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# scipy.linalg.lu_solve

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

  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.

    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

  See also

  `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