# Relative cost of matrix operations¶

In [1]:
#keep
import numpy as np
import scipy.linalg as spla
import scipy as sp

import matplotlib.pyplot as pt
%matplotlib inline

from time import time

np.alterdot()

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

Out[2]:
array([ 100,  122,  150,  185,  227,  279,  343,  421,  517,  636,  781,
959, 1178, 1447, 1778], dtype=int32)
In [3]:
#keep

def mat_mul(A):
return A.dot(A)

for name, f in [
("lu", spla.lu_factor),
("qr", spla.qr),
]:

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.loglog(n_values, times, label=name)

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

-----> lu
100
122
150
185
227
279
343
421
517
636
781
959
1178
1447
1778
-----> qr
100
122
150
185
227
279
343
421
517
636
781
959
1178
1447
1778

Out[3]:
<matplotlib.text.Text at 0x111afb0f0>
• Can we see the asymptotic cost ($O(n^3)$) of these algorithms from the plot?
In [3]: