MATLIB

MatLib is a little python 2D-matrix-handling library. The following documentation will guide you through!

Getting started:

pip install matlib

export n_digits=2 # precision: Optional[int], default is 3

Standard operations:

import matlib as ml

a = ml.Matrix([
    [1, 1],
    [1, 1],
    [1, 1],
    [1, 1]
])

b = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

print(a) # casting types

# [[1.00, 1.00]
#  [1.00, 1.00]
#  [1.00, 1.00]
#  [1.00, 1.00]]

print(a + b) # +, -, *, /, //, %

# [[3.00, 3.00]
#  [3.00, 3.00]
#  [3.00, 3.00]
#  [3.00, 3.00]]

print(a - 100) # +, -, *, /, //, %

# [[-99.00, -99.00]
#  [-99.00, -99.00]
#  [-99.00, -99.00]
#  [-99.00, -99.00]]

a *= 2.5 # inplace
print(a)

# [[2.50, 2.50]
#  [2.50, 2.50]
#  [2.50, 2.50]
#  [2.50, 2.50]]

Exponentiation:

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2]
])

print(a ** 3) # int

# [[32.00, 32.00]
#  [32.00, 32.00]]

Matrix multiplication:

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

b = ml.Matrix([
    [3, 3, 3, 3],
    [3, 3, 3, 3]
])

print(a @ b)

# [[12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]]

Transponing:

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

print(a.T)

# [[2.00, 2.00, 2.00, 2.00]
#  [2.00, 2.00, 2.00, 2.00]]

Getting the size:

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

print(a.size)

# (4, 2)

The functions:

1. Calculating the determinant of the matrix:

func: det(matrix: ml.Matrix) -> float

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2]
])

b = ml.det(a)
print(b)

# 0.0

2. Matrix multiplication:

func: mul(matrix_1: ml.Matrix, matrix_2: ml.Matrix ) -> ml.Matrix

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

b = ml.Matrix([
    [3, 3, 3, 3],
    [3, 3, 3, 3]
])

c = ml.mul(a, b)
print(c)

# [[12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]
#  [12.00, 12.00, 12.00, 12.00]]

3. Matrix exponentiation:

func: pow(matrix: ml.Matrix, exp: int = 1 ) -> ml.Matrix

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2]
])

b = ml.pow(a, 3)
print(b)

# [[32.00, 32.00]
#  [32.00, 32.00]]

4. Mqtrix transposing:

func: transpose(matrix: ml.Matrix) -> ml.Matrix

import matlib as ml

a = ml.Matrix([
    [2, 2],
    [2, 2],
    [2, 2],
    [2, 2]
])

b = transpose(a)
print(b)

# [[2.00, 2.00, 2.00, 2.00]
#  [2.00, 2.00, 2.00, 2.00]]

5. Least Squares method:

func: least_squares(matrix: ml.Matrix, matrix_ans: ml.Matrix ) -> ml.Matrix

Finds an approximate solution for a system of linear equations.

import matlib as ml

a = ml.Matrix([
    [1, 1],
    [2, 1],
    [1, 5],
    [4, 1]
])

b = ml.Matrix([    
    [1],
    [4],
    [3],
    [7]
])

c = ml.least_squares(a, b)
print(c)

# [[1.69]
#  [0.24]]

6. Gaussian Elimination method:

func: gaussian_elimination(matrix: ml.Matrix, matrix_ans: ml.Matrix ) -> ml.Matrix

Solves a system of linear equations using the Gaussian Elimination method. The program responds whether the answer to the system exists, does not exist or is an infinite amount of answers.

import matlib as ml

a = ml.Matrix([
    [3, 1, -2, 1],
    [2, 3, -1, 2],
    [1, -2, 2, -1],
    [1, 3, -1, 1]
    
])

b = ml.Matrix([
    [5],
    [4],
    [4],
    [0]
])

c = ml.gaussian_elimination(a, b)
print(c)

# [[ 2.00]
#  [-1.00]
#  [ 1.00]
#  [ 2.00]]

print(a @ c) # checking the answer

# [[5.00]
#  [4.00]
#  [4.00]
#  [0.00]]

a = ml.Matrix([
    [2, -4],
    [-3, 6],
])

b = ml.Matrix([
    [-1],
    [2]
])

c = gaussian_elimination(a, b)
print(c)

# System of equations cannot be solved
# [[]]