ltricot / automatic-differentiation

Differentiate and simplify computation graphs.

Automatic Differentiation

This is a differentiation algorithm created by Loan Tricot and Simon Dupouy in Python 3.

differentiate.py differentiates any expression.
simplify.py does very basic simplifications. It is used to simplify a bit the differentiated expressions.

differentiation

This algorithm views an expression as a tree. Each leaf-node is a number or a variable (x), and all the other nodes are values resulting of the basic operation (+-/*) made on each of their two sub-nodes.
For example:

simplification

The algorithm takes a tree defined by its first node. It then recursively browses the tree by exploring separately the left and the right sub-tree each time. The algorithm for the moment makes the following simplifications:

• x + 0 = x
• a + b = a+b (calculation)
• x * 0 = 0
• x * 1 = x
• a * b = ab (calculation)
• 0 / x = 0
• x / 1 = x
• x / x = 1

This program will be extended to develop and further simplify expressions, as well as work with power notations (x^a).
We will also try to implement it using regular expressions (RegExp).