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added support for inverse of 3x3 matrix (#7355)
* added support for inverse of 3x3 matrix * Modified Docstring and improved code * fixed an error * Modified docstring * Apply all suggestions from code review Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com> Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com> Co-authored-by: Christian Clauss <cclauss@me.com> Co-authored-by: Caeden Perelli-Harris <caedenperelliharris@gmail.com> Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com>
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Karthik Ayangar
GitHub
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9390565350
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@ -2,22 +2,25 @@ from __future__ import annotations
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from decimal import Decimal
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from numpy import array
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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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This function finds the inverse of a 2x2 and 3x3 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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Doctests for 2x2
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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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...
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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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@ -25,24 +28,128 @@ def inverse_of_matrix(matrix: list[list[float]]) -> list[list[float]]:
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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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Doctests for 3x3
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>>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]])
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[[2.0, 5.0, -4.0], [1.0, 1.0, -1.0], [-5.0, -12.0, 10.0]]
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>>> inverse_of_matrix([[1, 2, 2], [1, 2, 2], [3, 2, -1]])
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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([[],[]])
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Traceback (most recent call last):
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...
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ValueError: Please provide a matrix of size 2x2 or 3x3.
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>>> inverse_of_matrix([[1, 2], [3, 4], [5, 6]])
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Traceback (most recent call last):
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...
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ValueError: Please provide a matrix of size 2x2 or 3x3.
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>>> inverse_of_matrix([[1, 2, 1], [0,3, 4]])
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Traceback (most recent call last):
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...
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ValueError: Please provide a matrix of size 2x2 or 3x3.
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>>> inverse_of_matrix([[1, 2, 3], [7, 8, 9], [7, 8, 9]])
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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([[1, 0, 0], [0, 1, 0], [0, 0, 1]])
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[[1.0, 0.0, 0.0], [0.0, 1.0, 0.0], [0.0, 0.0, 1.0]]
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"""
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d = Decimal # An abbreviation for conciseness
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d = Decimal
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# Check if the provided matrix has 2 rows and 2 columns
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# 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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if len(matrix) == 2 and len(matrix[0]) == 2 and len(matrix[1]) == 2:
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# Calculate the determinant of the matrix
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determinant = float(
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d(matrix[0][0]) * d(matrix[1][1]) - d(matrix[1][0]) * d(matrix[0][1])
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)
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if determinant == 0:
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raise ValueError("This matrix has no inverse.")
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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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# 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 [
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[(float(d(n)) / determinant) or 0.0 for n in row] for row in swapped_matrix
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]
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elif (
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len(matrix) == 3
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and len(matrix[0]) == 3
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and len(matrix[1]) == 3
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and len(matrix[2]) == 3
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):
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# Calculate the determinant of the matrix using Sarrus rule
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determinant = float(
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(
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(d(matrix[0][0]) * d(matrix[1][1]) * d(matrix[2][2]))
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+ (d(matrix[0][1]) * d(matrix[1][2]) * d(matrix[2][0]))
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+ (d(matrix[0][2]) * d(matrix[1][0]) * d(matrix[2][1]))
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)
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- (
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(d(matrix[0][2]) * d(matrix[1][1]) * d(matrix[2][0]))
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+ (d(matrix[0][1]) * d(matrix[1][0]) * d(matrix[2][2]))
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+ (d(matrix[0][0]) * d(matrix[1][2]) * d(matrix[2][1]))
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)
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)
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if determinant == 0:
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raise ValueError("This matrix has no inverse.")
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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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# Creating cofactor matrix
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cofactor_matrix = [
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[d(0.0), d(0.0), d(0.0)],
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[d(0.0), d(0.0), d(0.0)],
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[d(0.0), d(0.0), d(0.0)],
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]
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cofactor_matrix[0][0] = (d(matrix[1][1]) * d(matrix[2][2])) - (
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d(matrix[1][2]) * d(matrix[2][1])
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)
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cofactor_matrix[0][1] = -(
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(d(matrix[1][0]) * d(matrix[2][2])) - (d(matrix[1][2]) * d(matrix[2][0]))
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)
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cofactor_matrix[0][2] = (d(matrix[1][0]) * d(matrix[2][1])) - (
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d(matrix[1][1]) * d(matrix[2][0])
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)
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cofactor_matrix[1][0] = -(
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(d(matrix[0][1]) * d(matrix[2][2])) - (d(matrix[0][2]) * d(matrix[2][1]))
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)
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cofactor_matrix[1][1] = (d(matrix[0][0]) * d(matrix[2][2])) - (
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d(matrix[0][2]) * d(matrix[2][0])
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)
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cofactor_matrix[1][2] = -(
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(d(matrix[0][0]) * d(matrix[2][1])) - (d(matrix[0][1]) * d(matrix[2][0]))
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)
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cofactor_matrix[2][0] = (d(matrix[0][1]) * d(matrix[1][2])) - (
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d(matrix[0][2]) * d(matrix[1][1])
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)
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cofactor_matrix[2][1] = -(
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(d(matrix[0][0]) * d(matrix[1][2])) - (d(matrix[0][2]) * d(matrix[1][0]))
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)
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cofactor_matrix[2][2] = (d(matrix[0][0]) * d(matrix[1][1])) - (
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d(matrix[0][1]) * d(matrix[1][0])
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)
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# Transpose the cofactor matrix (Adjoint matrix)
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adjoint_matrix = array(cofactor_matrix)
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for i in range(3):
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for j in range(3):
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adjoint_matrix[i][j] = cofactor_matrix[j][i]
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# Inverse of the matrix using the formula (1/determinant) * adjoint matrix
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inverse_matrix = array(cofactor_matrix)
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for i in range(3):
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for j in range(3):
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inverse_matrix[i][j] /= d(determinant)
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# Calculate the inverse of the matrix
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return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix]
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raise ValueError("Please provide a matrix of size 2x2 or 3x3.")
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