QR decomposition: Difference between revisions
Python solution
Walterpachl (talk | contribs) m (two missing 'n's inserted :-)) |
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{{works with|PARI/GP|2.6.0 and above}}
<lang parigp>matqr(M)</lang>
=={{header|Python}}==
{{libheader|numpy}}
<lang python>#!/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),
)), dtype=np.float64)
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), dtype=np.float64)
y = np.array((1, 6, 17, 34, 57, 86, 121, 162, 209, 262, 321), dtype=np.float64)
print('\npolyfit:\n', polyfit(x, y, 2))</lang>
{{out}}
<pre>
q:
[[-0.857143 0.394286 0.331429]
[-0.428571 -0.902857 -0.034286]
[ 0.285714 -0.171429 0.942857]]
r:
[[ -14. -21. 14.]
[ 0. -175. 70.]
[ 0. 0. -35.]]
polyfit:
[ 1. 2. 3.]
</pre>
=={{header|R}}==
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