Forward-mode automatic differentiation
The built-in jvp function computes the product of a seed vector
and the
Jacobian
of a function at some point. This can be used to compute
derivatives of functions.
def f x = f64.sqrt (x) * f64.sin (x)
def f' x = jvp f x 1> f' 2f64-0.26703531187166946jvp corresponds to differentiation by forward
accumulation,
and is most efficient for functions that have more outputs than
inputs. For a function with multiple inputs, you need multiple
applications of f' to compute the full derivative, each with a
one-hot seed vector:
def g (x, y) = f64.cos (x) * f64.sin (y)
def g' x y = (jvp g (x, y) (1, 0), jvp g (x, y) (0, 1))> g' 1f64 2f64(-0.7651474012342926,
-0.2248450953661529)