Relative cost of matrix factorizations¶

In [1]:
import numpy as np
import numpy.linalg as npla
import scipy.linalg as spla

import matplotlib.pyplot as pt

from time import time

In [2]:
n_values = (10**np.linspace(1, 3.25, 15)).astype(np.int32)
n_values

Out[2]:
array([  10,   14,   20,   30,   43,   63,   92,  133,  193,  279,  404,
585,  848, 1228, 1778], dtype=int32)
In [9]:
for name, f in [
("lu", spla.lu_factor),
("qr", npla.qr),
("svd", npla.svd)
]:

times = []
print("----->", name)

for n in n_values:
print(n)

A = np.random.randn(n, n)

start_time = time()
f(A)
times.append(time() - start_time)

pt.plot(n_values, times, label=name)

pt.grid()
pt.legend(loc="best")
pt.xlabel("Matrix size $n$")
pt.ylabel("Wall time [s]")

-----> lu
10
14
20
30
43
63
92
133
193
279
404
585
848
1228
1778
-----> qr
10
14
20
30
43
63
92
133
193
279
404
585
848
1228
1778
-----> svd
10
14
20
30
43
63
92
133
193
279
404
585
848
1228
1778

Out[9]:
<matplotlib.text.Text at 0x7f846db8ea90>
• The faster algorithms make the slower ones look bad. But... it's all relative.
• Is there a better way of plotting this?
• Can we see the asymptotic cost ($O(n^3)$) of these algorithms from the plot?