patrick-kidger

"""A 1-dimensional example of adaptive mesh refinement in JAX. In this case, a simple
implementation of quadrature.

Static shapes don't mean you can't do this. Heap allocation is *not* necessary!

Not extensively tested; any bugs leave a comment below.
"""

import functools as ft
from collections.abc import Callable

RicardoDominguez

"""Boundary value problem solver."""

import jax
import jax.numpy as jnp


# ------------------------------------------------------------------------------------------
# Linear solver for bordered almost block diagonal (BABD) systems
# ------------------------------------------------------------------------------------------
# Implementation as described in [1] Section 2.1 (structural orthogonal factorization).

apaszke

import torch                                                                                          
                                                                                                      
def jacobian(y, x, create_graph=False):                                                               
    jac = []                                                                                          
    flat_y = y.reshape(-1)                                                                            
    grad_y = torch.zeros_like(flat_y)                                                                 
    for i in range(len(flat_y)):                                                                      
        grad_y[i] = 1.                                                                                
        grad_x, = torch.autograd.grad(flat_y, x, grad_y, retain_graph=True, create_graph=create_graph)
        jac.append(grad_x.reshape(x.shape))