XAD - User ManualΒΆ Introduction Algorithmic Differentiation Background Finite Differences Forward Mode Adjoint Mode Higher Orders Basic Usage Prerequisite: Replace Active Variables Forward Mode Adjoint Mode Best Practices External Functions Example Algorithm External Function For Adjoint Mode External Function For Forward Mode Checkpointing Example Algorithm Checkpoint Callback Call-Site Other Usage Patterns Higher-Order Derivatives Example Algorithm Forward Over Adjoint Other Second-Order Modes Handling Discontinuities Reference Headers and Namespaces AD Mode Interface Adjoint Mode Type AReal Forward Mode Type FReal Expressions Mathematical Operations Complex Smoothed Mathematical Functions Global Functions Tape CheckpointCallback Exceptions Version Information GNU Free Documentation License Index Last update: February 2023