Module jet1vec 

Jet1Vec - multi-variable first-order forward-mode AD type.

A Jet1Vec carries a real value plus a vector of tangents (one per input variable). A single forward pass through a function built from Jet1Vec operations yields the value AND the full gradient — every partial ∂f/∂x_i — in one shot, without a tape.

This complements the other AD types in the crate:

• Jet1 — forward mode, one tangent direction.
• Jet2 — forward mode, one direction, second order.
• Jet1Vec (this type) — forward mode, many directions at once, first order.
• AReal — reverse mode (tape-based).

The tangent vector is stored as a plain Vec<T>. Every operator is implemented as a single fused loop over the tangent slice (no temporary intermediate buffers), and owned-value forms reuse the left operand’s allocation in place, so forward propagation is allocator-light and the inner loops are autovectorizable.

Typical use: seed each input variable x_i with Jet1Vec::variable(x_i, i, n), propagate through the function, then read the gradient from result.dual().

use xad_rs::Jet1Vec;
// f(x, y) = x^2 * y, at (x, y) = (3, 4)
// ∂f/∂x = 2xy = 24,  ∂f/∂y = x^2 = 9
let n = 2;
let x = Jet1Vec::variable(3.0, 0, n);
let y = Jet1Vec::variable(4.0, 1, n);
let f = &(&x * &x) * &y;
assert_eq!(f.real(), 36.0);
assert_eq!(f.partial(0), 24.0);
assert_eq!(f.partial(1), 9.0);

This module also contains NamedJet1Vec, a named wrapper over Jet1Vec that provides name-keyed gradient readback via a NamedForwardTape scope.

Structs

Jet1Vec

Multi-variable forward-mode dual number.

NamedJet1Vec

Labeled wrapper around the positional Jet1Vec type.