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Matrix Multiplication Algorithms with Python from scratch

Jaeho Kim kjh3690@unist.ac.kr

This is an implementation of matrix multiplication algorithm with python. The repository contains a report, code, and a jupyter file. All codes are in python

  1. Schoolbook Matrix multiplication
  2. Naive Divide and Conquer multiplication
  3. Strassen
  4. Strassen Optimized

Usage

To run the algorithm you should have a "input.txt" file in the directory where you are running the python scripts.

# Standard matrix multiplication
python schoolbook_multiplication.py
# Standard naive divide and conquer multiplication
python divide_and_conquer.py
# Standard Strassen 
python strassen_base.py
# Standard Strassen leaf size 4
python strassen_optimized_leaf4.py
# To compare everything and get time_comparison.csv
python all.py

There is also a Jupyter file to draw graphs.

Results

Time complexity for algorithms Time complexity for Strassens

Acknowledgement

It took me so long to figure out why Strassen takes longer implementation time than standard matrix multiplication even though it has a lower algorithm complexity. To answer this check stackoverflow.

Another article you can check out is here

For those who are just to lazy to check out, here is a simple answer. Our standard Strassen makes a recursive call until n equals to 1. This increases the constant time which in theory shouldn't be a problem. But you know, this isn't theory. Its real shiit! So it does matter in reality. We can opimize the time by calling the recusive call until n equals to 2,4,8 ~. Hope someone finds this useful.If I got it wrong please leave a comment on issue! would love to know

Please press star if this was helpful. Thank you

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