scipy.linalg.lu#
- scipy.linalg.lu(a, permute_l=False, 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, N) array_like
Array to decompose
- permute_lbool, optional
Perform the multiplication P*L (Default: do not permute)
- overwrite_abool, optional
Whether to overwrite data in a (may improve 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
- (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
Notes
This is a LU factorization routine written for SciPy.
Examples
>>> 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