# scipy.linalg.lu

scipy.linalg.lu(a, permute_l=False, overwrite_a=False, check_finite=True)

  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_l bool, optional

      Perform the multiplication P*L (Default: do not permute)

    overwrite_a bool, optional

      Whether to overwrite data in a (may improve performance)

    check_finite bool, 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

      >>> 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

scipy.linalg.eigvalsh_tridiagonal scipy.linalg.lu_factor