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48 lines
2.0 KiB
Python
48 lines
2.0 KiB
Python
from __future__ import annotations
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from decimal import Decimal
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def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
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"""
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A matrix multiplied with its inverse gives the identity matrix.
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This function finds the inverse of a 2x2 matrix.
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If the determinant of a matrix is 0, its inverse does not exist.
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Sources for fixing inaccurate float arithmetic:
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https://stackoverflow.com/questions/6563058/how-do-i-use-accurate-float-arithmetic-in-python
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https://docs.python.org/3/library/decimal.html
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>>> inverse_of_matrix([[2, 5], [2, 0]])
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[[0.0, 0.5], [0.2, -0.2]]
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>>> inverse_of_matrix([[2.5, 5], [1, 2]])
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Traceback (most recent call last):
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...
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ValueError: This matrix has no inverse.
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>>> inverse_of_matrix([[12, -16], [-9, 0]])
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[[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]]
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>>> inverse_of_matrix([[12, 3], [16, 8]])
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[[0.16666666666666666, -0.0625], [-0.3333333333333333, 0.25]]
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>>> inverse_of_matrix([[10, 5], [3, 2.5]])
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[[0.25, -0.5], [-0.3, 1.0]]
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"""
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D = Decimal # An abbreviation for conciseness
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# Check if the provided matrix has 2 rows and 2 columns, since this implementation only works for 2x2 matrices
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if len(matrix) != 2 or len(matrix[0]) != 2 or len(matrix[1]) != 2:
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raise ValueError("Please provide a matrix of size 2x2.")
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# Calculate the determinant of the matrix
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determinant = D(matrix[0][0]) * D(matrix[1][1]) - D(matrix[1][0]) * D(matrix[0][1])
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if determinant == 0:
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raise ValueError("This matrix has no inverse.")
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# Creates a copy of the matrix with swapped positions of the elements
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swapped_matrix = [[0.0, 0.0], [0.0, 0.0]]
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swapped_matrix[0][0], swapped_matrix[1][1] = matrix[1][1], matrix[0][0]
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swapped_matrix[1][0], swapped_matrix[0][1] = -matrix[1][0], -matrix[0][1]
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# Calculate the inverse of the matrix
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return [[float(D(n) / determinant) or 0.0 for n in row] for row in swapped_matrix]
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