""" Functions for 2D matrix operations """ from typing import List, Tuple def add(*matrix_s: List[list]) -> List[list]: """ >>> add([[1,2],[3,4]],[[2,3],[4,5]]) [[3, 5], [7, 9]] >>> add([[1.2,2.4],[3,4]],[[2,3],[4,5]]) [[3.2, 5.4], [7, 9]] >>> add([[1, 2], [4, 5]], [[3, 7], [3, 4]], [[3, 5], [5, 7]]) [[7, 14], [12, 16]] """ if all(_check_not_integer(m) for m in matrix_s): for i in matrix_s[1:]: _verify_matrix_sizes(matrix_s[0], i) return [[sum(t) for t in zip(*m)] for m in zip(*matrix_s)] def subtract(matrix_a: List[list], matrix_b: List[list]) -> List[list]: """ >>> subtract([[1,2],[3,4]],[[2,3],[4,5]]) [[-1, -1], [-1, -1]] >>> subtract([[1,2.5],[3,4]],[[2,3],[4,5.5]]) [[-1, -0.5], [-1, -1.5]] """ if ( _check_not_integer(matrix_a) and _check_not_integer(matrix_b) and _verify_matrix_sizes(matrix_a, matrix_b) ): return [[i - j for i, j in zip(*m)] for m in zip(matrix_a, matrix_b)] def scalar_multiply(matrix: List[list], n: int) -> List[list]: """ >>> scalar_multiply([[1,2],[3,4]],5) [[5, 10], [15, 20]] >>> scalar_multiply([[1.4,2.3],[3,4]],5) [[7.0, 11.5], [15, 20]] """ return [[x * n for x in row] for row in matrix] def multiply(matrix_a: List[list], matrix_b: List[list]) -> List[list]: """ >>> multiply([[1,2],[3,4]],[[5,5],[7,5]]) [[19, 15], [43, 35]] >>> multiply([[1,2.5],[3,4.5]],[[5,5],[7,5]]) [[22.5, 17.5], [46.5, 37.5]] >>> multiply([[1, 2, 3]], [[2], [3], [4]]) [[20]] """ if _check_not_integer(matrix_a) and _check_not_integer(matrix_b): rows, cols = _verify_matrix_sizes(matrix_a, matrix_b) if cols[0] != rows[1]: raise ValueError( f"Cannot multiply matrix of dimensions ({rows[0]},{cols[0]}) " f"and ({rows[1]},{cols[1]})" ) return [ [sum(m * n for m, n in zip(i, j)) for j in zip(*matrix_b)] for i in matrix_a ] def identity(n: int) -> List[list]: """ :param n: dimension for nxn matrix :type n: int :return: Identity matrix of shape [n, n] >>> identity(3) [[1, 0, 0], [0, 1, 0], [0, 0, 1]] """ n = int(n) return [[int(row == column) for column in range(n)] for row in range(n)] def transpose(matrix: List[list], return_map: bool = True) -> List[list]: """ >>> transpose([[1,2],[3,4]]) # doctest: +ELLIPSIS >> transpose([[1,2],[3,4]], return_map=False) [[1, 3], [2, 4]] """ if _check_not_integer(matrix): if return_map: return map(list, zip(*matrix)) else: return list(map(list, zip(*matrix))) def minor(matrix: List[list], row: int, column: int) -> List[list]: """ >>> minor([[1, 2], [3, 4]], 1, 1) [[1]] """ minor = matrix[:row] + matrix[row + 1 :] return [row[:column] + row[column + 1 :] for row in minor] def determinant(matrix: List[list]) -> int: """ >>> determinant([[1, 2], [3, 4]]) -2 >>> determinant([[1.5, 2.5], [3, 4]]) -1.5 """ if len(matrix) == 1: return matrix[0][0] return sum( x * determinant(minor(matrix, 0, i)) * (-1) ** i for i, x in enumerate(matrix[0]) ) def inverse(matrix: List[list]) -> List[list]: """ >>> inverse([[1, 2], [3, 4]]) [[-2.0, 1.0], [1.5, -0.5]] >>> inverse([[1, 1], [1, 1]]) """ # https://stackoverflow.com/questions/20047519/python-doctests-test-for-none det = determinant(matrix) if det == 0: return None matrix_minor = [ [determinant(minor(matrix, i, j)) for j in range(len(matrix))] for i in range(len(matrix)) ] cofactors = [ [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row])] for row in range(len(matrix)) ] adjugate = transpose(cofactors) return scalar_multiply(adjugate, 1 / det) def _check_not_integer(matrix: List[list]) -> bool: if not isinstance(matrix, int) and not isinstance(matrix[0], int): return True raise TypeError("Expected a matrix, got int/list instead") def _shape(matrix: List[list]) -> list: return len(matrix), len(matrix[0]) def _verify_matrix_sizes(matrix_a: List[list], matrix_b: List[list]) -> Tuple[list]: shape = _shape(matrix_a) + _shape(matrix_b) if shape[0] != shape[3] or shape[1] != shape[2]: raise ValueError( f"operands could not be broadcast together with shape " f"({shape[0], shape[1]}), ({shape[2], shape[3]})" ) return (shape[0], shape[2]), (shape[1], shape[3]) def main(): matrix_a = [[12, 10], [3, 9]] matrix_b = [[3, 4], [7, 4]] matrix_c = [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]] matrix_d = [[3, 0, 2], [2, 0, -2], [0, 1, 1]] print(f"Add Operation, {add(matrix_a, matrix_b) = } \n") print(f"Multiply Operation, {multiply(matrix_a, matrix_b) = } \n",) print(f"Identity: {identity(5)}\n") print(f"Minor of {matrix_c} = {minor(matrix_c, 1, 2)} \n") print(f"Determinant of {matrix_b} = {determinant(matrix_b)} \n") print(f"Inverse of {matrix_d} = {inverse(matrix_d)}\n") if __name__ == "__main__": import doctest doctest.testmod() main()