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linear-algebra

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About

This project builds on SymPy's Matrix class and is designed for students taking NUS MA1522 Linear Algebra for Computing. It has implementations of most of the algorithms taught during the course (as of Sem 1 AY24/25). Documentation of the code is still a work in progress.

Key Features

  1. Import matrices from \(\rm\LaTeX\) directly. \(\rm\LaTeX\) expression can be obtained from Canvas by right-clicking on the equations.
  2. Step-by-step workings for most algorithms (including LU Factorisation and SVD)

Installation and Usage

Installation

Prerequisites

This project is best supported in a Jupyter Notebook environment with Python 3.10+. You can download Python from here.

Install Dependencies

It is recommended to use a virtual environment for managing dependencies.

  1. Create a virtual environment:

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    python -m venv venv

  2. Activate the virtual environment:

    • On Windows:
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      venv\Scripts\activate
    • On macOS/Linux:
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      source venv/bin/activate

  3. Install the library:

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    pip install ma1522-linear-algebra
    It is recommended to use a Jupyter Notebook environment to run the code.
    Bash
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    pip install notebook

Usage

Create a Jupyter Notebook test.ipynb. Within the notebook, run the following code.

Python
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from ma1522 import *

# Create Matrix objects
A = Matrix([[1, 2, 3],
            [4, 5, 5],
            [7, 8, 9]])

b = Matrix([[1], 
            [2], 
            [3]])

# Join matrices along the columns via `row_join`. 
augmented_matrix = A.aug_line().row_join(b)

# `aug_line` adds a visual line that can be seen using `display`
display(augmented_matrix)

# Solution to the matrix equation Ax = b can be found using `solve`.
A.solve(rhs=b)

# Alternatively, the full steps with LU Factorisation can be found using `ref` with the appropriate options.
augmented_matrix.ref(verbosity=2)

Documentation of more functions can be found here.

More usage examples can be found under tutorials.

Live demonstration of the library can be found here.

FAQ

Development

Work in Progress

  • [ ] Better ref algorithm to determine boundary conditions for a given matrix.

Credits

I would like to thank @DenseLance for his contributions.