PieGrad

a python implementation of autograd. it automatically differentiates arbitrary functions written in python.

example

suppose we have function f and want to find its gradient f_prime.

from PieGrad import grad

def f(x):
	return 2*(x**3) + 1

f_prime = grad(f)  # return gradient of 6 * x ** 2
f_prime(2)  # prints 24

how dey do dat?

piegrad does something called "source code transformation". by applying a specific set of rules (eg decrement exponent by 1 and multiply coefficent by exponent), piegrad converts f's' ast to an ast corresponding to its gradient.

starting from root, we recursively traverse the ast with a dfs.

any node that is not a leaf is a binary operation (ast.binop). every ast.binop can be described with (left, op, right), where left refers to the left node, op refers to operation (eg ast.Add or ast.Pow), and right refers to the right child). each child can be a leaf or another ast.binop.

we traverse until we hit a leaf (ie not a ast.BinOp). how a leaf is evaluated depends on two factors: what is its type (eg is it a ast.Num? or is it ast.Name?) and what is its parent's type (eg is its parent node a ast.Pow?).