A package for Python that lets you create and perform various operations on Matrices sucjh as finding the adjoint, inverse, determinant of a matrix, etc..
Project description
Features
Addition, Multiplication, Division, Subraction operations supported between matrices and between a matrix and a int / float
Calculates:
Determinant
Inverse
Cofactor of a given element in the Matrix
Adjoint
Getting started
Creating a Matrix
To create a matrix, specify the order of the Matrix (mxn) where the first argument (m) is the number of rows in the matrix and the second argument (n) is the number of columns
We can use a nested list to represent a Matrix during initialization of an object In a nested list, the length of the outer list would be ‘m’ and the number of elements the inner lists have would be ‘n’
from matrix import Matrix
matrix_list = [
[1, 2, 3],
[4, 5, 6],
[7, 8, 9]
]
matrix1 = Matrix(3, 3, matrix_list)
print(matrix1)
#Prints:
# [ 1, 2, 3
# 4, 5, 6
# 7, 8, 9 ]
Operations on Matrices
Addition and Subraction
We can add and subract matrices extremely easily:
matrix_list2 = [
[0, 1, 3],
[5, 2, 7],
[7, 1, 9]
]
matrix2 = Matrix(3, 3, matrix_list2)
matrix3 = matrix1 + matrix2
print(matrix3)
#Prints:
# [ 1, 3, 6
# 9, 7, 13
# 14, 9, 18 ]
Adding an int / float to a matrix will perform the operation on all elements of the matrix and return a new matrix
matrix4 = matrix1 + 5
print(matrix4)
#Prints:
# [ 6, 7, 8
# 9, 10, 11
# 12, 13, 14 ]
# Same way,
print(matrix4 - matrix1)
# [ 5, 5, 5
# 5, 5, 5
# 5, 5, 5 ]
print(matrix1 - 3)
#Prints:
# [ -2, -1, 0
# 1, 2, 3
# 4, 5, 6 ]
Multiplication and Division
Matrix multiplication can only be implemented if the number of columns in the first matrix is equal to the number of rows in the other matrix. Basically: A m x n Matrix can only be multiplied with a n x l Matrix .
The order of the resultant Matrix will be m x l
Example:
# m x n * n x l : Gives m x l
# 2 x 3 * 3 x 2 : Gives 2 x 2
# 2 x 3 * 4 x 2 : Cannot mutliply
Internally, division is calculated by multiplying a matrix and the inverse of the other matrix therefore the same condition applies for division
print(matrix1 * 5)
# [ 5, 10, 15
# 20, 25, 30
# 35, 40, 45 ]
print(matrix1 * matrix2)
# [ 31, 8, 44
# 67, 20, 101
# 103, 32, 44 ]
Comparing matrices
Matrix == Matrix | 0 -> bool
Matrices can be compared for equality to another matrix Zero is used as an alias for a zero matrix
Functionalities
mathmatrix provides many functionalities for matrices out of the box:
Let’s create a sample matrix matrix to perform the operations on
from mathmatrix import Matrix
matrix = Matrix(3,3,[[1,2,3],[4,5,6],[7,8,9]])
Transposing a matrix
Matrix.transpose() -> Matrix
After creating a matrix, you can transpose a Matrix using the transpose() method of Matrix
print(matrix.transpose())
# [ 1, 4, 7
# 2, 5, 8
# 3, 6, 7 ]
Adjoint of a Matrix
Matrix.adjoint() -> Matrix
Adjoint of a matrix is calculated as the transpose of cofactor matrix of a Matrix It can be calculated using the adjoint() method
print(matrix.adjoint())
# [ -3, 6, -3
# 6, -12, 6
# -3, 6, -3 ]
Determinant of a Matrix
Matrix.determinant() -> int | float
print(matrix.determinant())
# 0
Inverse of a Matrix
Matrix.inverse() -> Matrix
Inverse of a matrix only exists for non-singular matrices ( Determinant of the Matrix should not be zero )
print(matrix.determinant())
# 0
# Since determinant is zero, if we try to calculate Inverse it will throw the error:
# ZeroDivisionError: Determinant of Matrix is zero, inverse of the matrix does not exist
Cofactor of an element
Matrix.cofactor(m:int, n:int) -> int | float
Specify the position of the desired element in row number (m) and column number (n) to calculate it’s corresponding cofactor
Chaining functions
Since functions return a new Matrix, you can chain many functions to get the desired output For example:
matrix.transpose().adjoint().determinant()
(matrix.determinant() * matrix.adjoint()).transpose()
are all completely valid
Additional Functions
Generating a zero matrix
gen_zero_matrix(m:int, n:int) -> Matrix
You can use the gen_zero_matrix function to create a zero matrix of a given order For example,
from mathmatrix import gen_zero_matrix, Matrix
zero3 = gen_zero_matrix(3,3)
print(zero3)
# [ 0, 0, 0
# 0, 0, 0
# 0, 0, 0 ]
print(zero3 == 0)
# True
Generating an identity matrix
gen_zero_matrix(m:int, n:int) -> Matrix
You can use the gen_zero_matrix function to create a zero matrix of a given order For example,
from mathmatrix import gen_zero_matrix, Matrix
zero3 = gen_zero_matrix(3,3)
print(zero3)
# [ 0, 0, 0
# 0, 0, 0
# 0, 0, 0 ]
print(zero3 == 0)
# True
Note: For any Matrix matrix,
print(matrix * matrix.inverse() == gen_identity_matrix(matrix.m, matrix.n))
# Always true (Inverse cannot be calculated for singular matrices so error is thrown in that case)
print((matrix - matrix) == gen_zero_matrix(matrix.m,matrix.n))
# Always true
Project details
Release history Release notifications | RSS feed
Download files
Download the file for your platform. If you're not sure which to choose, learn more about installing packages.
Source Distribution
Built Distribution
File details
Details for the file mathmatrix-0.5.tar.gz
.
File metadata
- Download URL: mathmatrix-0.5.tar.gz
- Upload date:
- Size: 7.5 kB
- Tags: Source
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/3.7.0 importlib_metadata/4.8.2 pkginfo/1.8.2 requests/2.22.0 requests-toolbelt/0.9.1 tqdm/4.62.3 CPython/3.8.10
File hashes
Algorithm | Hash digest | |
---|---|---|
SHA256 | 0ff619da04f745cd8059e1028f2e1b19c9122a023c41fc6eb0bac0699e54a796 |
|
MD5 | fa7dbc74fc447b146a55dffde2a8a0fd |
|
BLAKE2b-256 | e9893bd97980f8bdcf8803243a21a46d41559d9670e67e3dc1b0b515d014be08 |
File details
Details for the file mathmatrix-0.5-py3-none-any.whl
.
File metadata
- Download URL: mathmatrix-0.5-py3-none-any.whl
- Upload date:
- Size: 6.7 kB
- Tags: Python 3
- Uploaded using Trusted Publishing? No
- Uploaded via: twine/3.7.0 importlib_metadata/4.8.2 pkginfo/1.8.2 requests/2.22.0 requests-toolbelt/0.9.1 tqdm/4.62.3 CPython/3.8.10
File hashes
Algorithm | Hash digest | |
---|---|---|
SHA256 | d0ba8f7397b48c6b7d25898f93acfed8c14d0501a459462d2881c848a4c9eef4 |
|
MD5 | c7295fd406bbc59c0c290daf56ac2e8e |
|
BLAKE2b-256 | 22953fdb8cd069f1683a9a09796ca1df8091330c3f495e2a678463acb8c49b41 |