linear_algebra.gauss_jordan

Functions

gauss_jordan(→ tuple[numpy.ndarray, numpy.ndarray])

Performs Gauss-Jordan elimination on the system Ax = b to reduce A to its

Module Contents

linear_algebra.gauss_jordan.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