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improved implementation - all test passing now #6973

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64cef2e
Modified - Matrix/inverse_of_matrix.py - added implementation for inv…
kituuu Oct 10, 2022
5818223
[pre-commit.ci] auto fixes from pre-commit.com hooks
pre-commit-ci[bot] Oct 10, 2022
8afba69
Modified matrix/inverse_of_matrix.py all test passing now
kituuu Oct 11, 2022
3e9e2f1
Merge branch 'matrix3x3' of https://github.com/kituuu/Python into mat…
kituuu Oct 11, 2022
9f726f3
Improved docstring with more examples
kituuu Oct 11, 2022
89bfd24
Improved docstring
kituuu Oct 11, 2022
d2b54eb
deleted one example from docstring
kituuu Oct 11, 2022
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6 changes: 3 additions & 3 deletions .pre-commit-config.yaml
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Original file line number Diff line number Diff line change
Expand Up @@ -14,7 +14,7 @@ repos:
- id: requirements-txt-fixer

- repo: https://github.com/psf/black
rev: 22.8.0
rev: 22.10.0
hooks:
- id: black

Expand All @@ -26,7 +26,7 @@ repos:
- --profile=black

- repo: https://github.com/asottile/pyupgrade
rev: v2.38.2
rev: v3.0.0
hooks:
- id: pyupgrade
args:
Expand All @@ -42,7 +42,7 @@ repos:
- --max-line-length=88

- repo: https://github.com/pre-commit/mirrors-mypy
rev: v0.981
rev: v0.982
hooks:
- id: mypy
args:
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1 change: 1 addition & 0 deletions DIRECTORY.md
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Expand Up @@ -927,6 +927,7 @@
## Scheduling
* [First Come First Served](scheduling/first_come_first_served.py)
* [Highest Response Ratio Next](scheduling/highest_response_ratio_next.py)
* [Job Sequencing With Deadline](scheduling/job_sequencing_with_deadline.py)
* [Multi Level Feedback Queue](scheduling/multi_level_feedback_queue.py)
* [Non Preemptive Shortest Job First](scheduling/non_preemptive_shortest_job_first.py)
* [Round Robin](scheduling/round_robin.py)
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140 changes: 127 additions & 13 deletions matrix/inverse_of_matrix.py
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Expand Up @@ -6,13 +6,14 @@
def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
"""
A matrix multiplied with its inverse gives the identity matrix.
This function finds the inverse of a 2x2 matrix.
This function finds the inverse of a 2x2 and 3x3 matrix.
If the determinant of a matrix is 0, its inverse does not exist.

Sources for fixing inaccurate float arithmetic:
https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python
https://docs.python.org/3/library/decimal.html

Demo for 2x2
>>> inverse_of_matrix([[2, 5], [2, 0]])
[[0.0, 0.5], [0.2, -0.2]]
>>> inverse_of_matrix([[2.5, 5], [1, 2]])
Expand All @@ -25,24 +26,137 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
[[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]]
>>> inverse_of_matrix([[10, 5], [3, 2.5]])
[[0.25, -0.5], [-0.3, 1.0]]

Demo for 3x3
>>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]])
[[2.0, 1.0, -5.0], [5.0, 1.0, -12.0], [-4.0, -1.0, 10.0]]
>>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]])
Traceback (most recent call last):
...
ValueError: This matrix has no inverse.
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@cclauss cclauss Oct 11, 2022 •
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Please add some more doctests:

>>> inverse_of_matrix([])
>>> inverse_of_matrix([1])
>>> inverse_of_matrix([[], []])
>>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
>>> inverse_of_matrix([[1, 2, 3], [4, 5, 6]])

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Ok sir, I am adding

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Done sir


More examples:

>>> inverse_of_matrix([])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[],[]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2, 1], [0,3, 4]])
Traceback (most recent call last):
...
ValueError: Please provide a matrix of size 2x2 or 3x3.

>>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]])
Traceback (most recent call last):
...
ValueError: This matrix has no inverse.

