# coding: utf-8

# # Relative cost of matrix operations

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import numpy as np
import scipy.linalg as spla
import scipy as sp

import matplotlib.pyplot as pt

from time import time

np.alterdot()


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n_values = (10**np.linspace(2, 3.25, 15)).astype(np.int32)
n_values


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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]")


# * Can we see the asymptotic cost ($O(n^3)$) of these algorithms from the plot?

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