matrix.matrix_multiplication_recursion
======================================

.. py:module:: matrix.matrix_multiplication_recursion

.. autoapi-nested-parse::

   Perform matrix multiplication using a recursive algorithm.
   https://en.wikipedia.org/wiki/Matrix_multiplication



Attributes
----------

.. autoapisummary::

   matrix.matrix_multiplication_recursion.Matrix
   matrix.matrix_multiplication_recursion.matrices
   matrix.matrix_multiplication_recursion.matrix_1_to_4
   matrix.matrix_multiplication_recursion.matrix_5_to_8
   matrix.matrix_multiplication_recursion.matrix_5_to_9_high
   matrix.matrix_multiplication_recursion.matrix_5_to_9_wide
   matrix.matrix_multiplication_recursion.matrix_a
   matrix.matrix_multiplication_recursion.matrix_count_up
   matrix.matrix_multiplication_recursion.matrix_unordered


Functions
---------

.. autoapisummary::

   matrix.matrix_multiplication_recursion.is_square
   matrix.matrix_multiplication_recursion.matrix_multiply
   matrix.matrix_multiplication_recursion.matrix_multiply_recursive


Module Contents
---------------

.. py:function:: is_square(matrix: Matrix) -> bool

   >>> is_square([])
   True
   >>> is_square(matrix_1_to_4)
   True
   >>> is_square(matrix_5_to_9_high)
   False


.. py:function:: matrix_multiply(matrix_a: Matrix, matrix_b: Matrix) -> Matrix

   >>> matrix_multiply(matrix_1_to_4, matrix_5_to_8)
   [[19, 22], [43, 50]]


.. py:function:: matrix_multiply_recursive(matrix_a: Matrix, matrix_b: Matrix) -> Matrix

   :param matrix_a: A square Matrix.
   :param matrix_b: Another square Matrix with the same dimensions as matrix_a.
   :return: Result of matrix_a * matrix_b.
   :raises ValueError: If the matrices cannot be multiplied.

   >>> matrix_multiply_recursive([], [])
   []
   >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_8)
   [[19, 22], [43, 50]]
   >>> matrix_multiply_recursive(matrix_count_up, matrix_unordered)
   [[37, 61, 74, 61], [105, 165, 166, 129], [173, 269, 258, 197], [241, 373, 350, 265]]
   >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_wide)
   Traceback (most recent call last):
       ...
   ValueError: Invalid matrix dimensions
   >>> matrix_multiply_recursive(matrix_1_to_4, matrix_5_to_9_high)
   Traceback (most recent call last):
       ...
   ValueError: Invalid matrix dimensions
   >>> matrix_multiply_recursive(matrix_1_to_4, matrix_count_up)
   Traceback (most recent call last):
       ...
   ValueError: Invalid matrix dimensions


.. py:data:: Matrix

.. py:data:: matrices

.. py:data:: matrix_1_to_4
   :value: [[1, 2], [3, 4]]


.. py:data:: matrix_5_to_8
   :value: [[5, 6], [7, 8]]


.. py:data:: matrix_5_to_9_high
   :value: [[5, 6], [7, 8], [9]]


.. py:data:: matrix_5_to_9_wide
   :value: [[5, 6], [7, 8, 9]]


.. py:data:: matrix_a
   :value: [[1, 2], [3, 4]]


.. py:data:: matrix_count_up
   :value: [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]


.. py:data:: matrix_unordered
   :value: [[5, 8, 1, 2], [6, 7, 3, 0], [4, 5, 9, 1], [2, 6, 10, 14]]