Automatic Differentiation Library

AUTOmatic Derivatives & Jacobians
by djmaxus and you

• pre-alpha
• play-ready

Contents

• Automatic Differentiation Library
  • Contents
  • Motivation
  • Project goals
  • Anticipated features

Motivation

For the living (and for my heart), I do research & development in the area of computational mathematics and wrote 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 :crab:

• No more devastating hand-written derivatives!
• No more unsafe code!

Project goals

• Develop open-source automatic differentiation library for both academic and commercial computational mathematitians
• Gain experience of Rust programming

Anticipated features

• Basic dual arithmetics as standalone feature
• Number of variables to differentiate
  • single
  • multiple
    • static
    • dynamic
• Calculation tracking (partial derivatives of intermediate values)
• Third-party crates support (as features)
  • num
  • linear algebra crates
• Implement dual arithmetics as pure trait, then implement it for a few structures
• Advanced features

  • Inter-operability of different dual types (e.g., single and multiple dynamic)

  • Arbitrary type of dual number components

  • Rust-alike safety of interfaces

    e.g., Fn(...) -> Result<_,_> for binary operations and UUID-based tracking of variables

  • Numerical verification (or replacement) of derivatives (by definition)

  • Macro for automatic extensions of regular (i.e. non-dual) functions

  • no std

  • Optional calculation of derivatives

    • Iterator implementation as possible approach to lazy evaluation

You are very welcome to introduce issues to promote most wanted features or to report a bug.