Auto_DIff

This is the repo for SI211 Numeral Analysis in ShanghaiTech University mainly implementing automatic differentiation

description

This project contains four main modules.

• The ForwardDiff implements the forward mode of AD.
• The BackwardDiff implements the backward mode of AD.
• The ADDiff combines the forward mode and backward mode, and therefore, there are many unnecessary operations. Please use the single module if you do not need to obtain the results of the two methods at the same time.
• The Numerical_diff implements numerical difference with five points formula.

So far, only the combination of the atom operations +,−,∗,/,sin,cos are supported.

For more details, please refer to report.pdf.

performance

the time-consuming comparisons are:

method	time(s)
df	0.067
ADforward	63.538
ADbackward	0.286
Numerical diff	64.777

the accuracy comparisons are:

$$ acc_i = ||res_i − res_{df}||_2^2 $$

method	acc
ADforward	1.561 × 10−17
ADbackward	1.557 × 10−17
Numerical diff	1.775 × 10−11

the results can be reproduced by the scripts in folder script.