# QR decomposition
import re
import numpy as np
from collections import namedtuple
# functions
def get_q(a, Q, n):
    u = a
    if n != 0:
        for j in range(0, n):
            u = u - (a.dot(Q[j]) * Q[j])

    return u / np.linalg.norm(u)

def QR_decompose(A):
    Q = np.zeros(A.shape)

    for i in range(A.shape[0]):
        Q[i] = get_q(A[i], Q, i)

    R = Q.dot(A)

    return namedtuple("qr", ["Q", "R"])(Q.T, R)

# execution code
split_regex = r'[\/\\|, ]+'
elements = list(map(
                    float,
                    re.split(split_regex, input('Enter elements: '))
                ))
shape = list(map(
                    int,
                    re.split(split_regex, input('Enter shape (N rows x M columns: '))
                ))
A = np.array(elements).reshape(shape)
print ('A : \n' , A)
qr_decomposition = QR_decompose(A.T)
Q = qr_decomposition.Q
R = qr_decomposition.R
print ('Q : \n', Q)
print ('R : \n', R)
print ('Pass test: ' + str(np.array_equal(A, np.dot(Q, R))))