index.md

Documentation

Core framework

The Core framework of AutoDiff implements the abstract coordinate-free concepts of differentiation (see Mathematical background below). It offers class templates for evaluating and differentiating expressions of any value and derivative type. Through a plugin system, separate modules can provide concrete implementation of these concepts for particular combinations of value and derivative types.

• Variables
  • Creating variables from values
  • Variable getters and setters
  • Copying variables
• Expressions
  • Evaluating expressions
  • Custom expressions
  • Memory management in expressions
• Functions
  • Defining functions
  • Evaluating functions
  • Forward-mode differentiation
  • Reverse-mode differentiation (aka backpropagation)
  • Function compilation

Modules

AutoDiff is designed as a framework that can be extended by users with additional modules for specific value and derivative types. The following modules are currently available as part of the library:

• Basic module - scalar expressions with C++ built-in types
• Eigen module - expressions with scalars, Eigen arrays, and (dense) Eigen matrices

Applications

• Applications
  • Control flow
  • Computing the Jacobian matrix
  • Gradient computation
  • Element-wise gradient computation
  • Jacobian-vector products

Mathematical background

• Mathematical notes on the API
• Automatic differentiation and differential geometry
• Differentiation in local coordinates

Advanced topics

• Developer guide
• Class diagram