Differentiable finite difference tools in jax
pip install FiniteDiffXInstall development version
pip install git+https://github.com/ASEM000/FiniteDiffXIf you find it useful to you, consider giving it a star! 🌟
import jax.numpy as jnp
import finitediffx as fdx
# lets first define a vector valued function F: R^3 -> R^3
# F = F1, F2
# F1 = x^2 + y^3
# F2 = x^4 + y^3
# F3 = 0
# F = [x**2 + y**3, x**4 + y**3, 0]
x, y, z = [jnp.linspace(0, 1, 100)] * 3
dx, dy, dz = x[1] - x[0], y[1] - y[0], z[1] - z[0]
X, Y, Z = jnp.meshgrid(x, y, z, indexing="ij")
F1 = X**2 + Y**3
F2 = X**4 + Y**3
F3 = jnp.zeros_like(F1)
F = jnp.stack([F1, F2, F3], axis=0)
# ∇.F : the divergence of F
divF = fdx.divergence(
F,
step_size=(dx, dy, dz),
keepdims=False,
accuracy=6,
method="central",
)jax.grad, jax.value_and_grad finite difference counterpart to be used on
unimplemented rules in jax or
on non-traceable numpy code
import jax
from jax import numpy as jnp
import numpy as onp # Not jax-traceable
import finitediffx as fdx
import functools as ft
from jax.experimental import enable_x64
with enable_x64():
@fdx.fgrad
@fdx.fgrad
def np_rosenbach2_fdx_style_1(x, y):
"""Compute the Rosenbach function for two variables in numpy."""
return onp.power(1-x, 2) + 100*onp.power(y-onp.power(x, 2), 2)
@ft.partial(fdx.fgrad, derivative=2)
def np2_rosenbach2_fdx_style2(x, y):
"""Compute the Rosenbach function for two variables."""
return onp.power(1-x, 2) + 100*onp.power(y-onp.power(x, 2), 2)
@jax.grad
@jax.grad
def jnp_rosenbach2(x, y):
"""Compute the Rosenbach function for two variables."""
return jnp.power(1-x, 2) + 100*jnp.power(y-jnp.power(x, 2), 2)
print(np_rosenbach2_fdx_style_1(1.,2.))
print(np2_rosenbach2_fdx_style2(1.,2.))
print(jnp_rosenbach2(1., 2.))
# 402.0000951997936
# 402.0000000002219
# 402.0