Relative cost of matrix operations

In [1]:
import numpy as np
import scipy.linalg as la
import matplotlib as mpl
import matplotlib.pyplot as plt
import scipy.linalg as sla
%matplotlib inline


from time import time
In [2]:
n_values = (10**np.linspace(1, 4, 15)).astype(np.int32)
n_values
Out[2]:
array([   10,    16,    26,    43,    71,   117,   193,   316,   517,
         848,  1389,  2275,  3727,  6105, 10000], dtype=int32)
In [3]:
times_matmul = []
times_lu = []

for n in n_values:
    print(n)
    A = np.random.randn(n, n)
    start_time = time()
    A.dot(A)
    times_matmul.append(time() - start_time)
    start_time = time()
    la.lu(A)
    times_lu.append(time() - start_time)

10
16
26
43
71
117
193
316
517
848
1389
2275
3727
6105
10000
In [4]:
plt.plot(n_values, times_matmul, label='matmul')
plt.plot(n_values, times_lu, label='lu')
plt.grid()
plt.legend(loc="best")
plt.xlabel("Matrix size $n$")
plt.ylabel("Wall time [s]")
Out[4]:
Text(0, 0.5, 'Wall time [s]')
  • The faster algorithms make the slower ones look bad. But... it's all relative.
  • Can we get a better plot?
  • Can we see the asymptotic cost ($O(n^3)$) of these algorithms from the plot?
In [ ]:
plt.loglog(n_values, times_matmul, label='matmul')
plt.loglog(n_values, times_lu, label='lu')
plt.grid()
plt.legend(loc="best")
plt.xlabel("Matrix size $n$")
plt.ylabel("Wall time [s]")