# 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

b : array

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_b : bool, optional

Whether to overwrite data in b (may increase performance)

check_finite : bool, 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:
x : array

Solution to the system

lu_factor
LU factorize a matrix

Examples

>>> 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


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scipy.linalg.lu_factor

scipy.linalg.svd