`scipy.linalg._decomp_lu:lu_solve`

source: /scipy/linalg/_decomp_lu.py:134

Signature

def lu_solve(lu_and_piv, b, trans = 0, overwrite_b = False, check_finite = True)

Summary

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

Extended Summary

The documentation is written assuming array arguments are of specified "core" shapes. However, array argument(s) of this function may have additional "batch" dimensions prepended to the core shape. In this case, the array is treated as a batch of lower-dimensional slices; see linalg_batch for details.

Parameters

lu_and_piv : tuple

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

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) See tutorial_linalg_overwrite for details.

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

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

Aliases

scipy.linalg.lu_solve