Data commit

Task/QR-decomposition/Python/qr-decomposition.py

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+#!/usr/bin/env python3
+
+import numpy as np
+
+def qr(A):
+    m, n = A.shape
+    Q = np.eye(m)
+    for i in range(n - (m == n)):
+        H = np.eye(m)
+        H[i:, i:] = make_householder(A[i:, i])
+        Q = np.dot(Q, H)
+        A = np.dot(H, A)
+    return Q, A
+
+def make_householder(a):
+    v = a / (a[0] + np.copysign(np.linalg.norm(a), a[0]))
+    v[0] = 1
+    H = np.eye(a.shape[0])
+    H -= (2 / np.dot(v, v)) * np.dot(v[:, None], v[None, :])
+    return H
+
+# task 1: show qr decomp of wp example
+a = np.array(((
+    (12, -51,   4),
+    ( 6, 167, -68),
+    (-4,  24, -41),
+)))
+
+q, r = qr(a)
+print('q:\n', q.round(6))
+print('r:\n', r.round(6))
+
+# task 2: use qr decomp for polynomial regression example
+def polyfit(x, y, n):
+    return lsqr(x[:, None]**np.arange(n + 1), y.T)
+
+def lsqr(a, b):
+    q, r = qr(a)
+    _, n = r.shape
+    return np.linalg.solve(r[:n, :], np.dot(q.T, b)[:n])
+
+x = np.array((0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10))
+y = np.array((1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321))
+
+print('\npolyfit:\n', polyfit(x, y, 2))