nabla: Exact Derivatives via Automatic Differentiation

Implements forward-mode automatic differentiation using dual numbers with S4 classes. Supports exact arbitrary-order derivatives through recursive nesting of duals, with high-level functions for computing gradients, Hessian matrices, and Jacobians of arbitrary functions.

Core Types

dual: Constructor for dual numbers.
dual_variable: Shorthand for dual(x, 1).
dual_constant: Shorthand for dual(x, 0).
dual_vector: Container for indexable dual vectors.

Accessors

value: Extract the primal value.
deriv: Extract the derivative component.

Higher-Order Derivatives

dual_variable_n: Create a dual seeded for n-th order differentiation.
deriv_n: Extract the k-th derivative from a nested dual result.
differentiate_n: Compute f(x) and all derivatives up to order n.

Multi-Parameter Derivatives

D: Composable total derivative operator. D(f) returns the derivative function; apply k times for k-th order tensors.
gradient: Gradient of a scalar-valued function.
hessian: Hessian matrix of a scalar-valued function.
jacobian: Jacobian matrix of a vector-valued function.

References

Baydin, A. G., Pearlmutter, B. A., Radul, A. A., & Siskind, J. M. (2018). Automatic differentiation in machine learning: a survey. Journal of Machine Learning Research, 18(153), 1–43.

Author

Maintainer: Alexander Towell queelius@gmail.com (ORCID)