gram_schmidt.py

import numpy as np 

def gram_schmidt(vectors):
	q1 = vectors[0]/np.linalg.norm(vectors[0])
	result = [q1]
	for b in vectors[1:]:
		comp = b + rm_dupl_projctns(b, result)
		result.append(comp/np.linalg.norm(comp))
	return np.concatenate(result, axis=1)
		
		
def rm_dupl_projctns(b, result):
	total = 0
	for x in result:
		total -= np.matmul(x.T, b) * x
	return total
		
def get_projection(a, b):
	return np.matmul(a.T, b) * a
	
	
a = np.array([1,2,2]).reshape(3,1)
b = np.array([1,3,1]).reshape(3,1)
#c = np.array([0,1,1]).reshape(3,1)
vectors = [a, b]
x = gram_schmidt(vectors)
print(x)