>>> inverse_of_matrix([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
"""

D = Decimal # An abbreviation for conciseness

# Check if the provided matrix has 2 rows and 2 columns
# since this implementation only works for 2x2 matrices
if len(matrix) != 2 or len(matrix[0]) != 2 or len(matrix[1]) != 2:
raise ValueError("Please provide a matrix of size 2x2.")
if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
# Calculate the determinant of the matrix
determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D(
matrix[0][1]
)
if determinant == 0:
raise ValueError("This matrix has no inverse.")

# Creates a copy of the matrix with swapped positions of the elements
swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]

# Calculate the inverse of the matrix
return [
[float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix
]
elif (
len(matrix) == 3
and len(matrix[0]) == 3
and len(matrix[1]) == 3
and len(matrix[2]) == 3
):
# Calculate the determinant of the matrix using Sarrus rule
determinant = (
(D(matrix[0][0]) * D(matrix[1][1]) * D(matrix[2][2]))
+ (D(matrix[0][1]) * D(matrix[1][2]) * D(matrix[2][0]))
+ (D(matrix[0][2]) * D(matrix[1][0]) * D(matrix[2][1]))
) - (
(D(matrix[0][2]) * D(matrix[1][1]) * D(matrix[2][0]))
+ (D(matrix[0][1]) * D(matrix[1][0]) * D(matrix[2][2]))
+ (D(matrix[0][0]) * D(matrix[1][2]) * D(matrix[2][1]))
)
if determinant == 0:
raise ValueError("This matrix has no inverse.")

# Creating cofactor matrix
cofactor_matrix = [
[D(0.0), D(0.0), D(0.0)],
[D(0.0), D(0.0), D(0.0)],
[D(0.0), D(0.0), D(0.0)],
]
cofactor_matrix[0][0] = (D(matrix[1][1]) * D(matrix[2][2])) - (
D(matrix[1][2]) * D(matrix[2][1])
)
cofactor_matrix[0][1] = -(
(D(matrix[1][0]) * D(matrix[2][2])) - (D(matrix[1][2]) * D(matrix[2][0]))
)
cofactor_matrix[0][2] = (D(matrix[1][0]) * D(matrix[2][1])) - (
D(matrix[1][1]) * D(matrix[2][0])
)
cofactor_matrix[1][0] = -(
(D(matrix[0][1]) * D(matrix[2][2])) - (D(matrix[0][2]) * D(matrix[2][1]))
)
cofactor_matrix[1][1] = (D(matrix[0][0]) * D(matrix[2][2])) - (
D(matrix[0][2]) * D(matrix[2][0])
)
cofactor_matrix[1][2] = -(
(D(matrix[0][0]) * D(matrix[2][1])) - (D(matrix[0][1]) * D(matrix[2][0]))
)
cofactor_matrix[2][0] = (D(matrix[0][1]) * D(matrix[1][2])) - (
D(matrix[0][2]) * D(matrix[1][1])
)
cofactor_matrix[2][1] = -(
(D(matrix[0][0]) * D(matrix[1][2])) - (D(matrix[0][2]) * D(matrix[1][0]))
)
cofactor_matrix[2][2] = (D(matrix[0][0]) * D(matrix[1][1])) - (
D(matrix[0][1]) * D(matrix[1][0])
)

# Calculate the determinant of the matrix
determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D(matrix[0][1])
if determinant == 0:
raise ValueError("This matrix has no inverse.")
# Transpose the cofactor matrix (Adjoint matrix)
adjoint_matrix = [
[D(0.0), D(0.0), D(0.0)],
[D(0.0), D(0.0), D(0.0)],
[D(0.0), D(0.0), D(0.0)],
]
for i in range(3):
for j in range(3):
adjoint_matrix[i][j] = cofactor_matrix[j][i]

# Creates a copy of the matrix with swapped positions of the elements
swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
# Inverse of the matrix using the formula (1/determinant) * adjoint matrix
inverse_matrix = [[0.0, 0.0, 0.0], [0.0, 0.0, 0.0], [0.0, 0.0, 0.0]]
for i in range(3):
for j in range(3):
inverse_matrix[i][j] = float(adjoint_matrix[i][j]) / float(determinant)

# Calculate the inverse of the matrix
return [[float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix]
# Calculate the inverse of the matrix
return [[float(D(n)) or 0.0 for n in row] for row in inverse_matrix]
else:
raise ValueError("Please provide a matrix of size 2x2 or 3x3.")