autodiff Documentation

English documentation for Luna-Flow/autodiff 0.2.0.

Overview

autodiff provides forward-mode automatic differentiation over Luna Flow algebraic and arithmetic structures.

The current release introduces dual numbers:

Dual[T] = value + tangent ε, ε² = 0

This lets ordinary scalar functions written against Luna Flow arithmetic be evaluated together with their first derivative.

Current Surface

• Dual[T] with value and tangent.
• Constructors: Dual::new, Dual::constant, and Dual::variable.
• Accessors: Dual::value and Dual::tangent.
• Ring-level algebraic instances where the base scalar supports them.
• Checked division and checked square root through Luna-Flow/arithmetic.
• Elementary lifts for sqrt, exp, ln, sin, cos, and tan.
• Forward helpers: diff and value_and_diff.
• Linear algebra helpers: gradient, jacobian, value_and_gradient, and value_and_jacobian in autodiff/linalg.
• Polynomial helpers: dual-number evaluation and derivative-at-a-point helpers in autodiff/poly.

Documents

• Core API: core/api.md
• Tutorial: core/tutorial.md
• Design notes: core/design.md
• Ecosystem integration API: integration/api.md
• Ecosystem integration tutorial: integration/tutorial.md
• Ecosystem integration design: integration/design.md
• Documentation standard: doc_standard.md

Validation

Recommended checks:

moon check
./run_test.sh
moon info