https://github.com/tomstuart/dual_number
A Ruby implementation of dual numbers.
https://github.com/tomstuart/dual_number
Last synced: 7 months ago
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A Ruby implementation of dual numbers.
- Host: GitHub
- URL: https://github.com/tomstuart/dual_number
- Owner: tomstuart
- License: cc0-1.0
- Created: 2016-02-08T16:21:09.000Z (about 10 years ago)
- Default Branch: master
- Last Pushed: 2019-09-07T21:12:49.000Z (over 6 years ago)
- Last Synced: 2025-08-27T15:03:37.196Z (8 months ago)
- Language: Ruby
- Size: 12.7 KB
- Stars: 17
- Watchers: 2
- Forks: 1
- Open Issues: 0
-
Metadata Files:
- Readme: README.md
- License: LICENSE
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README
# dual_number
This library provides a Ruby implementation of [dual numbers](https://en.wikipedia.org/wiki/Automatic_differentiation), which are useful for forward mode [automatic differentiation](https://en.wikipedia.org/wiki/Automatic_differentiation).
It is intended to accompany the article [“Automatic differentiation in Ruby”](http://codon.com/automatic-differentiation-in-ruby).
That article explains the details, but here’s a brief demonstration:
```irb
$ irb -Ilib
>> require 'dual_number'
=> true
>> x = DualNumber(1, 2)
=> (1+2ε)
>> y = DualNumber(3, 4)
=> (3+4ε)
>> x + y
=> (4+6ε)
>> x * y
=> (3+10ε)
>> (x + 3) * 4
=> (16+8ε)
>> 3 + (4 * x)
=> (7+8ε)
```
One application of dual numbers is to use the second (“dual”) component to represent the derivative of the first (“real”) component. This lets us find the derivative of a function at a particular value by just passing in a dual number instead of a normal number:
```irb
>> def distance(time:)
time * Math.sin(time * time) + 1
end
=> :distance
>> value_and_derivative = distance(time: DualNumber(3, 1))
=> (2.2363554557252696-15.988226228682427ε)
>> value_and_derivative.real
=> 2.2363554557252696
>> value_and_derivative.dual
=> -15.988226228682427
```
If you have any questions, please get in touch via [Twitter](http://twitter.com/tomstuart) or [email](mailto:tom@codon.com). If you find any bugs or other problems with the code, please [open an issue](https://github.com/tomstuart/dual_number/issues/new).