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