jax.vjp(fun: Callable[[...], T], *primals: Any, has_aux: Literal[False] = False, reduce_axes: Sequence[Hashable] = ()) tuple[T, Callable][source]#
jax.vjp(fun: Callable[[...], tuple[T, U]], *primals: Any, has_aux: Literal[True], reduce_axes: Sequence[Hashable] = ()) tuple[T, Callable, U]

Compute a (reverse-mode) vector-Jacobian product of fun.

grad() is implemented as a special case of vjp().

  • fun – Function to be differentiated. Its arguments should be arrays, scalars, or standard Python containers of arrays or scalars. It should return an array, scalar, or standard Python container of arrays or scalars.

  • primals – A sequence of primal values at which the Jacobian of fun should be evaluated. The number of primals should be equal to the number of positional parameters of fun. Each primal value should be an array, a scalar, or a pytree (standard Python containers) thereof.

  • has_aux – Optional, bool. Indicates whether fun returns a pair where the first element is considered the output of the mathematical function to be differentiated and the second element is auxiliary data. Default False.


If has_aux is False, returns a (primals_out, vjpfun) pair, where primals_out is fun(*primals). If has_aux is True, returns a (primals_out, vjpfun, aux) tuple where aux is the auxiliary data returned by fun.

vjpfun is a function from a cotangent vector with the same shape as primals_out to a tuple of cotangent vectors with the same number and shapes as primals, representing the vector-Jacobian product of fun evaluated at primals.

>>> import jax
>>> def f(x, y):
...   return jax.numpy.sin(x), jax.numpy.cos(y)
>>> primals, f_vjp = jax.vjp(f, 0.5, 1.0)
>>> xbar, ybar = f_vjp((-0.7, 0.3))
>>> print(xbar)
>>> print(ybar)