linear_algebra.gauss_jordan
===========================

.. py:module:: linear_algebra.gauss_jordan


Functions
---------

.. autoapisummary::

   linear_algebra.gauss_jordan.gauss_jordan


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

.. py:function:: gauss_jordan(coefficients: numpy.ndarray, vertices: numpy.ndarray) -> tuple[numpy.ndarray, numpy.ndarray]

   Performs Gauss-Jordan elimination on the system Ax = b to reduce A to its
   Reduced Row Echelon Form (RREF) and transform b accordingly.

   Args:
       coefficients: A 2D NumPy array representing the coefficient matrix A.
       vertices: A column vector (2D NumPy array) representing the RHS b.

   Returns:
       A tuple containing:
           - RREF of matrix A
           - Transformed RHS vector b

   Raises:
       ValueError: If shapes of A and b are incompatible.

   See Also:
       https://en.wikibooks.org/wiki/Linear_Algebra/Gauss-Jordan_Reduction

   Examples:
       >>> import numpy as np
       >>> A = np.array([[1, 2, -1], [2, 4, -2], [3, 6, -3]])
       >>> b = np.array([[1], [2], [3]])
       >>> rref_A, rref_b = gauss_jordan(A, b)
       >>> np.allclose(rref_A, np.array([[1., 2., -1.], [0., 0., 0.], [0., 0., 0.]]))
       True
       >>> np.allclose(rref_b, np.array([[1.], [0.], [0.]]))
       True