matrix.sherman_morrison
=======================

.. py:module:: matrix.sherman_morrison


Classes
-------

.. autoapisummary::

   matrix.sherman_morrison.Matrix


Functions
---------

.. autoapisummary::

   matrix.sherman_morrison.test1


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

.. py:class:: Matrix(row: int, column: int, default_value: float = 0)

   <class Matrix>
   Matrix structure.


   .. py:method:: __add__(another: Matrix) -> Matrix

      <method Matrix.__add__>
      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]



   .. py:method:: __getitem__(loc: tuple[int, int]) -> Any

      <method Matrix.__getitem__>
      Return array[row][column] where loc = (row, column).
      Example:
      >>> a = Matrix(3, 2, 7)
      >>> a[1, 0]
      7



   .. py:method:: __mul__(another: float | Matrix) -> Matrix

      <method Matrix.__mul__>
      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]



   .. py:method:: __neg__() -> Matrix

      <method Matrix.__neg__>
      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]



   .. py:method:: __repr__() -> str


   .. py:method:: __setitem__(loc: tuple[int, int], value: float) -> None

      <method Matrix.__setitem__>
      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]



   .. py:method:: __str__() -> str

      <method Matrix.__str__>
      Return string representation of this matrix.



   .. py:method:: __sub__(another: Matrix) -> Matrix


   .. py:method:: sherman_morrison(u: Matrix, v: Matrix) -> Any

      <method Matrix.sherman_morrison>
      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]



   .. py:method:: transpose() -> Matrix

      <method Matrix.transpose>
      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]



   .. py:method:: validate_indices(loc: tuple[int, int]) -> bool

      <method Matrix.validate_indicies>
      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



   .. py:attribute:: array


.. py:function:: test1() -> None