8 releases
0.4.4 | Jan 8, 2023 |
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0.4.3 | Dec 9, 2022 |
0.3.1-alpha.1 | Aug 29, 2022 |
0.2.10 | Aug 22, 2022 |
0.0.3 |
|
#106 in Math
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29KB
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Automatic Differentiation Library
AUTOmatic Derivatives & Jacobians by djmaxus and you
Functionality
Single variables
use autodj::single::*;
let x : DualNumber = 2.0.into_variable();
// values can be borrowed for arithmetic operations
let f = x * x + &1.0.into();
assert_eq!(f.value(), 5.0);
assert_eq!(f.deriv(), 4.0);
// fmt::Display resembles Taylor expansion
assert_eq!(format!("{f}"), "5+4∆");
Multiple variables
Multivariate differentiation is based on multiple dual components. Such an approach requires no repetitive and "backward" differentiations. Each partial derivative is tracked separately from the start, and no repetitive calculations are made.
For built-in multivariate specializations,
independent variables can be created consistently using .into_variables()
method.
Static number of variables
use autodj::array::*;
// consistent set of independent variables
let vars : DualVariables<2> = [2.0, 3.0].into_variables();
let [x, y] = vars.get().to_owned();
let f = x * (y - 1.0.into());
assert_eq!(f.value(), 4.);
assert_eq!(f.grad() , &[2., 2.]);
assert_eq!(format!("{f}"), "4+[2.0, 2.0]∆");
Dynamic number of variables
use autodj::vector::*;
let x : DualVariables = vec![1., 2., 3., 4., 5.].into_variables();
let f : DualNumber = x.get()
.iter()
.map(|x : &DualNumber| x * &2.0.into())
.sum();
assert_eq!(f.value(), 30.);
f.grad()
.iter()
.for_each(|deriv| assert_eq!(deriv, &2.0) );
Generic dual numbers
// can be specialized for your needs
use autodj::common::Common;
Motivation
I do both academic & business R&D in the area of computational mathematics. As well as many of us, I've written a whole bunch of sophisticated Jacobians by hand.
One day, I learned about automatic differentiation based on dual numbers. Almost the same day, I learned about Rust as well 🦀
Then, I decided to:
- Make it automatic and reliable as much as possible
- Use modern and convenient ecosystem of Rust development
Project goals
- Develop open-source automatic differentiation library for both academic and commercial computational mathematicians
- Gain experience of Rust programming
Anticipated features
You are very welcome to introduce issues to promote most wanted features or to report a bug.
- Generic implementation of dual numbers
- Number of variables to differentiate
- single
- multiple
- static
- dynamic
- sparse
- Jacobians for efficient layouts in memory
- Named variables (UUID-based)
- Calculation tracking (partial derivatives of intermediate values)
- Third-party crates support (as features)
-
num
- linear algebra crates (
nalgebra
etc.)
-
- Advanced features
- Arbitrary number types beside
f64
- Inter-operability of different dual types (e.g., single and multiple dynamic)
- Numerical verification (or replacement) of derivatives (by definition)
- Macro for automatic extensions of regular (i.e. non-dual) functions
- Optional calculation of derivatives
- Iterator implementation as possible approach to lazy evaluation
- Arbitrary number types beside
Comparison with autodiff
As far as I noticed, autodj
currently has the following differences
- Multiple variables out of the box
fmt::Display
for statically-known number of variables- Left-to-right flow of many operations such as
.into-variables()
,.eval()
, etc. - Number type is restricted to
f64
- No utilization of
num
andnalgebra
crates
Some differences are planned to be eliminated as noted in the roadmap.
Within this crate, you may study & launch test target /tests/autodiff.rs
to follow some differences.
cargo test --test autodiff -- --show-output