's take the moving average of those numbers. First we set the average to the value +of the first number. + + + +Next we multiply the next number by alpha, multiply the current value by 1-alpha, and add +them to generate a new value. + + + +This continues until we are done. + + + +Notice how each of the values in the series decays by half each time a new value +is added, and the top of the bars in the lower portion of the image represents the +size of the moving average. It is a smoothed, or low-pass, average of the original +series. + +For further reading, see [Exponentially weighted moving average](http://en.wikipedia.org/wiki/Moving_average#Exponential_moving_average) on wikipedia. + +### Choosing Alpha + +Consider a fixed-size sliding-window moving average (not an exponentially weighted moving average) +that averages over the previous N samples. What is the average age of each sample? It is N/2. + +Now suppose that you wish to construct a EWMA whose samples have the same average age. The formula +to compute the alpha required for this is: alpha = 2/(N+1). Proof is in the book +"Production and Operations Analysis" by Steven Nahmias. + +So, for example, if you have a time-series with samples once per second, and you want to get the +moving average over the previous minute, you should use an alpha of .032786885. This, by the way, +is the constant alpha used for this repository's SimpleEWMA. + +### Implementations + +This repository contains two implementations of the EWMA algorithm, with different properties. + +The implementations all conform to the MovingAverage interface, and the constructor returns +that type. + +Current implementations assume an implicit time interval of 1.0 between every sample added. +That is, the passage of time is treated as though it's the same as the arrival of samples. +If you need time-based decay when samples are not arriving precisely at set intervals, then +this package will not support your needs at present. + +#### SimpleEWMA + +A SimpleEWMA is designed for low CPU and memory consumption. 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. + +#### VariableEWMA + +Unlike SimpleEWMA, this supports a custom age which must be stored, and thus uses more memory. +It also has a "warmup" time when you start adding values to it. It will report a value of 0.0 +until you have added the required number of samples to it. It uses some memory to store the +number of samples added to it. As a result it uses a little over twice the memory of SimpleEWMA. + +## Usage + +### API Documentation + +View the GoDoc generated documentation [here](http://godoc.org/github.com/VividCortex/ewma). + +```go +package main + +import "github.com/VividCortex/ewma" + +func main() { + samples := [100]float64{ + 4599, 5711, 4746, 4621, 5037, 4218, 4925, 4281, 5207, 5203, 5594, 5149, + } + + e := ewma.NewMovingAverage() //=> Returns a SimpleEWMA if called without params + a := ewma.NewMovingAverage(5) //=> returns a VariableEWMA with a decay of 2 / (5 + 1) + + for _, f := range samples { + e.Add(f) + a.Add(f) + } + + e.Value() //=> 13.577404704631077 + a.Value() //=> 1.5806140565521463e-12 +} +``` + +## Contributing + +We only accept pull requests for minor fixes or improvements. This includes: + +* Small bug fixes +* Typos +* Documentation or comments + +Please open issues to discuss new features. Pull requests for new features will be rejected, +so we recommend forking the repository and making changes in your fork for your use case. + +## License + +This repository is Copyright (c) 2013 VividCortex, Inc. All rights reserved. +It is licensed under the MIT license. Please see the LICENSE file for applicable license terms. |