matrixObj 1.1.2

A simple matrix module for basic matrix mathematical operations

matrixObj

A small simple matrix module for basic mathematical matrix operations. Create and make us of Matrix objects in your python codes, perform operations like Matrix Addition, Subtration, Multiplication and Scalar Division and other operations like (transpose, co-factor, inverse, minor, determinant, adjoint and elementary operation).

Installation

pip install matrixObj

Project Demo

from matrixObj import Matrix

You can create a new Matrix instance with any of the python number objects (int, float, complex and Fraction) eg.

matA = Matrix([5, 3, -1], [3, 5, 9], [0, 5, 2])

matB = Matrix([3.0, 4.5], [2.6, 5.2])

cmplxMat = Matrix([1+2j, 2+1j], [4-4j, 1-2j])

print(matA)
print(matB)
print(cmplxMat)

Output:
| 5      3      -1|
| 3      5       9|
| 0      5       2|

|3.0    4.5|
|2.6    5.2|

|(1+2j) (2+1j)|
|(4-4j) (1-2j)|

with Fraction object, you will have to import it from the fractions module

from fractions import Fraction

fracMat = Matrix([Fraction(1,3), Fraction(2,5)], [Fraction(1,2), Fraction(3,27)])

print(fracMat)

output:

|1/3    2/5|
|1/2    1/9|

Matrix Arithmetic Operations

A = Matrix([1, -3, 3], [4, 0, 2])
B = Matrix([4, 6, 0], [3, 0, 5])
C = Matrix([3, -2], [0, 4], [-1, 5])
D = Matrix([1, -3, 3], [4, 0, 2])

sumAB = A + B
productAC = A * C

print(sumAB)
print(productAC)
print(A == D)           # Matrix Equality

Output:
|5      3       3|
|7      0       7|

| 0      1|
|10      2|

True

Square Matrix Operations

matrixA = Matrix([1, 0, 4], [5, 2, 1], [1, 1, 1])

print(matrixA.determinant())    # The determinant of the matrix

print(matrixA.minor())          # The minor of the matrix

print(matrixA.cofactor())       # The Cofactor of the matrix

print(matrixA.inverse(infraction=True)) # Inverse of the matrix returned as a matrix of Fraction object

Output:
13

|  1      4       3|
| -4     -3       1|
| -8    -19       2|

| 1     -4       3|
| 4     -3      -1|
|-8     19       2|

| 1/13   4/13   -8/13|
|-4/13  -3/13   19/13|
| 3/13  -1/13    2/13|

Elementary Operations

mat = Matrix([3, 0, 1], [0, 2, 3], [5, -3, -1])

# Elementary Row operation
print(mat.elementary_operation(2, 3))           # Interchange row 2 and 3

print(mat.elementary_operation(1, scalar=2))    # Multiply row 1 by 2

print(mat.elementary_operation(1, 3, scalar=2)) # Multiply row 3 by 2, add the result to row 1

Output:
| 3      0       1|
| 5     -3      -1|
| 0      2       3|

| 6      0       2|
| 0      2       3|
| 5     -3      -1|

|13     -6      -1|
| 0      2       3|
| 5     -3      -1|

For Elementary column Operation set argument row=False eg.

# Elementary Column operation

print(mat.elementary_operation(2, 3, row=False))           # Interchanges column 2 and 3

| 3      1       0|
| 0      3       2|
| 5     -1      -3|

Modifying the Matrix

After initialization of a Matrix object, you can change, insert new and expand the rows/columns in the matrix eg.

mat = Matrix([1, 0, 2], [3, 1, 0])

mat.setrow(1, [5, -3, 2])       # Changes row 1 to [5, -3, 2]
mat.insertrow(2, [3, -3, 1])    # Inserts [3, -3, 1] in the second row
mat.expandrow([2, 5, 5])        # Appends row [2, 5, 5] to the matrix
mat.expandcolumn([4, 5, -4, 0]) # Appends column [4, 5, -4, 0]

print(mat)      # With all the modifications we should now have a 4x4 matrix

Output:
| 5     -3       2       4|
| 3     -3       1       5|
| 3      1       0      -4|
| 2      5       5       0|

Modifying by Slicing

Get, set or delete part/slice of the matrix. eg.

