# scipy.linalg.lu_solve#

scipy.linalg.lu_solve(lu_and_piv, b, trans=0, overwrite_b=False, check_finite=True)[source]#

Solve an equation system, a x = b, given the LU factorization of a

Parameters:
(lu, piv)

Factorization of the coefficient matrix a, as given by lu_factor. In particular piv are 0-indexed pivot indices.

barray

Right-hand side

trans{0, 1, 2}, optional

Type of system to solve:

trans

system

0

a x = b

1

a^T x = b

2

a^H x = b

overwrite_bbool, optional

Whether to overwrite data in b (may increase performance)

check_finitebool, optional

Whether to check that the input matrices contain 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:
xarray

Solution to the system

`lu_factor`

LU factorize a matrix

Examples

```>>> import numpy as np
>>> from scipy.linalg import lu_factor, lu_solve
>>> A = np.array([[2, 5, 8, 7], [5, 2, 2, 8], [7, 5, 6, 6], [5, 4, 4, 8]])
>>> b = np.array([1, 1, 1, 1])
>>> lu, piv = lu_factor(A)
>>> x = lu_solve((lu, piv), b)
>>> np.allclose(A @ x - b, np.zeros((4,)))
True
```