jax中的高阶多元导数

Question

I am confused about how to compute higher-order multivariate derivatives in jax.

For example, how do you compute d^2f / dx dy for

def f(x, y):
     return jnp.sin(jnp.dot(x, y.T))

where x, y in R^n, n >= 1?

I've been experimenting with jax.jvp and jax.partial , but I haven't had any success.

Answer 1

Since x and y are vector-valued and f(x, y) is a scalar, I believe you can compute what you're after by combining the jax.jacfwd and jax.jacrev functions with appropriate argnums:

import jax.numpy as jnp
from jax import jacfwd, jacrev

def f(x, y):
     return jnp.sin(jnp.dot(x, y.T))

d2f_dxdy = jacfwd(jacrev(f, argnums=1), argnums=0)
  
x = jnp.arange(4.0)
y = jnp.ones(4)

print(d2f_dxdy(x, y))

# DeviceArray([[0.96017027, 0.        , 0.        , 0.        ],
#              [0.2794155 , 1.2395858 , 0.2794155 , 0.2794155 ],
#              [0.558831  , 0.558831  , 1.5190012 , 0.558831  ],
#              [0.83824646, 0.83824646, 0.83824646, 1.7984167 ]],
#             dtype=float32)