# Getting part/slice of the matrix
matA = Matrix([2, 5, -4], [4, 5, 9], [-1, -8, 0], [7, 0, 5])

print(matA[1, 0])           # Gets first element in the second row 

print(matA[2])              # Gets the third row of the matrix

print(matA[:, -1])          # Gets the last column of the matrix 

print(matA[0:3])            # Gets the first, the second and the third row

print(matA[-1::-1, -1::-1]) # Gets the reverse of the matrix rows with each row also reversed

Output:
4

|-1    -8     0|

|-4     9     0     5|

| 2     5    -4|
| 4     5     9|
|-1    -8     0|

| 5     0     7|
| 0    -8    -1|
| 9     5     4|
|-4     5     2|

# Setting part/slice of the matrix
matA[1] = [-20, 40, 10]     # sets the second row
print(matA)

matA[:, 0] = [1, 2, 3, 4]   # sets the first column
print(matA)

Output:

|  2      5     -4|
|-20     40     10|
| -1     -8      0|
|  7      0      5|

|  1      5     -4|
|  2     40     10|
|  3     -8      0|
|  4      0      5|

All elements in a slice can be set to the same scalar value eg.

matA[-1] = 4        # Sets all the elements in the last row to 4
print(matA)

from fractions import Fraction
matA[:] = Fraction(1, 3)    # Sets all elements in the matrix to 1/3
print(matA)

Output:
| 2     5    -4|
| 4     5     9|
|-1    -8     0|
| 4     4     4|

|1/3    1/3    1/3|
|1/3    1/3    1/3|
|1/3    1/3    1/3|
|1/3    1/3    1/3|

Using the del() function to delete some part of the matrix, this can only delete complete row(s) or column...

matA = Matrix([2, 5, -4], [4, 5, 9], [-1, -8, 0], [7, 0, 5])

del(matA[1])            # Deletes the second row
print(matA)

Output:

| 2     5    -4|
|-1    -8     0|
| 7     0     5|

del(matA[:, 0])         # Deletes the first column
print(matA)

Output:

| 5    -4|
| 5     9|
|-8     0|
| 0     5|

del(matA[1:-1]) # Deletes the second row up to the last row
print(matA)

Output:

| 2     5    -4|
| 7     0     5|

NOTE: Using the methods (insertrow(), insertcolumn(), expandrow(), removerow() etc.) to modify matrix take indexes from 1 instead of slicing which takes indexes from 0

String Representation

The String Representation of the Matrix object (as can be seen from the examples above). All elements (four H_whitespaced from each other and rightly justified) in each row of the matrix are arranged in between two pipe charater "|" but guess what? You can change the this representation to any other desired representation with setrepr() method. eg. If your loyalty is to python (^_^) and you prefer to have your matrix represented as python list...

# Declear a function that takes exactly one argument and returns a str
# This argument will be the tuple of the matrix rows
# which will be supplied by the matrix class when invoking the function

def newrepr(matrix):
    return str(list(matrix))

Matrix.setrepr(newrepr)

mat = Matrix([4, 5, -1], [0, 1, 3], [5, 2, 7])
print(mat)

Output:
[[4, 5, -1], [0, 1, 3], [5, 2, 7]]

You can do str manipulation on the matrix parameter in the body of your defined function and simply return the desired str representantion for your matrix objects. To change back to the defaul representation, use resetrepr()

Other Methods of the Matrix class

• tranpose(): returns the transpose of matrix
• zero_matrix(): generates a zero matrix
• ones_matrix(): generates a ones matrix
• random_matrix(): generates a matrix with random numbers
• generate_identity_matrix(): generates identity matrix

Boolean Methods

• issquare()
• symmetric()
• skew()
• invertible() etc.