Ecosystem Integration API

This document describes the v0.2 bridge packages for Luna Flow ecosystem libraries.

autodiff/linalg

The linalg package uses immutable vectors and matrices from Luna-Flow/linear-algebra/immut.

• gradient(f, x) -> Vector[T]
• jacobian(f, x) -> Matrix[T]
• value_and_gradient(f, x) -> (T, Vector[T])
• value_and_jacobian(f, x) -> (Vector[T], Matrix[T])

gradient expects:

f : Vector[Dual[T]] -> Dual[T]
x : Vector[T]

jacobian expects:

f : Vector[Dual[T]] -> Vector[Dual[T]]
x : Vector[T]

The Jacobian uses the output-by-input convention:

J[row = output_index, col = input_index]

The package uses n-pass forward-mode seeding. It does not require or define field-level behavior for Dual[T].

autodiff/poly

The poly package bridges to Luna-Flow/luna-poly.

Dense univariate helpers:

• eval_dual(p, x_dual) -> Dual[T]
• value_and_derivative_at(p, x) -> (T, T)
• derivative_at(p, x) -> T

Sparse univariate-as-one-variable helpers:

• eval_sparse_dual(p, x_dual) -> Dual[T]
• sparse_value_and_derivative_at(p, x) -> (T, T)
• sparse_derivative_at(p, x) -> T

These functions evaluate existing Luna Poly representations over dual numbers. They do not perform symbolic differentiation and do not introduce a new polynomial representation.