gauss_jordan

gauss_jordan(a, b=None)

Gauss-Jordan elimination.

Mirrors the C# GaussJordanElimination.Solve(ref Matrix A, ref Matrix B): one full-pivot Gauss-Jordan reduction that produces a’s inverse and, when b is supplied, the solution set of a @ x = b. Unlike the C# ref, ref in-place API, a and b are never mutated in Python – both results come back as new arrays.

Parameters

Name	Type	Description	Default
a	array_like	A square 2D array, N x N.	required
b	array_like	A 1D array of length N, or a 2D array with N rows (the right-hand sides). Omit for the inverse alone, in which case solution is an N x 0 array.	None

Returns

Name	Type	Description
	dict	{"inverse": ndarray (N, N), "solution": ndarray (N, b.shape[1])}.

Examples

>>> from corehydropy import gauss_jordan
>>> a = [[1, 3, 3], [1, 4, 3], [1, 3, 4]]
>>> gauss_jordan(a)["inverse"]
array([[ 7., -3., -3.],
       [-1.,  1.,  0.],
       [-1.,  0.,  1.]])