Module api 

Closure-based API for automatic differentiation.

Provides top-level functions (grad, jvp, vjp, jacobian) that handle tape setup, variable creation, and derivative extraction. With the bytecode feature, adds record, hessian, hvp, sparse_jacobian, sparse_hessian, and more.

Functions

composed_hvpbytecode

Forward-over-reverse HVP via type-level composition.

grad

Compute the gradient of a scalar function f : R^n → R using reverse mode.

hessianbytecode

Full Hessian matrix via forward-over-reverse on a bytecode tape.

hessian_vecbytecode

Full Hessian matrix via batched forward-over-reverse.

hvpbytecode

Hessian-vector product via forward-over-reverse on a bytecode tape.

jacobian

Compute the full Jacobian of f : R^n → R^m using forward mode.

jvp

Jacobian-vector product (forward mode): (f(x), J·v).

recordbytecode

Record a function into a BytecodeTape that can be re-evaluated at different inputs without re-recording.

record_multibytecode

Record a multi-output function into a BytecodeTape.

sparse_hessianbytecode

Sparse Hessian via structural sparsity detection and graph coloring.

sparse_hessian_vecbytecode

Batched sparse Hessian: packs N colors per sweep using DualVec.

sparse_jacobianbytecode

Sparse Jacobian of a multi-output function via sparsity detection and coloring.

vjp

Vector-Jacobian product (reverse mode): (f(x), wᵀ·J).