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) -0.61430776 >>> print(ybar) -0.2524413
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