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# torch.func.jacfwd

torch.func.jacfwd(func, argnums=0, has_aux=False, *, randomness='error')

  Computes the Jacobian of `func` with respect to the arg(s) at index `argnum` using forward-mode autodiff

  Parameters:

    - func (function) – A Python function that takes one or more arguments, one of which must be a Tensor, and returns one or more Tensors

    - argnums (int or Tuple[int]) – Optional, integer or tuple of integers, saying which arguments to get the Jacobian with respect to. Default: 0.

    - has_aux (bool) – Flag indicating that `func` returns a `(output, aux)` tuple where the first element is the output of the function to be differentiated and the second element is auxiliary objects that will not be differentiated. Default: False.

    - randomness (str) – Flag indicating what type of randomness to use. See `vmap()` for more detail. Allowed: “different”, “same”, “error”. Default: “error”

  Returns:

    Returns a function that takes in the same inputs as `func` and returns the Jacobian of `func` with respect to the arg(s) at `argnums`. If `has_aux is True`, then the returned function instead returns a `(jacobian, aux)` tuple where `jacobian` is the Jacobian and `aux` is auxiliary objects returned by `func`.

  Note

  You may see this API error out with “forward-mode AD not implemented for operator X”. If so, please file a bug report and we will prioritize it. An alternative is to use `jacrev()`, which has better operator coverage.

  A basic usage with a pointwise, unary operation will give a diagonal array as the Jacobian

      >>> from torch.func import jacfwd
      >>> x = torch.randn(5)
      >>> jacobian = jacfwd(torch.sin)(x)
      >>> expected = torch.diag(torch.cos(x))
      >>> assert torch.allclose(jacobian, expected)

  `jacfwd()` can be composed with vmap to produce batched Jacobians:

      >>> from torch.func import jacfwd, vmap
      >>> x = torch.randn(64, 5)
      >>> jacobian = vmap(jacfwd(torch.sin))(x)
      >>> assert jacobian.shape == (64, 5, 5)

  If you would like to compute the output of the function as well as the jacobian of the function, use the `has_aux` flag to return the output as an auxiliary object:

      >>> from torch.func import jacfwd
      >>> x = torch.randn(5)
      >>>
      >>> def f(x):
      >>>   return x.sin()
      >>>
      >>> def g(x):
      >>>   result = f(x)
      >>>   return result, result
      >>>
      >>> jacobian_f, f_x = jacfwd(g, has_aux=True)(x)
      >>> assert torch.allclose(f_x, f(x))

  Additionally, `jacrev()` can be composed with itself or `jacrev()` to produce Hessians

      >>> from torch.func import jacfwd, jacrev
      >>> def f(x):
      >>>   return x.sin().sum()
      >>>
      >>> x = torch.randn(5)
      >>> hessian = jacfwd(jacrev(f))(x)
      >>> assert torch.allclose(hessian, torch.diag(-x.sin()))

  By default, `jacfwd()` computes the Jacobian with respect to the first input. However, it can compute the Jacboian with respect to a different argument by using `argnums`:

      >>> from torch.func import jacfwd
      >>> def f(x, y):
      >>>   return x + y ** 2
      >>>
      >>> x, y = torch.randn(5), torch.randn(5)
      >>> jacobian = jacfwd(f, argnums=1)(x, y)
      >>> expected = torch.diag(2 * y)
      >>> assert torch.allclose(jacobian, expected)

  Additionally, passing a tuple to `argnums` will compute the Jacobian with respect to multiple arguments

      >>> from torch.func import jacfwd
      >>> def f(x, y):
      >>>   return x + y ** 2
      >>>
      >>> x, y = torch.randn(5), torch.randn(5)
      >>> jacobian = jacfwd(f, argnums=(0, 1))(x, y)
      >>> expectedX = torch.diag(torch.ones_like(x))
      >>> expectedY = torch.diag(2 * y)
      >>> assert torch.allclose(jacobian[0], expectedX)
      >>> assert torch.allclose(jacobian[1], expectedY)

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