Associates a tensor value with a forward gradient, the tangent, to create a “dual tensor”, which is used to compute forward AD gradients. The result is a new tensor aliased to tensor with tangent embedded as an attribute as-is if it has the same storage layout or copied otherwise. The tangent attribute can be recovered with unpack_dual().

This function is backward differentiable.

Given a function f whose jacobian is J, it allows one to compute the Jacobian-vector product (jvp) between J and a given vector v as follows.

Example:

>>> with dual_level():
...   inp = make_dual(x, v)
...   out = f(inp)
...   y, jvp = unpack_dual(out)


Please see the forward-mode AD tutorial for detailed steps on how to use this API.