import numpy as np

# The following two functions calculate the LU decomposition of the given matrix
# A using either parital or full pivoting. The resulting lower and upper
# triangular matricies override the passed matrix. When using partial pivoting
# the return value is a permutation array of the indicies of the rows of A and
# when using full pivoting the corresponding function shall return a tuple of
# permuation arrays of the indicies of the rows and columns of A respectively.
# Thus the following equalities shall hold, at least approximately (that is up
# to numerical error):
#     A = np.array([[...], [...], ..., [...]])
#
#     partial = A.copy()
#     p = partialPivotLU(partial)
#     L, U = np.tril(partial, -1), np.triu(partial)
#     L = L + np.diag(np.ones(L.shape[0]))
#
#     L @ U == A[p, :] # up to numerical error
#
#     full = A.copy()
#     p, q = fullPivotLU(full)
#     L, U = np.tril(full, -1), np.triu(full)
#     L = L + np.diag(np.ones(L.shape[0]))
#
#     L @ U == A[p, q] # up to numerical error
#
# You can base your solution on the provided code from the scripture from the
# lecture, but note that there a full permutation matrix is contstructed and the
# LU decomposition is also not done in-place.
def partialPivotLU(A):
    return np.array([])

def fullPivotLU(A):
    return (np.array([]), np.array([]))

if __name__ == "__main__":
    print("Hello, World!")