Matrix Determinant Calculator

Python module to calculate matrix and minor-matrix determinants from NumPy arrays.

This project is for exploration purposes only. Same results, but much faster can be achieved by using sympy.Matrix.det()

Main goal

The module is intended to allow as-generic-as-posible determinant calculation, that does not rely on specific data-type. NumPy arrays of any dtype can be used as the source matrix.

The source ndarray.dtype objects should only support product (*) operation, sum() and negative() are optional. This includes generic Python objects, like:

• Fractions
• Decimals
• Numbers - numeric abstract classes
• NumPy polynomials
• Python integers PEP 237 - limited by available memory

Installation

The module can be installed from the GitHub repo:

pip install "git+https://github.com/trundev/numpy-determinant.git@main"

Usage

The main numpy_determinant.det() can be used just like the numpy.linalg.det():

>>> import numpy as np
>>> import numpy_determinant

>>> a = np.arange(9).reshape(3, 3)  # Some linearly dependent data
>>> a += a != 0         # Increase all elements, but the first one
>>> a
array([[0, 2, 3],
       [4, 5, 6],
       [7, 8, 9]])
>>> numpy_determinant.det(a)
3

Use Python unbounded integer objects:

>>> a = a.astype(object)    # Convert to unbounded integer objects
>>> a += 10**50             # Increase all elements by a huge number
array([[100000000000000000000000000000000000000000000000000,
        100000000000000000000000000000000000000000000000002,
        100000000000000000000000000000000000000000000000003],
       [100000000000000000000000000000000000000000000000004,
        100000000000000000000000000000000000000000000000005,
        100000000000000000000000000000000000000000000000006],
       [100000000000000000000000000000000000000000000000007,
        100000000000000000000000000000000000000000000000008,
        100000000000000000000000000000000000000000000000009]],
      dtype=object)
>>> numpy_determinant.det(a)
3

Compare to numpy and sympy

>>> np.linalg.det(a.astype(float))  # Determinant via numpy needs float input
np.float64(0.0)      # Wrong result, after float conversion and loss of significance
>>> import sympy
>>> sympy.Matrix(a).det()
3                    # Correct result, as SymPy can handle arbitrarily large integers

See test folder for more examples