# 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

```>>> import numpy as np
>>> 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
```