From 93905653506c684e393d984ad814af66af8ee0e9 Mon Sep 17 00:00:00 2001 From: Karthik Ayangar <66073214+kituuu@users.noreply.github.com> Date: Wed, 26 Oct 2022 14:06:40 +0530 Subject: [PATCH] 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 Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com> Co-authored-by: Christian Clauss Co-authored-by: Caeden Perelli-Harris Co-authored-by: Chris O <46587501+ChrisO345@users.noreply.github.com> --- matrix/inverse_of_matrix.py | 137 ++++++++++++++++++++++++++++++++---- 1 file changed, 122 insertions(+), 15 deletions(-) diff --git a/matrix/inverse_of_matrix.py b/matrix/inverse_of_matrix.py index 770ce39b5..e53d90df8 100644 --- a/matrix/inverse_of_matrix.py +++ b/matrix/inverse_of_matrix.py @@ -2,22 +2,25 @@ from __future__ import annotations from decimal import Decimal +from numpy import array + 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 + Doctests 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]]) Traceback (most recent call last): - ... + ... ValueError: This matrix has no inverse. >>> inverse_of_matrix([[12, -16], [-9, 0]]) [[0.0, -0.1111111111111111], [-0.0625, -0.08333333333333333]] @@ -25,24 +28,128 @@ 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]] + + Doctests for 3x3 + >>> inverse_of_matrix([[2, 5, 7], [2, 0, 1], [1, 2, 3]]) + [[2.0, 5.0, -4.0], [1.0, 1.0, -1.0], [-5.0, -12.0, 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. + + >>> 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 + d = Decimal # 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 = float( + 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.") - # 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] - # 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 = float( + ( + (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.") - # Calculate the inverse of the matrix - return [[float(d(n) / determinant) or 0.0 for n in row] for row in swapped_matrix] + # 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]) + ) + + # Transpose the cofactor matrix (Adjoint matrix) + adjoint_matrix = array(cofactor_matrix) + for i in range(3): + for j in range(3): + adjoint_matrix[i][j] = cofactor_matrix[j][i] + + # Inverse of the matrix using the formula (1/determinant) * adjoint matrix + inverse_matrix = array(cofactor_matrix) + for i in range(3): + for j in range(3): + inverse_matrix[i][j] /= d(determinant) + + # Calculate the inverse of the matrix + return [[float(d(n)) or 0.0 for n in row] for row in inverse_matrix] + raise ValueError("Please provide a matrix of size 2x2 or 3x3.")