Mixed partial derivatives

[Andreas Dutzler]

For a given function

$$f = f(x, y)$$

try to implement

$$∂(∂f / ∂x) / ∂y$$

[Andreas Dutzler]

I fear that with the current concept this is only possible by combining the unknowns, evaluate the hessian and split the result.

[Andreas Dutzler]

This is possible via manual scripting. It is realized by deactivating one dual component per variable.

import numpy as np

import tensortrax as tr
import tensortrax.math as tm

x = (np.eye(3).ravel() + np.arange(9)).reshape(3, 3)
y = (np.eye(3).ravel() + np.arange(10, 19)).reshape(3, 3)

fun = lambda x, y: tm.trace(x) * tm.linalg.det(y)

r = tr.Tensor(x)
r.init(hessian=True, Δx=False)

s = tr.Tensor(y)
s.init(hessian=True, δx=False)

f = fun(r, s)
dfdxdy = tr.Δδ(f)

Dfdxdy = np.einsum(
    "ij...,kl...->ijkl...", np.eye(3), np.linalg.det(y) * np.linalg.inv(y).T
)

assert np.allclose(dfdxdy, Dfdxdy)