linalg

A Python module implemented in C++ to perform linear algebra calculations.

Quickstart

Configure the provided CMakeLists.txt and build the module:

cmake -S . -B build
cmake --build build

The shared object file will be available in the root directory and can be imported directly in to Python.

Overview

The principle object in linalg is Matrix. It is constructed by passing a Python list of uniform length lists, and is stored C-contiguously.

import linalg
a = linalg.Matrix([[1,3,8],[7,11,12],[1,2,3]])

linalg supports a number of useful matrix operations, as exemplified here:

import linalg

a = linalg.Matrix([[1,3,8],[7,11,12],[1,2,3]])
b = linalg.Matrix([[5,7,56],[12,8,14],[4,5,6]])

print(a)
'''
Matrix([
    [1,  3,  8],
    [7, 11, 12],
    [1,  2,  3]
])
'''

print(a[1,2])
'''
12.0
'''

print(a + b)
'''
Matrix([
    [ 6, 10, 64],
    [19, 19, 26],
    [ 5,  7,  9]
])
'''

print(a - b)
'''
Matrix([
    [-4, -4, -48],
    [-5,  3,  -2],
    [-3, -3,  -3]
])
'''

c = a @ b

print(c)
'''
Matrix([
    [ 73,  71, 146],
    [215, 197, 618],
    [ 41,  38, 102]
])
'''

c.echelon_form()

print(c)
'''
Matrix([
    [73,    71,  146],
    [ 0, -12.1,  188],
    [ 0,     0, -9.1]
])
'''

print(c.det())
'''
8076.009765625
'''

Example

Matrix taking a list of lists for its constructor allows it to be easily interoperable with numpy.

import time
import linalg
import numpy as np

a = np.random.rand(10,10)
b = np.random.rand(10,10)

a = linalg.Matrix(a.tolist())
b = linalg.Matrix(b.tolist())

start = time.time()

c = a @ b

d = (c @ a) @ b

print(d)
'''
Matrix([
    [ 76.8, 64.2,   57, 59.7, 59.6,  64.4, 46.3,  69.4,  64.4,  65.3],
    [123.8,  103,   92, 96.4, 96.2, 103.1, 74.6, 112.1, 103.1, 104.3],
    [ 90.5, 75.8, 67.3, 70.7, 70.2,  75.8, 54.2,  81.8,  75.5,  76.8],
    [ 92.8, 77.1, 68.8,   72,   72,  77.4, 55.9,  83.9,  77.8,  78.3],
    [105.5,   88, 78.2,   82, 81.8,  88.1, 63.6,  95.4,  88.2,  89.4],
    [110.1, 92.4, 81.8, 85.8, 85.3,  92.4, 66.5,  99.7,  91.7,  93.9],
    [ 84.3, 70.2, 62.2, 65.6, 65.3,    70, 51.2,  76.3,  69.6,  71.1],
    [ 92.3, 76.7, 68.2, 71.6, 71.7,  77.1, 56.1,  83.5,  76.8,  78.2],
    [ 94.6, 79.1, 70.2, 73.5, 73.3,  79.2, 56.9,  85.5,  79.2,  80.4],
    [ 83.1, 69.4, 61.8, 64.6, 64.4,  69.5, 49.8,  75.1,  69.7,  70.5]
])
'''

print(d.det())
'''
9.80322162862115e-07 

Matrix has no inverse
'''

elapsed_time = time.time() - start


print("Elapsed time: %.6f seconds" % elapsed_time)
'''
Elapsed time: 0.000061 seconds
'''