linear_algebra.jacobi_iteration_method
======================================

.. py:module:: linear_algebra.jacobi_iteration_method

.. autoapi-nested-parse::

   Jacobi Iteration Method - https://en.wikipedia.org/wiki/Jacobi_method



Functions
---------

.. autoapisummary::

   linear_algebra.jacobi_iteration_method.jacobi_iteration_method
   linear_algebra.jacobi_iteration_method.strictly_diagonally_dominant


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

.. py:function:: jacobi_iteration_method(coefficient_matrix: numpy.typing.NDArray[numpy.float64], constant_matrix: numpy.typing.NDArray[numpy.float64], init_val: list[float], iterations: int) -> list[float]

   Jacobi Iteration Method:
   An iterative algorithm to determine the solutions of strictly diagonally dominant
   system of linear equations

   4x1 +  x2 +  x3 =  2
    x1 + 5x2 + 2x3 = -6
    x1 + 2x2 + 4x3 = -4

   x_init = [0.5, -0.5 , -0.5]

   Examples:

   >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
   >>> constant = np.array([[2], [-6], [-4]])
   >>> init_val = [0.5, -0.5, -0.5]
   >>> iterations = 3
   >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
   [0.909375, -1.14375, -0.7484375]


   >>> coefficient = np.array([[4, 1, 1], [1, 5, 2]])
   >>> constant = np.array([[2], [-6], [-4]])
   >>> init_val = [0.5, -0.5, -0.5]
   >>> iterations = 3
   >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
   Traceback (most recent call last):
       ...
   ValueError: Coefficient matrix dimensions must be nxn but received 2x3

   >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
   >>> constant = np.array([[2], [-6]])
   >>> init_val = [0.5, -0.5, -0.5]
   >>> iterations = 3
   >>> jacobi_iteration_method(
   ...     coefficient, constant, init_val, iterations
   ... )  # doctest: +NORMALIZE_WHITESPACE
   Traceback (most recent call last):
       ...
   ValueError: Coefficient and constant matrices dimensions must be nxn and nx1 but
               received 3x3 and 2x1

   >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
   >>> constant = np.array([[2], [-6], [-4]])
   >>> init_val = [0.5, -0.5]
   >>> iterations = 3
   >>> jacobi_iteration_method(
   ...     coefficient, constant, init_val, iterations
   ... )  # doctest: +NORMALIZE_WHITESPACE
   Traceback (most recent call last):
       ...
   ValueError: Number of initial values must be equal to number of rows in coefficient
               matrix but received 2 and 3

   >>> coefficient = np.array([[4, 1, 1], [1, 5, 2], [1, 2, 4]])
   >>> constant = np.array([[2], [-6], [-4]])
   >>> init_val = [0.5, -0.5, -0.5]
   >>> iterations = 0
   >>> jacobi_iteration_method(coefficient, constant, init_val, iterations)
   Traceback (most recent call last):
       ...
   ValueError: Iterations must be at least 1


.. py:function:: strictly_diagonally_dominant(table: numpy.typing.NDArray[numpy.float64]) -> bool

   >>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 4, -4]])
   >>> strictly_diagonally_dominant(table)
   True

   >>> table = np.array([[4, 1, 1, 2], [1, 5, 2, -6], [1, 2, 3, -4]])
   >>> strictly_diagonally_dominant(table)
   Traceback (most recent call last):
       ...
   ValueError: Coefficient matrix is not strictly diagonally dominant