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"""Lower-Upper (LU) Decomposition."""

# lower–upper (LU) decomposition - https://en.wikipedia.org/wiki/LU_decomposition

import numpy

def LUDecompose(table):

# Table that contains our data

# Table has to be a square array so we need to check first

rows, columns = numpy.shape(table)

L = numpy.zeros((rows, columns))

U = numpy.zeros((rows, columns))

if rows != columns:

return []

for i in range(columns):

for j in range(i - 1):

sum = 0

for k in range(j - 1):

sum += L[i][k] * U[k][j]

L[i][j] = (table[i][j] - sum) / U[j][j]

L[i][i] = 1

for j in range(i - 1, columns):

sum1 = 0

for k in range(i - 1):

sum1 += L[i][k] * U[k][j]

U[i][j] = table[i][j] - sum1

return L, U

if __name__ == "__main__":

matrix = numpy.array([[2, -2, 1],

[0, 1, 2],

[5, 3, 1]])

L, U = LUDecompose(matrix)

print(L)

print(U)

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