linear_algebra.src.gaussian_elimination_pivoting
================================================

.. py:module:: linear_algebra.src.gaussian_elimination_pivoting


Attributes
----------

.. autoapisummary::

   linear_algebra.src.gaussian_elimination_pivoting.example_matrix


Functions
---------

.. autoapisummary::

   linear_algebra.src.gaussian_elimination_pivoting.solve_linear_system


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

.. py:function:: solve_linear_system(matrix: numpy.ndarray) -> numpy.ndarray

   Solve a linear system of equations using Gaussian elimination with partial pivoting

   Args:
     - `matrix`: Coefficient matrix with the last column representing the constants.

   Returns:
     - Solution vector.

   Raises:
     - ``ValueError``: If the matrix is not correct (i.e., singular).

   https://courses.engr.illinois.edu/cs357/su2013/lect.htm Lecture 7

   Example:

   >>> A = np.array([[2, 1, -1], [-3, -1, 2], [-2, 1, 2]], dtype=float)
   >>> B = np.array([8, -11, -3], dtype=float)
   >>> solution = solve_linear_system(np.column_stack((A, B)))
   >>> np.allclose(solution, np.array([2., 3., -1.]))
   True
   >>> solve_linear_system(np.array([[0, 0, 0]], dtype=float))
   Traceback (most recent call last):
       ...
   ValueError: Matrix is not square
   >>> solve_linear_system(np.array([[0, 0, 0], [0, 0, 0]], dtype=float))
   Traceback (most recent call last):
       ...
   ValueError: Matrix is singular


.. py:data:: example_matrix