scipy.linalg.lu_factor¶
-
scipy.linalg.
lu_factor
(a, overwrite_a=False, check_finite=True)[source]¶ Compute pivoted LU decomposition of a matrix.
The decomposition is:
A = P L U
where P is a permutation matrix, L lower triangular with unit diagonal elements, and U upper triangular.
- Parameters
- a(M, M) array_like
Matrix to decompose
- overwrite_abool, optional
Whether to overwrite data in A (may increase performance)
- check_finitebool, 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.
- Returns
- lu(N, N) ndarray
Matrix containing U in its upper triangle, and L in its lower triangle. The unit diagonal elements of L are not stored.
- piv(N,) ndarray
Pivot indices representing the permutation matrix P: row i of matrix was interchanged with row piv[i].
See also
lu_solve
solve an equation system using the LU factorization of a matrix
Notes
This is a wrapper to the
*GETRF
routines from LAPACK.Examples
>>> from scipy.linalg import lu_factor >>> from numpy import tril, triu, allclose, zeros, eye >>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]]) >>> lu, piv = lu_factor(A) >>> piv array([2, 2, 3, 3], dtype=int32)
Convert LAPACK’s
piv
array to NumPy index and test the permutation>>> piv_py = [2, 0, 3, 1] >>> L, U = np.tril(lu, k=-1) + np.eye(4), np.triu(lu) >>> np.allclose(A[piv_py] - L @ U, np.zeros((4, 4))) True