QR2.py

import numpy as np
import math
from copy import deepcopy
from numpy import dot

# np.dot умножение матриц
def func():
    return 2 * (x**3) + 3 * (x**2) + 5 * x + 7


A = np.loadtxt("1.txt")
x = np.loadtxt


def QR(A):
    # копирование и транспонирование матрицы
    At = A.transpose()
    shape = np.shape(At)
    Qt = np.zeros((shape[0], shape[1]))
    r = np.zeros((shape[0], shape[0]))

    for i in range(shape[0]):
        for j in range(shape[1]):
            Qt[i][j] = At[i][j]

    norm = np.dot(Qt[0], Qt[0])
    for i in range(shape[1]):
        Qt[0][i] = Qt[0][i] / math.sqrt(norm)

    for k in range(1, shape[0]):
        for j in range(shape[0]):
            if j < k:
                Vkj = np.dot(Qt[j], Qt[k])
                Qt[k] = Qt[k] - Vkj * Qt[j]
                norm2 = dot(Qt[k], Qt[k])
                for i in range(shape[1]):
                    Qt[k][i] = Qt[k][i] / math.sqrt(norm2)

    for i in range(shape[0]):
        for j in range(shape[0]):
            if j >= i:
                r[i][j] = np.dot(At[j], Qt[i])
            else:
                r[i][j] = 0
    print(Qt)
    print("\n", r)
    return 0


QR(A)
Qb, rD = np.linalg.qr(A)
print("\n", Qb.T)
print("\n", rD)