qr_decomposition.py

import numpy as np 


def qr_decomposition(A):
	if A.shape[0] != A.shape[1]:
		return -1
	U = [0 for i in range(A.shape[0])]
	E = U
	
	"""get columns"""
	columns = [1 for i in range(A.shape[0])]
	for x in range(A.shape[1]):
		columns[x] = np.array([A[i][x] for i in range(A.shape[0])]).reshape(A.shape[0], 1)
	
	""" use gram schmidt """
	for i in range(len(columns)):
		""" get orthogonal vector """
		U[i] = columns[i] - total_projection(columns[i], U, i-1)
		"""normalize the vector"""
		E[i] = U[i]/norm(U[i])
	
	"""construct Q and R"""
	Q = np.array([i for i in E]).reshape(3,3).T
	R = np.matmul(Q.T, A)
	return Q, R


def compute_projection(a, u):
	inner_products = np.dot(a.T, u)/np.dot(u.T, u)
	return u * inner_products


def total_projection(a, U, k):
	total = 0
	for x in range(k+1):
		total += compute_projection(a, U[x])
	return total


def norm(v):
	return np.power(np.sum(np.power(v, 2)), 1/2)


A = np.array([12, -51, 4, 6, 167, -68, -4, 24, -41]).reshape(3,3)
matrices = qr_decomposition(A)
print(matrices)