symjax.tensor.linalg.lu¶
-
symjax.tensor.linalg.
lu
(a, permute_l=False, overwrite_a=False, check_finite=True)[source]¶ Compute pivoted LU decomposition of a matrix.
LAX-backend implementation of
lu()
. Original docstring below.The decomposition is:
A = P L U
where P is a permutation matrix, L lower triangular with unit diagonal elements, and U upper triangular.
- a : (M, N) array_like
- Array to decompose
- permute_l : bool, optional
- Perform the multiplication P*L (Default: do not permute)
- overwrite_a : bool, optional
- Whether to overwrite data in a (may improve performance)
- check_finite : bool, optional
- Whether to check that the input matrix contains only finite numbers. Disabling may give a performance gain, but may result in problems (crashes, non-termination) if the inputs do contain infinities or NaNs.
(If permute_l == False)
- p : (M, M) ndarray
- Permutation matrix
- l : (M, K) ndarray
- Lower triangular or trapezoidal matrix with unit diagonal. K = min(M, N)
- u : (K, N) ndarray
- Upper triangular or trapezoidal matrix
(If permute_l == True)
- pl : (M, K) ndarray
- Permuted L matrix. K = min(M, N)
- u : (K, N) ndarray
- Upper triangular or trapezoidal matrix
This is a LU factorization routine written for SciPy.
>>> from scipy.linalg import lu >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]) >>> p, l, u = lu(A) >>> np.allclose(A - p @ l @ u, np.zeros((4, 4))) True