from __future__ import annotations from typing import Any class Matrix: """ Matrix structure. """ def __init__(self, row: int, column: int, default_value: float = 0) -> None: """ Initialize matrix with given size and default value. Example: >>> a = Matrix(2, 3, 1) >>> a Matrix consist of 2 rows and 3 columns [1, 1, 1] [1, 1, 1] """ self.row, self.column = row, column self.array = [[default_value for _ in range(column)] for _ in range(row)] def __str__(self) -> str: """ Return string representation of this matrix. """ # Prefix s = f"Matrix consist of {self.row} rows and {self.column} columns\n" # Make string identifier max_element_length = 0 for row_vector in self.array: for obj in row_vector: max_element_length = max(max_element_length, len(str(obj))) string_format_identifier = f"%{max_element_length}s" # Make string and return def single_line(row_vector: list[float]) -> str: nonlocal string_format_identifier line = "[" line += ", ".join(string_format_identifier % (obj,) for obj in row_vector) line += "]" return line s += "\n".join(single_line(row_vector) for row_vector in self.array) return s def __repr__(self) -> str: return str(self) def validate_indices(self, loc: tuple[int, int]) -> bool: """ Check if given indices are valid to pick element from matrix. Example: >>> a = Matrix(2, 6, 0) >>> a.validate_indices((2, 7)) False >>> a.validate_indices((0, 0)) True """ if not (isinstance(loc, (list, tuple)) and len(loc) == 2): return False elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column): return False else: return True def __getitem__(self, loc: tuple[int, int]) -> Any: """ Return array[row][column] where loc = (row, column). Example: >>> a = Matrix(3, 2, 7) >>> a[1, 0] 7 """ assert self.validate_indices(loc) return self.array[loc[0]][loc[1]] def __setitem__(self, loc: tuple[int, int], value: float) -> None: """ Set array[row][column] = value where loc = (row, column). Example: >>> a = Matrix(2, 3, 1) >>> a[1, 2] = 51 >>> a Matrix consist of 2 rows and 3 columns [ 1, 1, 1] [ 1, 1, 51] """ assert self.validate_indices(loc) self.array[loc[0]][loc[1]] = value def __add__(self, another: Matrix) -> Matrix: """ Return self + another. Example: >>> a = Matrix(2, 1, -4) >>> b = Matrix(2, 1, 3) >>> a+b Matrix consist of 2 rows and 1 columns [-1] [-1] """ # Validation assert isinstance(another, Matrix) assert self.row == another.row assert self.column == another.column # Add result = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): result[r, c] = self[r, c] + another[r, c] return result def __neg__(self) -> Matrix: """ Return -self. Example: >>> a = Matrix(2, 2, 3) >>> a[0, 1] = a[1, 0] = -2 >>> -a Matrix consist of 2 rows and 2 columns [-3, 2] [ 2, -3] """ result = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): result[r, c] = -self[r, c] return result def __sub__(self, another: Matrix) -> Matrix: return self + (-another) def __mul__(self, another: float | Matrix) -> Matrix: """ Return self * another. Example: >>> a = Matrix(2, 3, 1) >>> a[0,2] = a[1,2] = 3 >>> a * -2 Matrix consist of 2 rows and 3 columns [-2, -2, -6] [-2, -2, -6] """ if isinstance(another, (int, float)): # Scalar multiplication result = Matrix(self.row, self.column) for r in range(self.row): for c in range(self.column): result[r, c] = self[r, c] * another return result elif isinstance(another, Matrix): # Matrix multiplication assert self.column == another.row result = Matrix(self.row, another.column) for r in range(self.row): for c in range(another.column): for i in range(self.column): result[r, c] += self[r, i] * another[i, c] return result else: msg = f"Unsupported type given for another ({type(another)})" raise TypeError(msg) def transpose(self) -> Matrix: """ Return self^T. Example: >>> a = Matrix(2, 3) >>> for r in range(2): ... for c in range(3): ... a[r,c] = r*c ... >>> a.transpose() Matrix consist of 3 rows and 2 columns [0, 0] [0, 1] [0, 2] """ result = Matrix(self.column, self.row) for r in range(self.row): for c in range(self.column): result[c, r] = self[r, c] return result def sherman_morrison(self, u: Matrix, v: Matrix) -> Any: """ Apply Sherman-Morrison formula in O(n^2). To learn this formula, please look this: https://en.wikipedia.org/wiki/Sherman%E2%80%93Morrison_formula This method returns (A + uv^T)^(-1) where A^(-1) is self. Returns None if it's impossible to calculate. Warning: This method doesn't check if self is invertible. Make sure self is invertible before execute this method. Example: >>> ainv = Matrix(3, 3, 0) >>> for i in range(3): ainv[i,i] = 1 ... >>> u = Matrix(3, 1, 0) >>> u[0,0], u[1,0], u[2,0] = 1, 2, -3 >>> v = Matrix(3, 1, 0) >>> v[0,0], v[1,0], v[2,0] = 4, -2, 5 >>> ainv.sherman_morrison(u, v) Matrix consist of 3 rows and 3 columns [ 1.2857142857142856, -0.14285714285714285, 0.3571428571428571] [ 0.5714285714285714, 0.7142857142857143, 0.7142857142857142] [ -0.8571428571428571, 0.42857142857142855, -0.0714285714285714] """ # Size validation assert isinstance(u, Matrix) assert isinstance(v, Matrix) assert self.row == self.column == u.row == v.row # u, v should be column vector assert u.column == v.column == 1 # u, v should be column vector # Calculate v_t = v.transpose() numerator_factor = (v_t * self * u)[0, 0] + 1 if numerator_factor == 0: return None # It's not invertible return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor)) # Testing if __name__ == "__main__": def test1() -> None: # a^(-1) ainv = Matrix(3, 3, 0) for i in range(3): ainv[i, i] = 1 print(f"a^(-1) is {ainv}") # u, v u = Matrix(3, 1, 0) u[0, 0], u[1, 0], u[2, 0] = 1, 2, -3 v = Matrix(3, 1, 0) v[0, 0], v[1, 0], v[2, 0] = 4, -2, 5 print(f"u is {u}") print(f"v is {v}") print(f"uv^T is {u * v.transpose()}") # Sherman Morrison print(f"(a + uv^T)^(-1) is {ainv.sherman_morrison(u, v)}") def test2() -> None: import doctest doctest.testmod() test2()