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' 2f64-0.26703531187166946f64jvp 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(-0.7651474012342926f64, -0.2248450953661529f64)